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Development of statistical method to

modeling tooth healthspan curves in

Korean

Hoi In Jung

The Graduate School

Yonsei University

Department of Dentistry

Development of statistical method to

modeling tooth healthspan curves in

Korean

A Dissertation

Submitted to the Department of Dentistry

and the Graduate School of Yonsei University

in partial fulfillment of the

requirements for the degree of

Doctor of Philosophy

Hoi In Jung

December 2013

This certifies that the Dissertation of

Hoi In Jung is approved.

Thesis Supervisor: Baek Il Kim

Thesis Committee: Ho Keun Kwon

Thesis Committee: Jong Hoon Choi

Thesis Committee: Young Sik Cho

Thesis Committee: Choong Ho Choi

The Graduate School

Yonsei University

December 2013

감사의 글

처음 예방치과학교실의 문을 열던 날처럼 추운 계절이 꼬박 여섯 번 지나갔습니다.

많은 것들이 변했지만 역시 가장 중요한 것은 그대로라고 생각했습니다. 한편으로는

무슨 발버둥을 그렇게 쳤나 싶어서 우습기도 하지만 다른 한편으로는 이곳을 선택한

것에 틀림이 없었다는 것에 안도감을 느낍니다.

먼저 저희 연구실의 두 분 교수님께 감사드립니다. 넓은 시야와 높은 안목으로 감

동을 주시는 권호근 교수님, 끊임없이 도전하는 삶의 모범을 보여주시는 김백일 교수

님께 많은 가르침을 받았습니다. 연구의 의미와 활용에 대해서 깊이 생각하게 해주시

고 논문에 꼭 필요한 부분을 짚어주신 연세대학교 구강내과학교실 최종훈 교수님, 남

서울대학교 치위생학과 조영식 교수님, 전남대학교 예방치과학교실 최충호 교수님께

감사드립니다.

탁월하고 아낌없는 가르침으로 제가 생산해내는 값에 조금 더 책임을 질 수 있게

해주신 연세대학교 보건대학원의 박소희 교수님과 연세대학교 수학과의 정혜영 교수

님께, 적절한 영문 표현을 고르기 위해 고심하며 자신의 논문처럼 고민해준 손 애슐

리 선생님에게 감사드립니다.

학위 과정 중 함께한 분들 덕분에 힘든 시간도 웃으며 보낼 수 있었습니다. 큰 힘

이 되어준 교실원 강시묵, 김보라, 이은송 선생님과 비서 문혜정 님에게 감사드립니

다. 현재는 같은 교실에 있지 않지만 오랜 시간 고락을 함께 했고 청할 때마다 아낌

없는 도움을 베풀어 주신 정승화, 김희은, 한선영 선생님에게 감사드립니다.

항상 격려해준 친구들이 없었다면 제 삶은 훨씬 더 척박해졌을 것입니다. 언제나

용기를 북돋워주고 깨달음을 주는 조언자 한선희, 열정으로 기운을 회복시켜 주는 오

혜인, 나의 한 부분과 같은 친구 이경하에게 감사드립니다.

하늘에서도 여전히 맑고 고우실 할머니께 천 번의 입맞춤을 보냅니다. 평생 바른

생각만을 하신 아버지와 어머니로부터 넘치는 사랑을 받고 자란 저는 행운아입니다.

연구자로서의 삶을 응원해주실 뿐 아니라 부족한 저를 항상 사랑해주시는 시아버님과

시어머님의 며느리가 된 것도 기적 같은 일입니다. 네 분 부모님께 깊은 감사의 말씀

을 드립니다. 가장 좋은 조언자로서 두 세계를 동시에 살 수 있게 해준 동생 회량에

게 감사드립니다.

무엇보다도 유일한 사람, 남편 김준혁 님에게는 감사하다는 말조차도 하기 조심스

럽습니다. 당신이 없는 삶은 상상할 수 없습니다. 그저 당신과 영원히 함께 하고 싶습

니다.

단지 한 발자국을 딛었다고 생각합니다. 기름진 곳 보다는 기름져야 할 곳으로 향

하고 싶다는 첫 마음은 변하지 않았습니다. 받은 사랑과 지식을 더불어 풍성히 누리

는 자가 되겠습니다. 깊이 갈고 인내하며 거두어가도록 하겠습니다.

2013년 12월

정회인 드림

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TABLE OF CONTENTS

LIST OF TABLES ·················································································································· ⅲ

LIST OF FIGURES ················································································································· ⅴ

ABSTRACT ······························································································································· ⅶ

1. INTRODUCTION ················································································································ 1

2. MATERIALS AND METHODS ····················································································· 5

2.1 Data sources ··················································································································· 5

2.2 Dental examination ·········································································································· 7

2.3 Definition of indices ······································································································ 8

2.4 Statistical curve smoothing procedures ··································································· 10

2.4.1 Age groupings ······································································································· 10

2.4.2 Curve smoothing stage ······················································································· 10

2.4.3 The transformation stage ··················································································· 13

2.5 Comparison between the DMF indices and alternative indices ······················· 14

3. RESULTS ······························································································································ 15

3.1 Estimated values of weighted empirical percentiles ············································ 15

3.1.1 ST index, male ····································································································· 15

3.1.2 ST index, female ·································································································· 17

3.1.3 FST index, male ··································································································· 19

3.1.4 FST index, female ······························································································· 21

3.1.5 PT index, male ····································································································· 23

3.1.6 PT index, female ·································································································· 25

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3.2 Estimated values of smoothed percentiles and 7-order polynomial model

parameters ······························································································································ 27

3.2.1 ST index, male ····································································································· 27

3.2.2 ST index, female ·································································································· 30

3.2.3 FST index, male ··································································································· 33

3.2.4 FST index, female ······························································································· 36

3.2.5 PT index, male ····································································································· 39

3.2.6 PT index, female ·································································································· 42

3.3 The calculation of dental health indices using estimated parameters of

7-order polynomial regression ·························································································· 45

3.4 Estimated values of L, M, and S parameters ······················································· 47

3.4.1 ST index, male ····································································································· 47

3.4.2 ST index, female ·································································································· 49

3.4.3 FST index, male ··································································································· 51

3.4.4 FST index, female ······························································································· 53

3.4.5 PT index, male ····································································································· 55

3.4.6 PT index, female ·································································································· 57

3.5 Calculation of percentile using L, M, and S parameters ··································· 62

3.6 Comparison between the DMF indices and dental health indices ·················· 64

4. DISCUSSION ························································································································ 69

5. CONCLUSION ···················································································································· 75

REFERENCES ··························································································································· 77

SUPPLEMENT ························································································································· 80

ABSTRACT (Korean) ·········································································································· 90

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LIST OF TABLES

Table 1. Unweighted sample size by sex, age and data source ·································· 6

Table 2. Variables selected for the study ··········································································· 7

Table 3. Dental health indicator calculation ······································································· 9

Table 4. Weighted selected percentiles for ST index by age: Male ····························· 16

Table 5. Weighted selected percentiles for ST index by age: Female ···················· 18

Table 6. Weighted selected percentiles for FST index by age: Male ······················ 20

Table 7. Weighted selected percentiles for FST index by age: Female ·················· 22

Table 8. Weighted selected percentiles for PT index by age: Male ························· 24

Table 9. Weighted selected percentiles for PT index by age: Female ····················· 26

Table 10. 7-order polynomial model parameters for ST by percentile: Male ········ 28

Table 11. Selected smoothed percentiles for ST by age: Male ·································· 28

Table 12. 7-order polynomial model parameters for ST by percentile: Female ···· 31

Table 13. Selected smoothed percentiles for ST index by age: Female ·················· 31

Table 14. 7-order polynomial model parameters for FST by percentile: Male ····· 34

Table 15. Selected smoothed percentiles for FST index by age: Male ··················· 34

Table 16. 7-order polynomial model parameters for FST index by age: Female 37

Table 17. Selected smoothed percentiles for FST index by age: Female ··············· 37

Table 18. 7-order polynomial model parameters for PT index by age: Male ······· 40

iv

Table 19. Selected smoothed percentiles for PT index by age: Male ······················ 40

Table 20. 7-order polynomial model parameters for PT index by age: Female ··· 43

Table 21. Selected smoothed percentiles for PT index by age: Female ·················· 43

Table 22. L, M, and S, parameters and selected smoothed percentiles for ST by age:

Male ·············································································································································· 48

Table 23. L, M, and S, parameters and selected smoothed percentiles for ST by

age: Female ································································································································ 50

Table 24. L, M, and S, parameters and selected smoothed percentiles for FST by

age: Male ···································································································································· 52

Table 25. L, M, and S, parameters and selected smoothed percentiles for FST by

age: Female ································································································································ 54

Table 26. L, M, and S, parameters and selected smoothed percentiles for PT by

age: Male ···································································································································· 56

Table 27. L, M, and S, parameters and selected smoothed percentiles for PT by

age: Female ································································································································ 58

Table 28. Frequency distribution of oral health related factors: Male ···························· 64

Table 29. Frequency distribution of oral health related factors: Female ······················· 65

Table 30. Beta coefficients and their significance levels of oral health related

factors and R square with DMFT index, ST index percentile, FST index percentile

and PT index percentile as dependent variables: Male ················································ 66

Table 31. Beta coefficients and their significance levels of oral health related factors

and R square with DMFT index, ST index percentile, FST index percentile and PT

index percentile as dependent variables: Female ·································································· 68

v

LIST OF FIGURES

Figure 1. Locally weighted regression ··············································································· 12

Figure 2. 7-order polynomial model ··················································································· 13

Figure 3. LMS transformation equation ·········································································· 13

Figure 4. Comparison of smoothed 5th, 25th, 50th, 75th, 95th percentile curves to

empirical data points, 20-80 ages: Male ST-for-age ···················································· 27

Figure 5. Comparison of 5th, 25th, 50th, 75th, 95th percentile curves smoothed by

LWR and polynomial regression, 20-80 ages: Male ST-for-age ······························· 29


empirical data points, 20-80 ages: Female ST-for-age ················································ 30


LWR and polynomial regression, 20-80 ages: Female ST-for-age ·························· 32


empirical data points, 20-80 ages: Male FST-for-age ················································· 33


LWR and polynomial regression, 20-80 ages: Male FST-for-age ···························· 35


empirical data points, 20-80 ages: Female FST-for-age ············································· 36


LWR and polynomial regression, 20-80 ages: Female FST-for-age ························ 38


empirical data points, 20-80 ages: Male PT-for-age ···················································· 39

vi


LWR and polynomial regression, 20-80 ages: Male PT-for-age ······························· 41


empirical data points, 20-80 ages: Female PT-for-age ················································ 42


LWR and polynomial regression, 20-80 ages: Female PT-for-age ··························· 44

Figure 16. Percentile calculation using LMS estimators ·················································46

Figure 17. Comparison of final 5th, 25th, 50th, 75th, 95th percentile curves to

empirical data points, 20-80 ages: Male ST-for-age ···················································· 59


empirical data points, 20-80 ages: Female ST-for-age ················································ 59


empirical data points, 20-80 ages: Male FST-for-age ················································· 60


empirical data points, 20-80 ages: Female FST-for-age ············································· 60


empirical data points, 20-80 ages: Male PT-for-age ···················································· 61


empirical data points, 20-80 ages: Female PT-for-age ················································ 61

Figure 23. Percentile calculation using LMS estimators ··············································· 63

vii

ABSTRACT

Development of statistical method to modeling tooth healthspan

curves in Korean

Jung Hoi In


The Graduate School, Yonsei University

The duration of teeth remaining in mouth is being increased by oral health

promotion and aging society. Thus it is necessary to develop oral health measure

focus on health rather than disease experience such as DMFT index. Tooth

healthspan curves visualize the decrease of sound teeth index (ST index),

functioning teeth index (FST index), and present teeth index (PT index) using

percentile curve. Previous versions of tooth healthspan curves were developed

without applying weighting and appropriate smoothing methods. Most of all, the

curves had limitation which could not provide accurate values because parametric

models were not employed. This study aims to construct statistical models for

tooth healthspan curves using representative national survey data, advanced

statistical smoothing procedures, and LMS technique. Moreover, the dental health

indices were compared with DMFT index to investigate their usefulness.

Data collected by Korean National Health and Nutrition Examination Survey

(KNHANES) IV and the first and second year of KNHANES V (2010-2011) was

used. Subjects with interview of health and dental examination data aged 16 to 89

years were included. The empirical percentiles of ST index, FST index and PT

index specified for sex and age groups were calculated. The empirical percentile

curves were smoothed with locally weighted regression followed by 7-order

polynomial regression procedures. The modified LMS procedure was performed to

approximate smoothed curves and estimate transformation parameters. The

multiple linear regression whose dependent variable were indices and explanatory

viii

variables were oral health related factors was performed. The results are listed as

follows.

1. The sex-specific smoothed percentile curves for ST index-for-age, FST

index-for-age, and PT index-for-age were constructed. The smoothed percentile

curves were closely matched to empirical percentile curves.

2. The parameters lambda, sigma, and mu were estimated to enable computation

of exact z-score and percentiles for every single values for ST index, FST index,

and PT index.

3. The explained proportion of variance was highest as of 10% in male and

female in their 20's and was decreased to only 5% in 80’s male and female by

age when the dependent variable was DMFT and explanatory variables were age,

family income, level of education, area of residence, perception of dental health and

dental examination within 1 year in multiple linear regression. Otherwise, the

explained proportion of variance were 9-26% and greater than any other indices

when the dependent variable was the percentile of FST index for male. The

explanatory variables were family income, level of education, area of residence,

perception of dental health and dental examination within 1 year in multiple linear

regression. For female, the explained proportion of variance were 8-10%, greater

than any other indices in 20’s and 30’s when the dependent variable were ST

index and the explained proportion of variance were 14-17%, greater than any

other indices in 40's to 70's when the dependent variables were FST index.

The study resulted in construction of tooth healthspan curves with sex and age

group of specific estimated parameter L, M, and S to calculate exact z-score and

percent in continuous manner. Moreover the percentiles of FST index were

explained better than DMFT index especially in elderly population. The tooth

healthspan curves provide comprehensive information in intuitive way. The curves

can be used to provide highly accurate information for individual and expected to

be a practical tool in clinical and public health setting providing diagnosis

reference and to reach appropriate goal.

Key words: Oral health, Representative survey, Percentile curve, DMFT index,

FST index, Modified LMS procedure

1

Development of statistical method to modeling tooth healthspan

curves in Korean

<Directed by Professor Baek-Il Kim>


The Graduate School, Yonsei University

Jung Hoi In

1. Introduction

In order to measure status of health, operationally defining the health is

necessary. Point of view from both of these two statements, health as merely

absence of disease and as complete state of physical well-being, consist of

limitation. Speaking of oral health based on first statement, edentulous state is

consider as a good health. According to the perspective based on second

statement, condition which has 32 teeth with no damage can be defined as a

healthy state, which it seems to be unrealistic. One way to define the health is to

determine reference value from the distribution in the normative population (Daly

et al., 2013). Tooth damage is accumulated necessarily by age. Thus utilize

distribution categorized by age is essential in order to suggest oral health

reference by distribution of tooth condition in the normative population.

Concept of percentile curve is widely known and used in the growth chart to

assess and monitor the health among pediatric population. Growth chart is an

2

important tool for evaluating nutrition and health status of both individual and

population. Until growth period is completed, physical measurements like height

and weight are increased, proportional to age. However, variation exist in speed

and amount of increase. Percentile curve is a method that can simultaneously

display variation which occur naturally and gain physical measurements. Korea

Centers for Disease Control and Prevention (KCDC) released 2007 Korean National

Growth Charts in Korean children and adolescents. This revised standard version

of the chart is developed to apply advanced statistical methodology used in 2000

CDC growth chart of the United States and the WHO child growth standards of

World Health Organization (KCDC, 2007). Both the 2000 CDC growth charts and

WHO child growth standards were developed to provide proper statistical model

instead of empirical measurement describing population only. The previous version,

1998 Korean National Growth Charts in Korean children and adolescents,

conducted empirical percentile calculation and curve smoothing to provide

percentile values of empirical measurement. Using the 1998 Korean National

Growth Charts, proper reading of a table was necessary in order to obtain a

percentile of a measurement. When the value was not displayed in the table, user

could utilize a figure to acquire a range, but not a numerical value. To overcome

this limitation, 2007 Korean Growth Charts were developed by applying model

approach. By using a model, numerical value can be obtained with function. Odds

of error to occur can be decreased and any exact value can be calculated even

when the table is not presented. The modified LMS method (Cole, 1990;

Kuczmarski et al., 2002) was applied to revised version of growth chart in Korean

children and adolescents so that estimation of percentile for empirical measurement

is possible. LMS abbreviation stands for Box-Cox transformation power lambda

(L), median (M), and standardized coefficient of variation (S).

Osada (1989) introduced concept of the percentile curves to oral health research.

3

He made the percentile curve for present teeth index-for-age and predicted that in

order to retain about 20 teeth at age of 80's, he or she would expect to have at

least 27.8 and 24.9 number of teeth when they are in their 60's and 70's based on

the curve (Osada, 1999). Kim (2004) compared the oral health status between

Japanese and Korean adults using the percentile curves for present teeth

index-for-age and sound teeth index-for-age. This was the first study calculated

the percentile curves for oral health indices-for-age in Korean. Kim (2009)

constructed percentile curves for sound teeth index-for-age, functioning teeth

index-for-age, and present teeth index-for-age, and suggested the term 'Tooth

life curve' to make users easily understand the meaning of the curve. Jeong

(2011) used the percentile curves of PT index to determine association between

diabetes and oral health. National survey data from the 2000, 2006 Korean National

Oral Health Survey was used in Kim's study (2004) and Kim's study (2009),

respectively. However, the number of study subject was limited because it was

conducted in one year and there was high rate of non respondent in adult sample.

From analytical aspect, appropriate weight application was absent. Jeong (2011)

used data of Korean National Health and Nutrition Examination Survey

(KNHANES) IV which is well designed and conducted. However, the parametric

model was not introduced which enables calculation and prediction. To overcome

these shortcomings, using data from the survey which is well designed and

conducted and applying recently developed advanced statistical methods to the data

is needed.

Functioning teeth index (FST index) is one of an alternative index of dental

health which was suggested by Sheiham (1987). It is devised to overcome the

shortcomings of DMFT index which had been widely used to measure oral health

status. It is calculated by sum of treated teeth and sound teeth. The FST index

was compared to DMFT index in several studies by calculating linear regressions

4

using the indices as dependent variables. The studies reported that oral health

related factors explained the variance in a larger proportion for the FST index

than DMFT index (Benigeri et al., 1998; Marcenes and Sheiham, 1993). The FST

index was used as primary variable in the study for change in oral health status

of German from 1989 to 2005 (Holtfreter et al., 2013). Holst and Schuller (2011)

used two more alternative indices, sound teeth index (ST index), and present teeth

index (PT index), other than FST index to investigate change in oral health

inequality of Norwegian adult.

The purpose of the study was to develop tooth healthspan curve for three

alternative indices of dental health using data from comprehensive national survey,

improved statistical smoothing and transformation procedures. The comparison

between DMF index and percentile of indices were also conducted to provide

better tool for dental care providers who evaluate and monitor the dental health

status of adults in Korea.

5

2. Materials and methods

2.1 Data sources

This study used the data collected in the Korean National Health and Nutrition

Examination Survey (KNHANES) IV and the first and second year data of

KNHANES V (2010-2011). The data was downloaded at August 1st, 2013. The

oral health examination in KNHANES has been conducted since 2007 annually and

sum of 5 year's data from 2007 to 2011 have been officially released. The

KNHANES is a cross-sectional, national representative survey. The sampling

frame of KNHANES IV was based on the 2005 population and housing census in

Korea. 2009 Registration survey data and 2008 Korean KB-Housing data for

apartment was used as a sampling frame for KNHANES V (Park, 2010). A

stratified multistage probability sampling was performed for the household units,

and all family members over 1 year of the selected household were the sample

subjects. Total of 31,145 individuals from the sampling frame was included and

the participation rate was 78.4% in KNHANES IV. and 21,527 individuals was

included and the participation rate was 81.2% in the first and second year of

KNHANES V. Subjects with interview of health and examination data were

selected as potential participants in the study among whole subject. A potential

analytical sample was 31,283 subjects (13,463 men, 17,820 women). The subjects

with aged 16 to 89 years were included and the subjects which had missing in

dentition status were excluded from analysis set. A final analytic set consist of

30,513 subjects (13,120 men, 17,393 women). Sample sizes stratified by age, sex,

and data source used to create each chart are shown in tables 1. Variables related

with sex, age, survey design and dentition status were selected to construct tooth

healthspan curves. Five more variables, family income, level of education, area of

6

residence, perception of Dental examination within 1 year were selected to

compare dental health indices to DMF index (Table 2).

Table 1. Unweighted sample size by sex, age and data source

KNHANES IV KNHANES V Total

Sex

Male 7,606 5,514 13,120

Female 10,157 7,236 17,393

Age

16-24 years 1,829 1,204 3,033

25-34 years 2,690 1,702 4,392

35-44 years 3,557 2,515 6,072

45-54 years 3,233 2,268 5,501

55-64 years 2,598 2,159 4,757

65-74 years 2,633 1,939 4,572

75-84 years 1,103 873 1,976

85-89 years 120 90 210

Total 17,763 12,750 30,513

KNHANES: Korean National Health and Nutrition Examination Survey

7

Table 2. Variables selected for the study

Category Name Description

Sociodemographic sex

age

ho_incm Household income

edu Level of education

town_t Area of residence

Survey design psu Primary sampling unit

kstrata Strata for variance estimation

wt_itvex Interview-examination weight

Dental health O_tooth numberB Dentition status of buccal surface

O_tooth numberD Dentition status of distal surface

O_tooth numberO Dentition status of occlusal surface

O_tooth numberM Dentition status of mesial surface

O_tooth numberL Dentition status of lingual surface

Oral health survey OR1 Perception of dental health

OR1_2 Dental examination within 1 year

2.2 Dental examination

Calibrated examiner conducted dental examination. Dentition status were

examined for caries and restorations according to the criteria of the World Health

Organization (WHO) with modification (Park, 2012; WHO, 1997). Dentition status

was recorded at tooth surface level into any of the nine categories; sound surface

(code 0), decayed surface (code 1), filled surface as a result of caries (code 3),

missing surface as a result of caries (code 4), missing surface as a result of any

other reason (code 5), surface with sealant (code 6), filled surface as a result of

caries (code 7), unerupted surface (code 8), and unrecordable surface (code 9). A

detailed description of the criteria for diagnosis and coding use was published in

the Standardization for Oral Health Survey in KNHANES (Park, 2012). The teeth

8

which had been lost were recorded as either missing teeth due to caries or due to

any other reason by asking the survey participant reason for tooth loss.

2.3 Definition of indices

The calculation of dental health indices was based on 28 teeth excluding third

molars. The surfaces recorded as code 3 and code 7 were defined as health related

filled surface, code 4 and code 5 were defined as health related missing surface,

and code 0,6, and 9 were defined as sound surface to calculate alternative indices

of dental health. Dentition status was recorded in surface level and transformation

to teeth level was performed. The teeth which had at least one decayed surface

were defined as decayed teeth, the teeth which had missing surface only were

defined as missing teeth, and teeth which had at least one filled surface without

any decayed or missing surface were defined as filled teeth. Moreover, the teeth

which had health related missing surface were only defined as health related

missing teeth, and teeth which had at least one health related filled surface

without any decayed or missing surface were defined as health related filled teeth.

The decayed teeth index, missing teeth index and filled teeth index were

calculated by sum of the decayed teeth, missing teeth and filled teeth in subject

level, respectively. Health related missing teeth index and health related filled teeth

index were calculated by sum of the health related missing teeth and health

related filled teeth in subject level. Finally the DMFT index, ST index, FST index,

and PT index were calculated by following formula DT index+MT index+FT

index, 28-(DT index+Health related MT index+Health related FT index), ST

index+FT index, and 28-(Health related MT index), respectively (Table 3).

9

Table 3. Dental health indicator calculation

Level Variable name Definition

Tooth

SurfaceDecayed surface Recorded as code 1

Missing surface Recorded as code 4

Filled surface Recorded as code 3

Health related missing surface Recorded as code 4 or code 5 or code 8

Health related filled surface Recorded as code 3 or code 7

Sound surface Recorded as code 0 or code 6 or code 9

Tooth Decayed tooth Tooth with at least one decayed surface

Missing tooth Tooth which all surfaces are missing surface of

Filled tooth Tooth with at least one filled surface withoutdecayed surface

Health related missing tooth Tooth which all surfaces are health relatedmissing surface of

Health related filled tooth Tooth with at least one health related filledsurface without decayed surface

Subject DT index The number of decayed tooth

MT index The number of missing tooth

FT index The number of filled tooth

Health related MT index The number of health related missing tooth

Health related FT index The number of health related filled tooth

DMFT index DT index + MT index + FT index

ST index 28 - (DT index + Health related MT index +Health related FT index)

FST index ST index + Health related FT index

PT index 28 - Health related MT index

DT: decayed teeth, MT: missing teetn, FT: filled teeth, ST: sound teeth, FST: functioningteeth, PT: present teeth

Observed mean with standard deviation, and five percentiles for each dental

health indices by sex and age are shown in supplement table 3-8.

10

2.4 Statistical curve smoothing procedures

The weighted average of survey-specific sample weights were used according

to recommendation of KNHANES analytic guideline (KCDC, 2013). The statistical

procedures used in 2000 CDC growth chart and 2007 Korean growth charts were

applied to construct tooth healthspan curve. Statistical procedures to estimated

values of weighted empirical percentiles were consist of two stages; first stage

was curve smoothing stage to produce smoothed curves for selected percentiles

and second stage was transformation stage to estimate parameters which were

used to calculate additional percentiles of any given observation.

2.4.1 Age groupings

Before smoothing, data were grouped by two years or more of age in order to

ensure a sufficient number of observation for the development of charts relating

dental health index to age. From 16 to 17 years and from 22 to 77 years, the

empirical percentile estimates were made at 2-year intervals; from 18 to 21 years

and from 78 to 81 years, the empirical percentile estimates were made at 4-year

intervals; and from 82 to 89 years, empirical percentile estimates were made at

8-year intervals due to very small number of observations. Each age group was

categorized by the midpoint of an age range. For example, age 21 years included

ages from 20.00 years to 21.99 years of age.

2.4.2 Curve smoothing stage

For each dental health index, nineteen weighted empirical percentiles (from 5th

to 95th at intervals of 5) at the midpoints of each age groups were estimated

using SAS procedure SURVEYMEANS. NOMCAR option was used to avoid bias

caused by missing values. The irregular lines of connecting empirical percentile

11

values needed to be smoothed to make clinically useful percentile curves.

Two-step smoothing was applied to produce the tooth healthspan curves. In the

first step of smoothing, locally weighted regression (LWR) was applied using SAS

procedure LOESS. The LWR does not give any parameter estimates, but provides

an intermediate smoothed curve for further parametric smoothing. A weight

function of locally weighted regression applies larger weights to data points near

the value to be estimated than values which is far off, where X0 is the midpoint

age at which the value is smoothed, Xi is the i th age from the central age and

the value to which the weight is being assigned, and ΔX is the age range covered

by the width of the moving regression window (Figure 1-A). Windows for each

of the values to be estimated overlap and are referred to as moving regression

windows. The weighted least squares regression is applied to the values in each

moving regression window to provide the smoothed estimate at X0. The resulting

estimates from each regression window form a smoothed curve (Figure 1-B). The

width of the LWR moving window for tooth healthspan curves was chosen after

several trials which had various smoothing parameter from 0.2 t0 0.6 to balance

the degree of smoothness and fit to the estimated weighted empirical percentiles.

As a result, twelve data points were selected as a width of moving regression

window. When smoothing the value at age of 20 years, another data point at ages

under 20 years were necessary for stable end of percentile curves. The empirical

percentiles from 16.00 to 17.99 years was used as additional data point for

smoothing. For the value at age 80 years, the empirical percentiles from 80.00

years to 87.99 years was used.

12

Figure 1. Locally weighted regression

(A) Scatter plot with raw data

(B) Smoothed plot after applying locally weighted regression

In the second step of smoothing, polynomial regression was applied in weighted

13

empirical percentile curves. A 7-order polynomial model which had seven

parameters was used (Figure 2).

f(t) = ß0 + ß1t + ß2t2 + ß3t3 + ß4t4 + ß5t5 + ß6t6 + ß7t7

t: age calculated as midpoint of the age rangef(t): the value of dental health indicesß0-7: parameters to be estimatedFigure 2. 7-order polynomial model

The smoothing stage resulted in every chart having a parametric form with

estimated parameters specific for each selected percentile. The estimation of

parameters in nonlinear regression were performed using SAS procedure NLIN.

root mean square error was used to the fit of the models.

2.4.3 The transformation stage

Three parameters L, M and S are estimated in modified LMS procedure (CDC,

2002) and they refer the median (M), the generalized coefficient of variation (S),

and the power in the Box-Cox transformation (L), respectively. The LMS

transformation equation is following (Figure 3).

X = M (1 + LSZ)1/L (L ≠ 0)X = M exp(SZ) (L = 0)

X: the value of dental health indicesZ: z-score that corresponds to the selected percentileFigure 3. LMS transformation equation

The L means the degree of skewness. In the equation, X is the value of dental

health indices and Z is the z-score that corresponds to the percentile. Using the

LMS equation, observed dental health index X can be connected to the Z score

with estimate values of L, M and S. For example, a z-score of 0.3319 corresponds

to the 63th percentile. In the case of tooth healthspan curves, with the L, M, and

S parameters, it is possible to evaluate any single measure in a population as an

14

exact z-score or percentile. In the modified LMS approach, empirical percentile

curves were initially smoothed and parametric models were generated, as described

above. Then, at each age, a group of 5 equations was produced by specifying the

LMS equations for the smoothed percentiles in previous curve smoothing stage. A

simultaneous solution for the three parameters was generated using the SAS

procedure NLIN. The set of L, M, and S parameters was determinated as the best

solution to the LMS equations by the sum of squared errors minimization.

2.5 Comparison between the DMF indices and alternative

indices.

The percentile values of ST index, FST index and PT index calculated LMS

transformation equations were compared to DMFT index using multiple linear

regression. Six explanatory variables, age, family income, level of education, area

of residence, perception of dental health and Dental examination within 1 year

were selected among the variables used in the study of Benigeri et al. (1998).

The age was included only in the regression model which used DMFT index as a

dependent variable because percentile values of three alternative variables were

estimated in specifying age groups. SAS procedure SURVEYFREQ and

SURVEYREG was used. In SURVEYREG procedure, the DOMAIN statement was

used to analysis subgroups stratified by sex and age groups of 10 years intervals.

15

3. Results

3.1 Estimated values of weighted empirical percentiles

3.1.1 ST index, male

The weighted empirical percentile distributions of ST index among male is

shown in table 4. The estimated median of ST index in male was 22.76 at 20

year, 22.60 at 41 year, 16.51 at 61 year, and 4.32 at 80 year. The difference

between median and 90th percentile was 4.74 and difference between median and

10th percentile was 6.77 at 20 year. The distribution of lower percentiles was

wider than of upper percentiles. This trend was more clear in order ages; the

difference between median and 90th percentile was 7.76 and difference between

median and 10th percentile was 16.51 at 61 year. Since the ST index of 10th

percentile was reduced to 0, the difference between median and 10th percentile

was decreased to 4.32 at 80 years but the difference between median and 90th

percentile was increased to 13.28.

16

Table 4. Weighted selected percentiles for ST index by age: Male

Midpointages

Percentiles

10th

25th

50th

75th

90th

20 15.99 19.27 22.76 26.29 27.50

23 14.79 19.13 22.18 24.80 27.19

25 14.85 19.11 22.18 24.65 26.93

27 14.55 18.56 22.02 25.42 27.13

29 15.10 19.06 22.71 25.75 27.35

31 15.03 18.76 22.27 25.37 27.25

33 15.90 19.99 23.36 25.95 27.33

35 15.69 19.30 23.18 25.81 27.31

37 16.92 19.69 23.26 25.99 27.32

39 15.60 19.40 22.79 25.93 27.32

41 14.66 18.57 22.60 25.70 27.06

43 13.97 18.30 22.29 25.35 27.05

45 14.74 18.27 22.55 25.49 27.21

47 14.47 18.15 22.33 25.49 27.27

49 13.15 18.14 22.35 25.19 27.02

51 13.39 17.94 21.97 24.95 27.06

53 10.14 15.69 20.61 24.28 26.52

55 6.54 13.64 19.85 23.64 25.83

57 2.32 9.97 18.38 23.58 26.06

59 2.09 9.03 16.70 22.43 25.53

61 0.00 8.71 16.51 21.43 24.27

63 0.51 8.18 17.09 22.71 25.47

65 0.00 5.39 14.59 19.94 23.96

67 0.00 3.89 13.41 20.82 24.45

69 0.00 2.83 9.97 17.46 23.19

71 0.00 1.54 9.61 17.69 21.87

73 0.00 1.32 10.22 17.85 22.76

75 0.00 0.00 7.68 15.39 21.92

77 0.00 0.00 4.07 11.41 20.31

80 0.00 0.00 4.32 11.79 17.60

17

3.1.2 ST index, female

The weighted empirical percentile distributions of ST index among female is

shown in table 5. The estimated median of ST index in female was 21.26 at 20


between median and 90th percentile was 5.26 and difference between median and

10th percentile was 6.31 at 20 year. The distribution of lower percentiles was

wider than of upper percentiles. This trend was more clear in order ages; the

difference between median and 90th percentile was 8.84 and difference between

median and 10th percentile was 13.02 at 61 year. Since the ST index of 10th

percentile was reduced to 0, the difference between median and 10th percentile

was decreased to 2.7 at 80 years but the difference between median and 90th

percentile was increased to 14.98.

18

Table 5. Weighted selected percentiles for ST index by age: Female

Midpointages

Percentiles

10th

25th

50th

75th

90th

20 14.95 18.12 21.26 24.21 26.52

23 15.10 18.06 20.55 23.48 26.25

25 13.82 16.95 19.99 23.15 25.75

27 13.84 16.92 20.04 23.52 26.16

29 14.11 16.95 19.94 23.30 25.96

31 13.89 17.29 20.05 23.75 26.59

33 14.59 17.59 20.45 23.91 26.82

35 14.07 17.76 20.89 24.48 26.40

37 14.87 18.06 21.48 24.94 26.77

39 14.59 17.69 21.38 24.72 26.99

41 14.32 17.52 20.74 24.45 26.64

43 13.42 17.35 20.63 24.06 26.48

45 12.40 16.50 20.12 23.92 26.62

47 11.47 15.71 19.43 23.25 26.21

49 11.46 15.84 19.79 23.79 25.94

51 9.03 14.16 19.28 23.57 25.96

53 9.63 14.23 18.96 22.86 25.70

55 5.27 11.43 16.57 21.90 25.64

57 5.40 11.12 17.28 21.55 25.38

59 4.87 10.17 16.88 21.75 25.09

61 2.28 9.39 15.30 20.09 24.14

63 0.97 6.47 14.20 19.91 23.66

65 0.44 6.60 13.53 20.21 23.38

67 0.00 4.45 12.40 18.37 22.15

69 0.00 3.30 10.33 17.48 21.64

71 0.00 1.24 8.76 16.11 21.21

73 0.00 0.01 7.74 15.95 21.17

75 0.00 0.00 4.54 12.40 19.21

77 0.00 0.00 4.32 13.27 19.69

80 0.00 0.00 2.70 9.89 17.68

19

3.1.3 FST index, male

The weighted empirical percentile distributions of FST index among male is

shown in table 6. The estimated median of FST index in male was 27.12 at 20


between median and 90th percentile was 0.7, which was less than 1, and

difference between median and 10th percentile was 3.91 at 20 year. The

distribution of lower percentiles was wider than of upper percentiles. This trend

was more clear in order ages; the difference between median and 90th percentile

was 4.00 and difference between median and 10th percentile was 15.79 at 61 year.

Since the FST index of 10th percentile was reduced to 0, the difference between

median and 10th percentile was decreased to 10.41 at 80 years but the difference

between median and 90th percentile was increased to 13.51.

20

Table 6. Weighted selected percentiles for FST index by age: Male

Midpointages

Percentiles

10th

25th

50th

75th

90th

20 23.21 25.53 27.12 27.56 27.82

23 23.34 25.26 27.04 27.52 27.81

25 23.69 25.69 27.04 27.52 27.81

27 22.98 25.35 26.93 27.49 27.79

29 23.31 25.44 27.00 27.50 27.80

31 23.59 25.18 26.87 27.48 27.79

33 23.63 25.69 27.09 27.54 27.82

35 24.16 25.93 27.06 27.53 27.81

37 24.10 25.78 27.04 27.52 27.81

39 23.24 25.27 26.80 27.46 27.78

41 22.73 25.08 26.54 27.36 27.74

43 21.86 24.76 26.49 27.39 27.75

45 22.65 24.73 26.35 27.35 27.74

47 21.23 24.29 26.41 27.38 27.75

49 21.39 24.13 26.03 27.23 27.69

51 21.15 23.84 25.76 27.13 27.65

53 17.44 22.45 25.37 26.85 27.54

55 13.17 21.08 24.84 26.75 27.52

57 10.03 18.61 24.49 26.45 27.39

59 8.24 17.97 22.93 25.92 27.07

61 7.38 17.19 23.17 25.72 27.17

63 7.78 17.02 23.53 25.92 27.20

65 5.22 13.71 21.47 25.34 26.70

67 4.10 13.29 20.80 25.20 26.78

69 1.99 9.31 18.49 24.58 26.58

71 1.36 8.46 17.60 23.26 25.92

73 1.47 9.07 19.44 24.09 26.33

75 0.00 4.46 14.53 22.60 25.39

77 0.00 1.96 8.87 20.98 25.45

80 0.00 3.18 10.41 18.60 23.92

21

3.1.4 FST index, female

The weighted empirical percentile distributions of FST index among female is

shown in table 7. The estimated median of FST index in female was 27.05 at 20


between median and 90th percentile was 0.76, which was less than 1, and

difference between median and 10th percentile was 3.78 at 20 year. The

distribution of lower percentiles was wider than of upper percentiles. This trend

was more clear in order ages; the difference between median and 90th percentile

was 3.53 and difference between median and 10th percentile was 11.17 at 61 year.

Since the FST index of 10th percentile was reduced to 0, the difference between

median and 10th percentile was decreased to 8.86 at 80 years but the difference

between median and 90th percentile was increased to 15.21.

22

Table 7. Weighted selected percentiles for FST index by age: Female

Midpointages

Percentiles

10th

25th

50th

75th

90th

20 23.27 25.32 27.05 27.52 27.81

23 23.40 25.05 26.96 27.49 27.80

25 23.29 25.21 27.01 27.51 27.80

27 23.50 25.50 27.05 27.53 27.81

29 23.28 25.02 26.86 27.48 27.79

31 23.62 25.52 27.04 27.52 27.81

33 23.78 25.83 27.07 27.54 27.81

35 23.45 25.46 27.04 27.52 27.81

37 23.91 25.78 26.99 27.50 27.80

39 24.01 25.73 27.06 27.53 27.81

41 23.62 25.62 27.01 27.51 27.80

43 23.43 25.44 26.75 27.44 27.77

45 22.58 24.75 26.52 27.38 27.75

47 22.19 24.67 26.45 27.37 27.75

49 21.32 24.35 26.24 27.33 27.73

51 19.38 23.28 26.00 27.21 27.69

53 18.99 23.15 25.7 27.17 27.67

55 16.27 21.82 24.98 26.73 27.51

57 15.15 20.94 24.52 26.71 27.51

59 15.06 20.60 24.33 26.54 27.44

61 12.63 19.56 23.80 26.16 27.33

63 8.16 16.75 22.56 25.65 27.12

65 7.16 16.06 22.50 25.74 27.00

67 5.23 12.78 21.33 25.01 26.73

69 2.80 10.23 20.02 24.30 26.48

71 1.47 7.78 17.53 23.44 26.35

73 0.00 7.38 16.86 23.04 25.87

75 0.00 3.03 13.56 20.96 25.04

77 0.00 3.14 12.01 21.17 25.24

80 0.00 2.30 8.86 18.22 24.07

23

3.1.5 PT index, male

The weighted empirical percentile distributions of PT index among male is


year, 27.05 at 41 year, 23.46 at 61 year, and 12.35 at 80 year. There is slight

difference of 0.48 between median and 90th percentile at 20 year. The difference

between median and 10th percentile was 1.22. It was bigger difference compared

with that of upper percentile, however, smaller compared with differences of ST

index and FST index. The difference between median and 90th percentile was 3.86

and difference between median and 10th percentile was 15.66 at 61 year. Since the

PT index of 10th percentile was reduced to 0, the difference between median and

10th percentile was decreased to 12.33 at 80 years but the difference between

median and 90th percentile was markedly increased to 12.60.

24

Table 8. Weighted selected percentiles for PT index by age: Male

Midpointages

Percentiles

10th

25th

50th

75th

90th

20 26.18 27.11 27.40 27.70 27.88

23 26.07 27.07 27.38 27.69 27.88

25 26.21 27.09 27.39 27.70 27.88

27 25.83 27.02 27.35 27.67 27.87

29 25.72 26.83 27.31 27.65 27.86

31 25.34 26.92 27.33 27.66 27.87

33 25.68 26.82 27.31 27.65 27.86

35 25.67 26.81 27.31 27.65 27.86

37 25.33 26.63 27.27 27.64 27.85

39 24.60 26.22 27.16 27.58 27.83

41 24.16 25.81 27.05 27.53 27.81

43 23.15 25.50 26.91 27.48 27.79

45 23.69 25.27 26.77 27.46 27.78

47 22.24 25.10 26.85 27.48 27.79

49 22.19 24.73 26.48 27.37 27.75

51 21.83 24.47 26.30 27.29 27.72

53 18.42 23.14 25.80 27.10 27.64

55 14.83 21.66 25.28 27.02 27.61

57 10.77 19.45 25.13 26.87 27.56

59 9.50 18.88 23.64 26.28 27.31

61 7.80 17.85 23.46 26.03 27.32

63 8.52 17.97 24.13 26.40 27.40

65 5.81 14.59 22.13 25.84 27.08

67 4.65 14.81 21.85 25.63 27.14

69 2.34 10.69 19.75 25.02 26.94

71 1.73 9.01 18.46 24.14 26.26

73 1.91 10.16 20.49 24.76 26.76

75 0.00 4.96 16.10 23.43 25.77

77 0.00 2.54 10.51 21.77 25.88

80 0.02 3.54 12.35 21.29 24.95

25

3.1.6 PT index, female

The weighted empirical percentile distributions of PT index among female is


year, 27.19 at 41 year, 24.23 at 61 year, and 9.94 at 80 year. There is slight

difference of 0.51 between median and 90th percentile at 20 year. The difference

between median and 10th percentile was 1.86 at 20 year. It was bigger difference

compared with that of upper percentile, however, smaller compared with

differences of ST index and FST index. The difference between median and 90th

percentile was 3.19 and difference between median and 10th percentile was 10.14

at 61 year. Since the PT index of 10th percentile was reduced to 0, the difference

between median and 10th percentile was decreased to 9.94 at 80 years but the

difference between median and 90th percentile was markedly increased to 14.88.

26

Table 9. Weighted selected percentiles for PT index by age: Female

Midpointages

Percentiles

10th

25th

50th

75th

90th

20 25.50 27.04 27.36 27.68 27.87

23 25.18 27.00 27.34 27.67 27.87

25 24.80 26.91 27.32 27.66 27.86

27 25.34 26.82 27.31 27.66 27.86

29 24.40 26.17 27.23 27.61 27.85

31 24.66 26.46 27.26 27.63 27.85

33 25.24 26.62 27.28 27.64 27.86

35 24.90 26.37 27.24 27.62 27.85

37 25.21 26.41 27.23 27.61 27.85

39 25.07 26.37 27.22 27.61 27.84

41 24.73 26.21 27.19 27.59 27.84

43 24.44 26.08 27.15 27.57 27.83

45 23.37 25.48 26.99 27.50 27.80

47 23.09 25.24 26.80 27.46 27.78

49 22.26 25.01 26.68 27.44 27.78

51 20.72 24.10 26.33 27.35 27.74

53 20.43 23.64 26.13 27.29 27.72

55 17.22 22.29 25.36 27.08 27.63

57 15.57 21.68 24.76 27.03 27.61

59 16.23 21.42 24.72 26.71 27.52

61 14.09 20.18 24.23 26.36 27.42

63 8.63 17.55 23.3 26.04 27.28

65 7.46 17.04 23.16 26.03 27.22

67 5.51 14.53 21.84 25.39 26.84

69 2.87 11.31 20.72 24.99 26.71

71 1.69 8.45 18.07 24.27 26.65

73 0 7.82 17.79 23.39 26.14

75 0 3.92 14.29 21.61 25.39

77 0 3.63 13.32 22.23 25.64

80 0 2.93 9.94 19.36 24.82

27

3.2 Estimated values of smoothed percentiles and 7-order

polynomial model parameters


After smoothing procedure using LWR, The residual sum of squares of the 10th

smoothed percentile curve was 34.3327. The residual sum of squares was reduced

as it went to the upper percentile and it was 9.5068 in 90th smoothed percentile

curve. Compared to the upper smoothed percentiles, lower smoothed percentiles

were reflect the original value more closely (Figure 4).

Residual Sum of Squares

10thpercentile 25

thpercentile 50

thpercentile 75

thpercentile 90

thpercentile

34.3327 19.8265 17.7853 17.0485 9.5068

Figure 4. Comparison of LWR smoothed 5th, 25th, 50th, 75th, 95th percentile

curves to empirical data points, 20-80 ages: Male ST-for-age

The ß0-ß7 parameters rounded off the numbers to five decimal places that were

used to create parametric smoothed curve are presented in table 10. The smoothed

28

percentile distributions of ST index among male is shown in table 11. The visual

comparison between the result of two step smoothing using LWR and polynomial

regression was showed in figure 5.

Table 10. 7-order polynomial model parameters for ST by percentile: Male

percentile ß0†

ß1†

ß2†

ß3†

ß4†

ß5†

ß6†

ß7†

10 -206.37595 42.41574 -3.23575 0.12790 -0.00283 0.00004 0.00000 0.00000

25 -34.85086 9.93554 -0.71038 0.02547 -0.00049 0.00000 0.00000 0.00000

50 9.30963 2.77457 -0.21762 0.00839 -0.00017 0.00000 0.00000 0.00000

75 3.78339 4.68031 -0.39015 0.01659 -0.00039 0.00001 0.00000 0.00000

90 -18.97567 8.87089 -0.68490 0.02768 -0.00063 0.00001 0.00000 0.00000†Values were rounded off the numbers to five decimal places

Table 11. Selected smoothed percentiles for ST by age: Male

Midpointages

Percentiles10th

25th

50th

75th

90th

20 16.40 19.59 22.76 25.74 27.4323 15.77 19.37 22.64 25.59 27.3225 15.35 19.21 22.60 25.53 27.2427 15.09 19.11 22.59 25.52 27.1929 15.02 19.07 22.62 25.54 27.1831 15.13 19.09 22.67 25.58 27.1933 15.33 19.14 22.73 25.64 27.2335 15.54 19.19 22.79 25.69 27.2737 15.67 19.21 22.81 25.71 27.3039 15.63 19.15 22.80 25.71 27.3041 15.37 18.98 22.72 25.65 27.2843 14.83 18.67 22.57 25.55 27.2145 14.01 18.19 22.32 25.39 27.1047 12.92 17.54 21.98 25.17 26.9649 11.59 16.70 21.53 24.89 26.7751 10.09 15.68 20.96 24.55 26.5553 8.47 14.49 20.29 24.15 26.3155 6.82 13.16 19.50 23.69 26.0457 5.22 11.73 18.60 23.17 25.7559 3.74 10.22 17.60 22.59 25.4461 2.46 8.70 16.51 21.93 25.1063 1.41 7.19 15.33 21.20 24.7165 0.62 5.76 14.09 20.39 24.2867 0.10 4.45 12.79 19.48 23.7669 0.00 3.29 11.45 18.45 23.1571 0.00 2.33 10.08 17.31 22.4273 0.00 1.56 8.69 16.04 21.5575 0.00 0.99 7.29 14.65 20.5377 0.13 0.60 5.89 13.15 19.3580 0.18 0.24 3.82 10.75 17.35

29


LWR and polynomial regression, 20-80 ages: Male ST-for-age

30


After smoothing procedure using LWR, the residual sum of squares of the 10th

smoothed percentile curve was 14.3824. Compared to the smoothed percentiles of

male, smoothed percentiles of female were reflect the original value more closely.

The residual sum of squares was reduced as it went to the upper percentile and

it was 6.3530 in 90th smoothed percentile curve (Figure 6).


10thpercentile 25

thpercentile 50

thpercentile 75

thpercentile 90

thpercentile

14.3824 12.7047 9.9709 9.1885 6.3530


curves to empirical data points, 20-80 ages: Female ST-for-age



percentile distributions of ST index among female is shown in table 13. The

visual comparison between the result of two step smoothing using LWR and

polynomial regression was showed in figure 7.

31

Table 12. 7-order polynomial model parameters for ST by percentile: Female

percentile ß0†

ß1†

ß2†

ß3†

ß4†

ß5†

ß6†

ß7†

10 -82.09388 19.43413 -1.52466 0.06121 -0.00137 0.00002 0.00000 0.00000

25 20.22340 0.27432 -0.03871 0.00099 0.00001 0.00000 0.00000 0.00000

50 30.30993 -0.77330 0.00892 0.00072 -0.00003 0.00000 0.00000 0.00000

75 3.81976 4.79655 -0.42473 0.01874 -0.00045 0.00001 0.00000 0.00000

90 12.98964 2.96572 -0.24942 0.01056 -0.00025 0.00000 0.00000 0.00000†Values were rounded off the numbers to five decimal places

Table 13. Selected smoothed percentiles for ST index by age: Female

Midpointages

Percentiles

10th

25th

50th

75th

90th

20 15.60 18.23 21.04 24.15 26.54

23 14.99 17.86 20.72 23.91 26.41

25 14.64 17.70 20.61 23.84 26.37

27 14.41 17.60 20.56 23.83 26.36

29 14.28 17.54 20.55 23.87 26.38

31 14.24 17.51 20.57 23.95 26.42

33 14.24 17.49 20.59 24.04 26.47

35 14.22 17.46 20.61 24.12 26.52

37 14.13 17.39 20.61 24.18 26.56

39 13.92 17.27 20.57 24.20 26.58

41 13.56 17.06 20.48 24.17 26.57

43 13.03 16.75 20.33 24.07 26.52

45 12.31 16.32 20.11 23.91 26.43

47 11.42 15.77 19.80 23.68 26.29

49 10.37 15.07 19.41 23.39 26.11

51 9.21 14.24 18.93 23.04 25.89

53 7.96 13.28 18.34 22.64 25.62

55 6.68 12.19 17.66 22.17 25.31

57 5.41 11.01 16.87 21.66 24.96

59 4.21 9.75 15.99 21.09 24.57

61 3.11 8.44 15.01 20.46 24.13

63 2.16 7.11 13.93 19.76 23.65

65 1.38 5.82 12.78 18.99 23.11

67 0.78 4.58 11.55 18.14 22.52

69 0.36 3.45 10.25 17.18 21.86

71 0.10 2.45 8.90 16.11 21.13

73 0.00 1.60 7.52 14.92 20.33

75 0.00 0.93 6.13 13.62 19.45

77 0.01 0.42 4.73 12.21 18.49

80 0.07 0.00 2.70 9.97 16.93

32


LWR and polynomial regression, 20-80 ages: Female ST-for-age

33





curve (Figure 8).


10thpercentile 25

thpercentile 50

thpercentile 75

thpercentile 90

thpercentile

33.2323 24.1884 29.9415 5.5001 6.4120


curves to empirical data points, 20-80 ages: Male FST-for-age



percentile distributions of FST index among male is shown in table 15. The visual



34

Table 14. 7-order polynomial model parameters for FST index by age: Male

percentile ß0†

ß1†

ß2†

ß3†

ß4†

ß5†

ß6†

ß7†

10 -111.62420 24.92106 -1.85009 0.07122 -0.00153 0.00002 0.00000 0.00000

25 34.60989 -1.92933 0.16800 -0.00790 0.00022 0.00000 0.00000 0.00000

50 24.41184 0.73116 -0.07566 0.00392 -0.00011 0.00000 0.00000 0.00000

75 -9.03059 7.03982 -0.54983 0.02262 -0.00053 0.00001 0.00000 0.00000

90 -3.04555 5.88766 -0.45550 0.01856 -0.00043 0.00001 0.00000 0.00000†Values were rounded off the numbers to five decimal places

Table 15. Selected smoothed percentiles for FST index by age: Male

Midpointages

Percentiles

10th

25th

50th

75th

90th

20 23.51 25.41 27.04 27.60 27.88

23 23.42 25.44 27.02 27.55 27.84

25 23.29 25.46 27.02 27.50 27.80

27 23.23 25.49 27.02 27.47 27.77

29 23.26 25.50 27.01 27.46 27.76

31 23.35 25.51 26.99 27.47 27.77

33 23.48 25.50 26.96 27.49 27.78

35 23.57 25.46 26.91 27.50 27.80

37 23.57 25.39 26.84 27.51 27.82

39 23.41 25.27 26.75 27.50 27.82

41 23.06 25.08 26.63 27.46 27.81

43 22.47 24.81 26.47 27.40 27.78

45 21.63 24.45 26.29 27.31 27.74

47 20.53 23.97 26.07 27.19 27.68

49 19.20 23.37 25.81 27.06 27.61

51 17.65 22.64 25.50 26.91 27.54

53 15.93 21.76 25.14 26.74 27.46

55 14.11 20.74 24.72 26.56 27.39

57 12.22 19.58 24.22 26.37 27.31

59 10.35 18.28 23.63 26.15 27.23

61 8.54 16.87 22.93 25.91 27.14

63 6.86 15.36 22.12 25.61 27.03

65 5.34 13.78 21.18 25.24 26.88

67 4.03 12.16 20.09 24.78 26.68

69 2.95 10.53 18.84 24.21 26.40

71 2.09 8.92 17.43 23.50 26.04

73 1.44 7.37 15.86 22.63 25.56

75 0.97 5.89 14.15 21.60 24.96

77 0.63 4.50 12.31 20.41 24.24

80 0.23 2.59 9.42 18.38 22.95

35


LWR and polynomial regression, 20-80 ages: Male FST-for-age

36

3.2.4 FST index, female




curve (Figure 10). Compared to the smoothed percentiles of male, smoothed

percentiles of female were reflect the original value more closely.


10thpercentile 25

thpercentile 50

thpercentile 75

thpercentile 90

thpercentile

17.9663 17.3116 4.9773 4.0654 2.1926


curves to empirical data points, 20-80 ages: Female FST-for-age






37

Table 16. 7-order polynomial model parameters for FST index by age: Female

percentile ß0†

ß1†

ß2†

ß3†

ß4†

ß5†

ß6†

ß7†

10 43.05531 -4.08737 0.35709 -0.01701 0.00047 -0.00001 0.00000 0.00000

25 107.32744 -15.44583 1.18507 -0.04814 0.00112 -0.00001 0.00000 0.00000

50 35.93223 -1.35947 0.07758 -0.00199 0.00002 0.00000 0.00000 0.00000

75 11.38453 3.17382 -0.25353 0.01069 -0.00026 0.00000 0.00000 0.00000


Table 17. Selected smoothed percentiles for FST index by age: Female

Midpointages

Percentiles

10th

25th

50th

75th

90th

20 23.38 25.19 27.00 27.56 27.84

23 23.41 25.28 27.00 27.53 27.82

25 23.45 25.40 27.02 27.51 27.80

27 23.50 25.50 27.04 27.50 27.79

29 23.55 25.56 27.05 27.50 27.79

31 23.59 25.58 27.05 27.50 27.79

33 23.62 25.55 27.03 27.51 27.80

35 23.61 25.49 27.00 27.52 27.81

37 23.54 25.40 26.94 27.51 27.81

39 23.40 25.30 26.86 27.50 27.81

41 23.15 25.16 26.76 27.48 27.80

43 22.77 24.99 26.64 27.43 27.78

45 22.23 24.75 26.49 27.38 27.76

47 21.51 24.44 26.30 27.30 27.72

49 20.60 24.02 26.08 27.21 27.68

51 19.48 23.46 25.81 27.09 27.64

53 18.16 22.74 25.48 26.96 27.58

55 16.65 21.84 25.08 26.79 27.52

57 14.98 20.75 24.59 26.59 27.44

59 13.16 19.46 24.00 26.35 27.35

61 11.27 17.99 23.30 26.05 27.23

63 9.34 16.34 22.46 25.67 27.09

65 7.45 14.57 21.47 25.22 26.91

67 5.67 12.70 20.33 24.66 26.68

69 4.06 10.80 19.02 23.99 26.38

71 2.70 8.93 17.54 23.18 26.02

73 1.61 7.15 15.90 22.23 25.59

75 0.85 5.51 14.11 21.15 25.07

77 0.38 4.04 12.22 19.94 24.47

80 0.10 2.16 9.28 17.94 23.46

38


LWR and polynomial regression, 20-80 ages: Female FST-for-age

39





curve (Figure 12).


10thpercentile 25

thpercentile 50

thpercentile 75

thpercentile 90

thpercentile

29.8470 25.7281 27.4259 5.4189 4.1850


curves to empirical data points, 20-80 ages: Male PT-for-age






40

Table 18. 7-order polynomial model parameters for PT index by age: Male

percentile ß0†

ß1†

ß2†

ß3†

ß4†

ß5†

ß6†

ß7†

10 -95.65381 22.65091 -1.67298 0.06366 -0.00135 0.00002 0.00000 0.00000

25 43.18705 -3.16749 0.25860 -0.01128 0.00028 0.00000 0.00000 0.00000

50 15.69641 2.40317 -0.19904 0.00865 -0.00021 0.00000 0.00000 0.00000

75 1.08673 5.11299 -0.39809 0.01633 -0.00038 0.00001 0.00000 0.00000


Table 19. Selected smoothed percentiles for PT index by age: Male

Midpointages

Percentiles

10th

25th

50th

75th

90th

20 26.68 27.10 27.42 27.76 27.93

23 26.28 27.06 27.38 27.72 27.90

25 25.96 27.03 27.36 27.67 27.87

27 25.70 26.98 27.34 27.64 27.84

29 25.52 26.91 27.33 27.63 27.84

31 25.42 26.82 27.31 27.63 27.84

33 25.35 26.71 27.29 27.63 27.85

35 25.26 26.56 27.26 27.63 27.86

37 25.10 26.39 27.20 27.63 27.86

39 24.81 26.17 27.13 27.61 27.86

41 24.35 25.90 27.02 27.58 27.85

43 23.67 25.56 26.89 27.52 27.82

45 22.76 25.15 26.72 27.45 27.79

47 21.61 24.64 26.51 27.36 27.74

49 20.24 24.04 26.26 27.25 27.69

51 18.66 23.31 25.97 27.13 27.64

53 16.92 22.46 25.63 26.99 27.58

55 15.05 21.48 25.23 26.84 27.53

57 13.13 20.37 24.76 26.68 27.48

59 11.20 19.13 24.21 26.50 27.42

61 9.33 17.77 23.58 26.28 27.35

63 7.57 16.30 22.84 26.03 27.26

65 5.96 14.74 21.98 25.72 27.14

67 4.56 13.13 20.99 25.34 26.98

69 3.37 11.47 19.86 24.86 26.76

71 2.42 9.81 18.58 24.28 26.46

73 1.68 8.18 17.14 23.58 26.08

75 1.14 6.59 15.56 22.74 25.60

77 0.75 5.07 13.85 21.78 25.02

80 0.31 2.93 11.15 20.15 24.00

41


LWR and polynomial regression, 20-80 ages: Male PT-for-age

42





curve (Figure 14).


10thpercentile 25

thpercentile 50

thpercentile 75

thpercentile 90

thpercentile

24.5620 16.1574 4.9026 4.1744 2.6351


curves to empirical data points, 20-80 ages: Female PT-for-age






43

Table 20. 7-order polynomial model parameters for PT index by age: Female

percentile ß0†

ß1†

ß2†

ß3†

ß4†

ß5†

ß6†

ß7†

10 57.24871 -6.12961 0.51202 -0.02361 0.00063 -0.00001 0.00000 0.00000

25 103.22729 -14.38426 1.11065 -0.04545 0.00106 -0.00001 0.00000 0.00000

50 25.35779 0.64680 -0.07044 0.00371 -0.00011 0.00000 0.00000 0.00000

75 12.45629 2.98559 -0.23741 0.00996 -0.00024 0.00000 0.00000 0.00000

90 15.24084 2.43381 -0.19020 0.00784 -0.00018 0.00000 0.00000 0.00000 †Values were rounded off the numbers to five decimal places

Table 21. Selected smoothed percentiles for PT index by age: Female

Midpointages

Percentiles

10th

25th

50th

75th

90th

20 25.56 26.86 27.35 27.71 27.90

23 25.34 26.82 27.32 27.68 27.88

25 25.23 26.83 27.31 27.65 27.86

27 25.14 26.81 27.30 27.63 27.85

29 25.06 26.75 27.30 27.62 27.84

31 24.99 26.65 27.30 27.62 27.84

33 24.92 26.52 27.28 27.62 27.84

35 24.83 26.37 27.25 27.62 27.85

37 24.70 26.20 27.21 27.62 27.85

39 24.51 26.03 27.15 27.61 27.85

41 24.24 25.84 27.06 27.58 27.84

43 23.84 25.63 26.95 27.55 27.83

45 23.30 25.37 26.82 27.50 27.80

47 22.58 25.05 26.64 27.43 27.77

49 21.66 24.63 26.43 27.35 27.74

51 20.53 24.10 26.17 27.25 27.70

53 19.19 23.41 25.86 27.14 27.65

55 17.64 22.55 25.48 27.00 27.60

57 15.90 21.50 25.02 26.83 27.53

59 14.01 20.26 24.46 26.62 27.46

61 12.02 18.83 23.80 26.35 27.36

63 9.98 17.22 23.00 26.03 27.24

65 7.97 15.47 22.07 25.63 27.09

67 6.07 13.61 20.98 25.13 26.89

69 4.34 11.70 19.72 24.53 26.63

71 2.87 9.80 18.29 23.80 26.31

73 1.71 7.95 16.70 22.95 25.92

75 0.88 6.21 14.95 21.96 25.46

77 0.39 4.63 13.07 20.86 24.92

80 0.12 2.55 10.13 19.04 23.99

44


LWR and polynomial regression, 20-80 ages: Female PT-for-age

45

3.3 The calculation of dental health indices using estimated

parameters of 7-order polynomial regression

The example of applying 7-order parameter polynomial model for PT index

calculation is displayed in figure 10. Using a graph, PT index correspond to 10th

percentile of female at 40 year can be figured out range only; it would be in the

range of 24 to 25 (Figure 16-A). With parameters, PT index can be calculated

precisely. The result of calculation was 24.29 in following example with

parameters of 10th percentile curve of female and at age of 40 year (Figure 16-C).

46

Figure 16. Percentile calculation using LMS estimators

(A) PT-for-age percentile chart

(B) Estimated parameters of 7-order polynomial model

(C) Equation for PT index calculation

47

3.4 Estimated values of L, M, and S parameters


In the distribution of ST index of male, the estimated value of L was 1.9328 in

lower percentile group and 7.5957 in upper percentile group at 20 year (Table 22).

The value of L greater than 1 means the distribution is skewed to the left and if

the value of L is less than 1 means the distribution is skewed to right. When the

value of L is equal to 1, the distribution has a bell shape with no skewness. The

skewness was decreased by age and the L value of lower percentile group was

-0.1225 and of upper percentile group was 1.0331 at 80 year. The distribution of

upper percentile group showed higher skewness than lower percentile group. The

S value which is an indicator of variation were 0.1856 in lower percentile group

and 0.3188 in upper percentile group at 20 year. The variation was increased by

age and the S value of lower percentile group was 4.5281 and of upper percentile

group was 3.1818. The estimated values of M which indicates median were similar

between lower percentile groups and upper percentile groups. It implies the

differences between lower percentile groups and upper percentile groups were

caused by shape of distributions rather than median.

48

Table 22 L, M, and S, parameters and selected smoothed percentiles for ST by age:Male

Midpoint Lower percentiles Upper percentiles

ages LL ML SL 10th25th

LU MU SU 50th75th90th

20 1.9328 22.6462 0.1856 16.47 19.62 7.5957 22.6684 0.3188 22.67 25.75 27.30

23 1.8524 22.5839 0.2001 15.95 19.34 7.0626 22.5386 0.3058 22.54 25.60 27.20

25 1.6892 22.6141 0.2151 15.60 19.15 7.0070 22.4865 0.3037 22.49 25.53 27.13

27 1.5482 22.6610 0.2272 15.39 19.02 7.0988 22.4762 0.3042 22.48 25.51 27.09

29 1.4512 22.7065 0.2339 15.32 18.98 7.2792 22.5056 0.3059 22.51 25.53 27.09

31 1.4064 22.7403 0.2348 15.38 19.01 7.4988 22.5639 0.3078 22.56 25.57 27.11

33 1.4228 22.7550 0.2309 15.50 19.08 7.7126 22.6349 0.3091 22.63 25.63 27.14

35 1.5070 22.7450 0.2240 15.61 19.16 7.8785 22.6995 0.3097 22.70 25.68 27.17

37 1.6483 22.7061 0.2170 15.65 19.20 7.9586 22.7374 0.3097 22.74 25.71 27.20

39 1.8038 22.6357 0.2128 15.55 19.17 7.9234 22.7288 0.3098 22.73 25.71 27.20

41 1.9089 22.5318 0.2147 15.25 19.02 7.7578 22.6553 0.3108 22.66 25.66 27.17

43 1.9149 22.3887 0.2249 14.72 18.72 7.4647 22.5008 0.3144 22.50 25.55 27.10

45 1.8178 22.1960 0.2449 13.94 18.24 7.0642 22.2523 0.3220 22.25 25.38 26.99

47 1.6506 21.9389 0.2754 12.92 17.57 6.5884 21.9001 0.3354 21.90 25.15 26.85

49 1.4551 21.6018 0.3171 11.68 16.72 6.0720 21.4382 0.3562 21.44 24.86 26.68

51 1.2635 21.1700 0.3700 10.27 15.69 5.5458 20.8638 0.3858 20.86 24.51 26.47

53 1.0937 20.6312 0.4345 8.74 14.49 5.0320 20.1777 0.4258 20.18 24.10 26.23

55 0.9524 19.9759 0.5106 7.17 13.16 4.5442 19.3833 0.4773 19.38 23.64 25.97

57 0.8403 19.1972 0.5980 5.62 11.73 4.0890 18.4862 0.5415 18.49 23.11 25.68

59 0.7565 18.2899 0.6958 4.15 10.24 3.6687 17.4939 0.6190 17.49 22.53 25.37

61 0.7034 17.2432 0.8002 2.80 8.75 3.2827 16.4153 0.7102 16.42 21.89 25.02

63 0.6737 15.9479 0.9025 1.69 7.29 2.9290 15.2600 0.8151 15.26 21.17 24.62

65 0.5725 14.5581 1.0619 1.04 5.79 2.6051 14.0376 0.9333 14.04 20.38 24.16

67 0.4981 13.0510 1.2206 0.63 4.52 2.3087 12.7576 1.0644 12.76 19.48 23.63

69 0.4356 11.8573 1.3958 0.37 3.53 2.0380 11.4280 1.2094 11.43 18.48 23.00

71 0.3586 10.8668 1.6954 0.16 2.49 1.7922 10.0555 1.3720 10.06 17.35 22.25

73 0.3358 9.2108 1.8106 0.10 1.91 1.5717 8.6447 1.5624 8.64 16.10 21.37

75 0.2924 7.0794 2.0792 0.04 1.16 1.3783 7.1995 1.8038 7.20 14.71 20.35

77 0.2672 5.7474 2.2751 0.02 0.80 1.2147 5.7250 2.1476 5.72 13.20 19.18

80 -0.1225 4.6875 4.5281 0.06 0.35 1.0331 3.4823 3.1818 3.48 10.79 17.22

49


In the distribution of ST index of female, the estimated value of L was 1.5823

in lower percentile group and 3.6830 in upper percentile group at 20 year (Table

23). The skewness was decreased by age and the L value of lower percentile

group was -13.2642 and of upper percentile group was 1.0200 at 80 year. The S

value which is an indicator of variation were 0.1843 in lower percentile group and

0.2815 in upper percentile group at 20 year. The variation was increased by age

and the S value of lower percentile group was 118.8847 and of upper percentile

group was 4.6253 at 80 years. The estimated values of M which indicates median

were similar between lower percentile groups and upper percentile groups.

50

Table 23. L, M, and S, parameters and selected smoothed percentiles for ST by age:Female




20 1.5823 20.9465 0.1843 15.58 18.24 3.6830 20.9560 0.2815 20.96 24.20 26.36

23 1.5529 20.7431 0.1988 15.00 17.85 3.2996 20.6309 0.2866 20.63 23.96 26.24

25 1.5237 20.7041 0.2089 14.68 17.67 3.1992 20.5119 0.2902 20.51 23.88 26.21

27 1.4750 20.7010 0.2173 14.46 17.55 3.2202 20.4524 0.2959 20.45 23.86 26.20

29 1.4184 20.7108 0.2232 14.35 17.48 3.3395 20.4356 0.3043 20.44 23.89 26.23

31 1.3669 20.7184 0.2266 14.31 17.45 3.5238 20.4445 0.3149 20.44 23.96 26.28

33 1.3347 20.7137 0.2280 14.30 17.44 3.7343 20.4627 0.3271 20.46 24.04 26.33

35 1.3355 20.6895 0.2284 14.27 17.41 3.9319 20.4744 0.3396 20.47 24.11 26.39

37 1.3756 20.6400 0.2290 14.17 17.35 4.0824 20.4649 0.3516 20.46 24.16 26.43

39 1.4443 20.5604 0.2314 13.96 17.23 4.1607 20.4206 0.3621 20.42 24.17 26.44

41 1.5136 20.4463 0.2374 13.60 17.02 4.1544 20.3286 0.3711 20.33 24.13 26.43

43 1.5519 20.2925 0.2487 13.07 16.71 4.0636 20.1775 0.3790 20.18 24.04 26.38

45 1.5405 20.0914 0.2666 12.37 16.28 3.9004 19.9570 0.3868 19.96 23.89 26.30

47 1.4802 19.8328 0.2919 11.50 15.71 3.6858 19.6585 0.3963 19.66 23.68 26.17

49 1.3846 19.5048 0.3254 10.47 15.02 3.4449 19.2746 0.4092 19.27 23.40 26.01

51 1.2707 19.0949 0.3672 9.32 14.18 3.2014 18.7995 0.4276 18.80 23.06 25.80

53 1.1523 18.5914 0.4179 8.08 13.22 2.9740 18.2288 0.4538 18.23 22.66 25.55

55 1.0387 17.9843 0.4778 6.80 12.15 2.7729 17.5597 0.4898 17.56 22.20 25.26

57 0.9350 17.2665 0.5473 5.52 10.98 2.6001 16.7904 0.5383 16.79 21.68 24.93

59 0.8435 16.4334 0.6271 4.29 9.74 2.4508 15.9209 0.6018 15.92 21.10 24.55

61 0.7655 15.4833 0.7177 3.16 8.46 2.3165 14.9528 0.6833 14.95 20.46 24.12

63 0.7030 14.4145 0.8186 2.15 7.17 2.1876 13.8899 0.7857 13.89 19.75 23.65

65 0.6518 13.2353 0.9328 1.30 5.89 2.0561 12.7380 0.9122 12.74 18.96 23.11

67 0.5616 11.9942 1.0826 0.81 4.69 1.9172 11.5055 1.0666 11.51 18.08 22.51

69 0.4699 10.7743 1.2938 0.43 3.50 1.7696 10.2029 1.2537 10.20 17.11 21.83

71 0.4065 9.2882 1.4956 0.23 2.54 1.6157 8.8430 1.4824 8.84 16.03 21.08

73 0.3133 8.2267 1.9403 0.07 1.53 1.4607 7.4401 1.7703 7.44 14.85 20.24

75 0.2880 6.5625 2.1108 0.03 1.05 1.3118 6.0106 2.1558 6.01 13.56 19.31

77 0.2385 5.2842 2.5493 0.01 0.58 1.1772 4.5737 2.7296 4.57 12.18 18.31

80 -13.2642 0.9395 118.8847 0.53 0.56 1.0200 2.4597 4.6253 2.46 10.00 16.68

51


In the distribution of FST index of male, the estimated value of L was 2.5892

in lower percentile group and 48.2937, which was markedly high, in upper

percentile group at 20 year (Table 24). The skewness was decreased by age and

the L value of lower percentile group was 0.4010 and of upper percentile group

was 2.3005 at 80 year. The S value which is an indicator of variation were 0.0965

in lower percentile group and 0.0551 in upper percentile group at 20 year. The

variation was increased by age and the S value of lower percentile group was

1.5160 and of upper percentile group was 2.5290 at 80 year. The estimated values

of M which indicates median were similar between lower percentile groups and

upper percentile groups.

52

Table 24. L, M, and S, parameters and selected smoothed percentiles for FST by age:Male




20 2.5892 27.2364 0.0965 23.47 25.36 48.2937 27.0224 0.0551 27.02 27.60 27.87

23 3.9063 27.1832 0.0883 23.41 25.40 40.5217 27.0093 0.0448 27.01 27.55 27.82

25 4.4253 27.1871 0.0864 23.35 25.41 32.6013 27.0083 0.0363 27.01 27.50 27.78

27 4.7146 27.1875 0.0850 23.33 25.43 27.1358 27.0067 0.0317 27.01 27.47 27.76

29 4.9342 27.1665 0.0828 23.37 25.45 26.1654 27.0013 0.0311 27.00 27.46 27.75

31 5.1929 27.1178 0.0795 23.46 25.47 29.5425 26.9874 0.0341 26.99 27.47 27.76

33 5.5666 27.0423 0.0754 23.54 25.47 35.4131 26.9580 0.0413 26.96 27.49 27.77

35 6.0952 26.9447 0.0711 23.59 25.46 41.0135 26.9078 0.0527 26.91 27.50 27.79

37 6.7087 26.8319 0.0679 23.54 25.40 44.1454 26.8341 0.0674 26.83 27.51 27.81

39 7.1536 26.7128 0.0672 23.37 25.29 44.2238 26.7360 0.0829 26.74 27.50 27.81

41 7.1268 26.5948 0.0704 23.02 25.10 41.8385 26.6120 0.0967 26.61 27.46 27.80

43 6.5610 26.4802 0.0785 22.46 24.81 37.8942 26.4599 0.1075 26.46 27.40 27.77

45 5.6606 26.3649 0.0924 21.67 24.41 33.2145 26.2767 0.1157 26.28 27.31 27.72

47 4.6870 26.2401 0.1123 20.65 23.90 28.4656 26.0583 0.1230 26.06 27.19 27.66

49 3.8060 26.0938 0.1387 19.40 23.24 24.1313 25.7988 0.1320 25.80 27.05 27.60

51 3.0780 25.9117 0.1717 17.95 22.46 20.4753 25.4909 0.1452 25.49 26.90 27.52

53 2.5027 25.6775 0.2114 16.33 21.53 17.5397 25.1258 0.1651 25.13 26.73 27.45

55 2.0569 25.3736 0.2579 14.58 20.46 15.2122 24.6930 0.1944 24.69 26.54 27.37

57 1.7131 24.9814 0.3112 12.77 19.26 13.3222 24.1807 0.2356 24.18 26.33 27.29

59 1.4475 24.4819 0.3710 10.94 17.94 11.7172 23.5754 0.2913 23.58 26.11 27.21

61 1.7059 23.4029 0.3765 8.48 16.78 10.2946 22.8629 0.3643 22.86 25.84 27.12

63 1.4518 22.6269 0.4440 6.78 15.27 9.0018 22.0284 0.4565 22.03 25.53 27.01

65 1.2479 21.7064 0.5190 5.25 13.70 7.8190 21.0578 0.5697 21.06 25.15 26.86

67 1.0835 20.6261 0.6011 3.92 12.09 6.7430 19.9387 0.7051 19.94 24.67 26.66

69 0.9497 19.3734 0.6903 2.81 10.48 5.7744 18.6618 0.8639 18.66 24.09 26.39

71 0.7256 18.1727 0.8378 2.27 8.78 4.9136 17.2229 1.0485 17.22 23.36 26.03

73 0.6467 16.4611 0.9400 1.59 7.28 4.1587 15.6251 1.2639 15.63 22.49 25.55

75 0.5775 14.6338 1.0528 1.07 5.87 3.5065 13.8812 1.5203 13.88 21.44 24.97

77 0.5051 12.7719 1.2037 0.64 4.49 2.9532 12.0169 1.8384 12.02 20.24 24.26

80 0.4010 9.7455 1.5160 0.23 2.61 2.3005 9.0911 2.5290 9.09 18.18 23.00

53

3.4.4 functioning teeth, female

In the distribution of FST index of female, the estimated value of L was 1.1856

in lower percentile group and 42.7462, which was markedly high, in upper

percentile group at 20 year (Table 25). The skewness was decreased by age and

the L value of lower percentile group was 0.3444 and of upper percentile group

was 1.9556 at 80 year. The S value which is an indicator of variation were 0.1100

in lower percentile group and 0.0498 in upper percentile group at 20 year. The

variation was increased by age and the S value of lower percentile group was

1.7651 and of upper percentile group was 2.1702 at 80 year. The estimated values

of M which indicates median were similar between lower percentile groups and

upper percentile groups.

54

Table 25. L, M, and S, parameters and selected smoothed percentiles for FST by age:Female




20 1.1856 27.1856 0.1100 23.30 25.15 42.7462 26.9885 0.0498 26.99 27.56 27.83

23 2.0331 27.1350 0.1003 23.38 25.23 38.7906 26.9850 0.0445 26.99 27.53 27.81

25 2.9698 27.1323 0.0921 23.46 25.33 34.7810 27.0036 0.0384 27.00 27.51 27.79

27 3.5541 27.1480 0.0870 23.55 25.42 31.6503 27.0239 0.0341 27.02 27.50 27.78

29 3.7231 27.1642 0.0848 23.63 25.47 30.4199 27.0381 0.0323 27.04 27.49 27.77

31 3.5696 27.1679 0.0845 23.69 25.49 31.3940 27.0406 0.0329 27.04 27.50 27.78

33 3.2637 27.1522 0.0852 23.72 25.48 34.1242 27.0267 0.0360 27.03 27.51 27.79

35 3.0488 27.1123 0.0859 23.71 25.44 37.5224 26.9927 0.0417 26.99 27.52 27.80

37 3.1812 27.0441 0.0857 23.63 25.37 40.2754 26.9365 0.0499 26.94 27.52 27.80

39 3.7633 26.9466 0.0842 23.46 25.28 41.4580 26.8573 0.0600 26.86 27.50 27.80

41 4.5905 26.8261 0.0827 23.20 25.15 40.8582 26.7548 0.0714 26.75 27.48 27.79

43 5.2532 26.6931 0.0834 22.82 24.97 38.7932 26.6277 0.0832 26.63 27.43 27.78

45 5.4647 26.5532 0.0878 22.30 24.72 35.7632 26.4730 0.0955 26.47 27.37 27.75

47 5.2216 26.4023 0.0969 21.61 24.37 32.2321 26.2859 0.1088 26.29 27.29 27.71

49 4.6853 26.2287 0.1112 20.73 23.91 28.5520 26.0596 0.1239 26.06 27.20 27.67

51 4.0281 26.0176 0.1312 19.65 23.32 24.9568 25.7853 0.1423 25.79 27.08 27.62

53 3.3681 25.7533 0.1577 18.35 22.58 21.5822 25.4518 0.1654 25.45 26.94 27.56

55 2.7671 25.4209 0.1916 16.85 21.66 18.4948 25.0463 0.1946 25.05 26.77 27.49

57 2.2490 25.0067 0.2342 15.17 20.57 15.7195 24.5540 0.2315 24.55 26.57 27.42

59 1.8169 24.4984 0.2871 13.34 19.30 13.2593 23.9589 0.2773 23.96 26.32 27.32

61 1.4649 23.8837 0.3517 11.43 17.84 11.1066 23.2446 0.3334 23.24 26.02 27.21

63 1.1840 23.1485 0.4298 9.49 16.23 9.2471 22.3949 0.4009 22.39 25.64 27.06

65 0.9652 22.2743 0.5224 7.59 14.48 7.6611 21.3949 0.4813 21.39 25.18 26.87

67 0.8007 21.2355 0.6294 5.81 12.64 6.3252 20.2322 0.5765 20.23 24.62 26.62

69 0.6840 19.9981 0.7483 4.20 10.77 5.2130 18.8984 0.6898 18.90 23.93 26.31

71 0.6110 18.5210 0.8736 2.81 8.92 4.2978 17.3909 0.8263 17.39 23.11 25.91

73 0.5957 16.7270 0.9854 1.61 7.18 3.5530 15.7151 0.9949 15.72 22.15 25.43

75 0.5329 14.7788 1.1408 0.87 5.49 2.9543 13.8865 1.2103 13.89 21.04 24.85

77 0.4992 12.3416 1.2178 0.60 4.29 2.4792 11.9350 1.4978 11.94 19.79 24.18

80 0.3444 9.3829 1.7651 0.12 2.03 1.9556 8.8869 2.1702 8.89 17.74 23.03

55


In the distribution of PT index of male, the estimated value of L was 64.3250 in

lower percentile group and 81.7860 in upper percentile group at 20 year (Table 25).

The skewness was decreased by age and the L value of lower percentile group

was 0.4016 and of upper percentile group was 2.8438 at 80 year. The S value

which is an indicator of variation were 0.0094 in lower percentile group and 0.0316

in upper percentile group at 20 year. The variation was increased by age and the

S value of lower percentile group was 1.5137 and of upper percentile group was

2.3293 at 80 year. The estimated values of M which indicates median were similar

between lower percentile groups and upper percentile groups.

56

Table 26. L, M, and S, parameters and selected smoothed percentiles for PT by age:Male




20 64.3250 27.3292 0.0094 26.71 27.11 81.7860 27.4230 0.0316 27.42 27.76 27.92

23 35.5069 27.3992 0.0165 26.35 27.01 63.7383 27.3775 0.0274 27.38 27.71 27.89

25 93.3446 27.3338 0.0104 26.09 27.03 49.3795 27.3467 0.0237 27.35 27.67 27.86

27 19.4485 27.5137 0.0283 25.84 26.87 39.8744 27.3229 0.0217 27.32 27.64 27.84

29 16.4145 27.5234 0.0324 25.67 26.79 36.1142 27.3067 0.0212 27.31 27.62 27.83

31 14.5850 27.4952 0.0351 25.55 26.71 37.2777 27.2938 0.0223 27.29 27.62 27.83

33 13.3434 27.4344 0.0370 25.45 26.61 41.6238 27.2773 0.0250 27.28 27.63 27.84

35 12.4071 27.3485 0.0387 25.32 26.50 46.8352 27.2487 0.0294 27.25 27.63 27.85

37 11.6501 27.2446 0.0410 25.12 26.35 50.5811 27.2007 0.0355 27.20 27.63 27.85

39 10.8695 27.1293 0.0447 24.80 26.16 51.3497 27.1272 0.0430 27.13 27.61 27.85

41 9.7763 27.0099 0.0511 24.33 25.90 48.9759 27.0240 0.0516 27.02 27.58 27.83

43 8.3344 26.8920 0.0614 23.66 25.56 44.3920 26.8875 0.0608 26.89 27.52 27.81

45 6.7951 26.7766 0.0764 22.79 25.13 38.8769 26.7147 0.0709 26.71 27.45 27.77

47 5.4053 26.6587 0.0968 21.70 24.59 33.4451 26.5026 0.0828 26.50 27.35 27.73

49 4.2701 26.5290 0.1232 20.40 23.94 28.6407 26.2479 0.0977 26.25 27.24 27.68

51 3.3893 26.3749 0.1557 18.91 23.16 24.6181 25.9468 0.1171 25.95 27.11 27.63

53 2.7204 26.1812 0.1946 17.25 22.26 21.3109 25.5944 0.1426 25.59 26.97 27.57

55 2.2149 25.9304 0.2401 15.47 21.22 18.5716 25.1841 0.1761 25.18 26.81 27.52

57 1.8312 25.6040 0.2921 13.61 20.05 16.2526 24.7074 0.2196 24.71 26.64 27.46

59 2.1419 24.7601 0.2991 11.09 19.01 14.2386 24.1538 0.2753 24.15 26.45 27.40

61 1.7991 24.1937 0.3576 9.20 17.63 12.4529 23.5107 0.3453 23.51 26.23 27.33

63 1.5251 23.5091 0.4236 7.42 16.15 10.8498 22.7642 0.4316 22.76 25.96 27.24

65 1.3048 22.6897 0.4973 5.79 14.60 9.4047 21.8995 0.5358 21.90 25.64 27.12

67 1.1262 21.7203 0.5790 4.37 12.98 8.1054 20.9024 0.6596 20.90 25.24 26.95

69 0.9796 20.5883 0.6691 3.17 11.35 6.9454 19.7606 0.8048 19.76 24.75 26.74

71 0.7445 19.5305 0.8165 2.57 9.61 5.9205 18.4655 0.9745 18.47 24.14 26.45

73 0.6575 17.9608 0.9246 1.81 8.05 5.0266 17.0149 1.1741 17.01 23.42 26.08

75 0.5819 16.2740 1.0448 1.21 6.57 4.2583 15.4157 1.4136 15.42 22.56 25.63

77 0.5070 14.5454 1.1991 0.74 5.14 3.6094 13.6877 1.7102 13.69 21.57 25.09

80 0.4016 11.7319 1.5137 0.27 3.15 2.8438 10.9420 2.3293 10.94 19.89 24.14

57


In the distribution of PT index of female, the estimated value of L was 16.1214

in lower percentile group and 64.7654 in upper percentile group at 20 year (Table

25). The skewness was decreased by age and the L value of lower percentile

group was 0.3532 and of upper percentile group was 2.3147 at 80 year. The S

value which is an indicator of variation were 0.0310 in lower percentile group and

0.0311 in upper percentile group at 20 year. The variation was increased by age

and the S value of lower percentile group was 1.7215 and of upper percentile

group was 2.2342 at 80 year. The estimated values of M which indicates median

were similar between lower percentile groups and upper percentile groups.

58

Table 27. L, M, and S, parameters and selected smoothed percentiles for PT by age:Female




20 16.1214 27.4432 0.0310 25.75 26.75 64.7654 27.3503 0.0311 27.35 27.71 27.89

23 14.7140 27.4803 0.0352 25.52 26.69 54.9857 27.3107 0.0291 27.31 27.68 27.87

25 71.4223 27.3060 0.0148 25.42 26.83 47.5530 27.2958 0.0263 27.30 27.65 27.85

27 13.3135 27.5664 0.0398 25.31 26.67 42.2512 27.2878 0.0243 27.29 27.63 27.84

29 12.2268 27.5790 0.0425 25.21 26.62 39.4827 27.2837 0.0234 27.28 27.62 27.83

31 10.8988 27.5652 0.0456 25.12 26.55 39.0783 27.2790 0.0236 27.28 27.62 27.83

33 9.3346 27.5293 0.0494 25.02 26.45 40.5914 27.2682 0.0251 27.27 27.62 27.83

35 7.6936 27.4758 0.0538 24.91 26.33 43.2503 27.2457 0.0279 27.25 27.62 27.84

37 6.3823 27.4041 0.0583 24.76 26.19 45.9543 27.2061 0.0322 27.21 27.62 27.84

39 5.8487 27.3089 0.0618 24.55 26.03 47.5505 27.1456 0.0383 27.15 27.61 27.84

41 6.1192 27.1873 0.0641 24.26 25.86 47.3349 27.0611 0.0459 27.06 27.58 27.83

43 6.6403 27.0459 0.0665 23.85 25.64 45.2986 26.9497 0.0552 26.95 27.54 27.82

45 6.7897 26.8946 0.0714 23.31 25.37 41.9288 26.8081 0.0661 26.81 27.49 27.79

47 6.3936 26.7358 0.0802 22.61 25.02 37.8371 26.6319 0.0791 26.63 27.42 27.76

49 5.6347 26.5616 0.0939 21.72 24.56 33.5198 26.4157 0.0951 26.42 27.34 27.73

51 4.7503 26.3589 0.1131 20.62 23.98 29.2950 26.1520 0.1151 26.15 27.23 27.69

53 3.8973 26.1127 0.1387 19.29 23.25 25.3329 25.8321 0.1402 25.83 27.11 27.64

55 3.1481 25.8081 0.1715 17.75 22.35 21.7108 25.4448 0.1717 25.44 26.96 27.59

57 2.5224 25.4307 0.2129 16.02 21.28 18.4560 24.9774 0.2110 24.98 26.78 27.52

59 2.0149 24.9667 0.2643 14.13 20.02 15.5712 24.4153 0.2592 24.42 26.57 27.44

61 1.6109 24.4019 0.3271 12.14 18.58 13.0471 23.7427 0.3177 23.74 26.30 27.34

63 1.2945 23.7200 0.4028 10.12 16.97 10.8663 22.9433 0.3877 22.94 25.97 27.22

65 1.0515 22.9002 0.4922 8.13 15.22 9.0059 22.0013 0.4707 22.00 25.56 27.05

67 0.8700 21.9154 0.5952 6.27 13.37 7.4383 20.9022 0.5691 20.90 25.06 26.84

69 0.7410 20.7320 0.7095 4.57 11.48 6.1334 19.6350 0.6863 19.64 24.45 26.57

71 0.6590 19.3104 0.8300 3.09 9.60 5.0602 18.1935 0.8283 18.19 23.72 26.23

73 0.6549 17.5311 0.9283 1.75 7.83 4.1877 16.5789 1.0047 16.58 22.86 25.82

75 0.5677 15.5342 1.0710 1.09 6.13 3.4867 14.8032 1.2312 14.80 21.86 25.32

77 0.4803 13.6634 1.2657 0.59 4.55 2.9302 12.8924 1.5337 12.89 20.75 24.75

80 0.3532 10.6612 1.7215 0.15 2.39 2.3147 9.8788 2.2342 9.88 18.90 23.76

59

The graphical comparison between curves produced by LMS method and

empirical percentile curves are shown in Figure 17-22.

Figure 17. Comparison of smoothed 5th, 25th, 50th, 75th, 95th percentile curves

drawn from L, M, and S parameters to empirical data points, 20-80 ages: Male

ST-for-age


drawn from L, M, and S parameters to empirical data points, 20-80 ages: Female

ST-for-age

60

Figure 19. 1omparison of smoothed 5th, 25th, 50th, 75th, 95th percentile curves


FST-for-age


drawn from L, M, and S parameters to empirical data points, 20-80 ages:

Female FST-for-age

61

Figure 21 Comparison of smoothed 5th, 25th, 50th, 75th, 95th percentile curves


PT-for-age


drawn from L, M, and S parameters to empirical data points, 20-80 ages:

Female PT-for-age

62

3.5 Calculation of percentile using L, M, and S parameters

The example of applying L, M, and S parameters for percentile calculation

assuming 45 aged women is displayed in figure 23. Using a graph, percentile can

be figured out only in range; it would be in the range of 10th to 25th (Figure

23-A). With L, M, and S parameters, the percentile can be calculated precisely.

The result of calculation was —1.111 of z-score in following example and

corresponding percentile was 13.65th (Figure 23-C).

63

Figure 23. Percentile calculation using LMS estimators

(A) PT-for-age percentile chart

(B) Estimated LMS values

(C) Equation for percentile calculation

64

3.6 Comparison between the DMF indices and dental health

indices.

The frequency distribution of oral health related factors in subjects are

presented in Table 28-29. The family income was divided into four categories

using monthly average family equivalent income which is adjusted for the

numbers of family.

Table 28. Frequency distribution of oral health related factors: Male

VariablesAge groups

20-29 years 30-39 years 40-49 years 50-59 years 60-69 years 70-79 years

Family income

Low 168 (12.62) 147 (6.77) 188 (8.32) 235 (11.18) 586 (26.90) 824 (56.76)

Mid-low 356 (25.76) 598 (25.87) 529 (24.76) 497 (23.83) 668 (32.56) 348 (22.64)

Mid-upper 431 (31.08) 848 (36.13) 809 (33.33) 609 (27.83) 456 (21.76) 164 (10.81)

Upper 441 (30.54) 744 (31.23) 852 (33.59) 812 (37.16) 367 (18.78) 127 (9.79)

Level of education

Under elementaryschool graduate 3 (0.16) 18 (0.78) 118 (5.42) 463 (21.71) 791 (37.35) 793 (53.36)

Middle schoolgraduate 23 (1.94) 57 (2.73) 223 (9.64) 470 (22.10) 480 (24.14) 232 (16.35)

High school graduate 881 (64.69) 886 (39.20) 974 (42.37) 708 (32.95) 550 (25.80) 266 (17.12)

University andpost-graduate

503 (33.20) 1,376 (57.29) 1,076 (42.58) 530 (23.24) 282 (12.71) 186 (13.16)

Area of residence

Urban 1,236 (87.63) 2,009 (85.41) 1,927 (79.92) 1,624 (76.92) 1,406 (73.04) 872 (64.89)

Rural 187 (12.37) 354 (14.59) 491 (20.08) 573 (23.08) 716 (26.96) 633 (35.11)

Perception ofdental health

Very poor 63 (4.44) 158 (6.76) 207 (8.70) 286 (13.28) 220 (10.12) 150 (10.70)

Poor 497 (35.22) 846 (36.83) 952 (39.75) 855 (38.54) 932 (45.97) 671 (44.20)

Fair 652 (46.59) 1036 (43.26) 931 (38.42) 740 (34.44) 653 (29.53) 470 (30.44)

Good 185 (12.20) 290 (12.22) 296 (11.96) 268 (11.91) 285 (13.39) 196 (13.84)

Very good 21 (1.56) 22 (0.92) 25 (1.17) 41 (1.83) 24 (0.99) 15 (0.82)

Dental examinationwithin 1 year

No 1,082 (76.42) 1,591 (67.78) 1,623 (68.51) 1,575 (71.55) 1,554 (72.86) 1,202 (79.11)

Yes 335 (23.58) 760 (32.22) 787 (31.49) 613 (28.45) 555 (27.14) 296 (20.89)

Values are unweighted n and weighted (%)

65

Table 29. Frequency distribution of oral health related factors: Female

VariablesAge groups

20-29 years 30-39 years 40-49 years 50-59 years 60-69 years 70-79 years

Family income

Low 168 (9.78) 194 (6.68) 269 (9.19) 439 (14.16) 1,084 (40.90) 1,208 (59.68)

Mid-low 479 (26.10) 850 (26.72) 717 (25.87) 795 (28.09) 784 (30.87) 379 (19.10)

Mid-upper 598 (31.60) 1,243 (37.42) 960 (30.22) 788 (27.60) 414 (16.09) 210 (11.51)

Upper 654 (32.53) 1,022 (29.18) 1,103 (34.72) 907 (30.15) 307 (12.14) 172 (9.70)

Level of education

Under elementaryschool graduate

12 (0.61) 29 (1.09) 255 (8.59) 1,172 (39.17) 1,933 (72.77) 1,797 (89.72)

Middle schoolgraduate

35 (1.88) 83 (2.75) 435 (14.90) 698 (24.22) 319 (12.53) 97 (5.16)

High school graduate 858 (46.90) 1,529 (46.56) 1,546 (50.12) 815 (27.80) 292 (11.50) 87 (4.09)

University andpost-graduate 1,006 (50.61) 1,697 (49.60) 845 (26.39) 273 (8.81) 87 (3.21) 21 (1.02)

Area of residence

Urban 1,677 (88.10) 2,881 (86.33) 2,511 (82.23) 2,234 (78.33) 1,795 (73.24) 1,170 (65.15)

Rural 251 (11.90) 471 (13.67) 591 (17.77) 745 (21.67) 865 (26.76) 871 (34.85)

Perception ofdental health

Very poor 98 (5.40) 181 (5.26) 199 (7.05) 272 (8.71) 224 (8.70) 158 (7.41)

Poor 677 (36.19) 1,266 (37.88) 1,186 (38.32) 1,270 (43.96) 1,228 (46.28) 940 (47.30)

Fair 925 (47.08) 1,590 (47.73) 1,347 (42.46) 1,096 (35.43) 892 (32.86) 666 (32.00)

Good 204 (10.66) 289 (8.59) 333 (11.33) 295 (10.42) 292 (11.43) 253 (12.57)

Very good 15 (0.67) 16 (0.52) 25 (0.84) 37 (1.49) 20 (0.73) 14 (0.72)

Dental examinationwithin 1 year

No 1,327 (69.53) 2,358 (71.48) 2,112 (68.56) 2,188 (73.78) 2,087 (78.72) 1,711 (83.53)

Yes 590 (30.47) 981 (28.52) 979 (31.44) 776 (26.22) 566 (21.28) 310 (16.47)

Values are unweighted n and weighted (%)

It showed that the variance in percentile of FST index was explained a greater

proportion than the variance in other indices in male. The explained proportion of

the variance in DMFT index was decreased by age. The percentage of the

explained variance in 50's were highest and it was 7% for the DMFT index, 14%

for the ST index, 26% for the FST index and 23% for the PT index (Table 30).

66

Table 30. Beta coefficients and their significance levels of oral health related factorsand R square with DMFT index, ST index percentile, FST index percentile and PTindex percentile as dependent variables: Male

Explanatory variablesDMFT index ST index

percentileFST indexpercentile

PT indexpercentile

β R2

β R2

β R2

β R2

20-29 years

Age -0.14 *

0.10

-

0.10

-

0.15

-

0.04

Family income 0.38 ** -1.89 * 0.61 -1.11Level of education 0.31 1.24 9.04 *** 5.13 **Area of residence -0.99 ** 6.71 ** -3.95 1.95Perception of dental health -1.54 *** 10.88 *** 16.14 *** 7.46 ***Dental examination within 1 yr 0.56 ** -4.22 * 3.57 -2.35

30-39 yearss

Age -0.11 ***

0.10

-

0.12

-

0.16

-

0.10

Family income 0.02 0.08 2.01 * 2.35 **Level of education 0.63 *** -4.23 *** 4.57 ** 2.58Area of residence -0.26 1.00 0.41 -2.07Perception of dental health -1.29 *** 11.56 *** 16.04 *** 12.12 ***Dental examination within 1 yr 0.85 *** -7.83 *** 0.76 -4.82 **

40-49 years

Age -0.05

0.09

-

0.14

-

0.21

-

0.17

Family income 0.06 -0.62 2.12 * 0.84Level of education 0.24 ** -2.05 * 2.10 * 2.39 **Area of residence 0.19 -2.68 -5.05 ** -4.06 *Perception of dental health -1.17 *** 12.48 *** 16.61 *** 15.78 ***Dental examination within 1 yr 0.40 ** -4.26 ** -0.85 -2.49

50-59 years

Age 0.20 ***

0.07

-

0.14

-

0.26

-

0.23

Family income 0.02 -0.65 1.11 0.67Level of education 0.18 0.32 3.50 *** 3.26 ***Area of residence 0.19 -2.97 -4.30 * -4.53 **Perception of dental health -1.01 *** 11.72 *** 15.25 *** 14.62 ***Dental examination within 1 yr 0.34 -1.68 3.37 * 2.01

60-69 years

Age 0.21 ***

0.06

-

0.10

-

0.16

-

0.14

Family income -0.01 0.63 1.13 1.07Level of education -0.42 ** 1.46 3.14 *** 2.68 ***Area of residence 1.01 ** -1.04 -2.71 -2.10Perception of dental health 0.97 *** 10.28 *** 11.93 *** 11.47 ***Dental examination within 1 yr -0.42 -0.65 1.91 0.66

70-79 years

Age 0.27 ***

0.05

-

0.06

-

0.09

-

0.08

Family income 0.03 3.01 ** 3.96 *** 3.58 ***Level of education -0.37 1.43 1.80 * 1.41Area of residence 1.46 ** -3.32 -4.08 * -3.31Perception of dental health 1.08 *** 6.25 *** 6.92 *** 6.50 ***Dental examination within 1 yr -0.26 2.36 5.98 ** 5.93 **

β: Beta coefficients; R2: R square; Significance level: *P < 0.05, **P < 0.01, ***P<0.001

67

The variables explained highest proportion of the percentile of DMFT index

variance in women in 20's and of ST index variance in 30's. From 40 to 80

years, the proportion of the explained variance in percentile of FST index was

greater than any other indices. The proportion of the explained variance of DMFT

were decreased by age. The proportion of the explained variance in 50's were

highest and it was 8% for the DMFT index, 13% for the ST index, 22% for the

FST index and 19% for the PT index (Table 31).

68

Table 31. Beta coefficients and their significance levels of oral health related factorsand R square with DMFT index, ST index percentile, FST index percentile and PTindex percentile as dependent variables: Female

Explanatory variablesDMFT index

ST indexpercentile

FST indexpercentile

PT indexpercentile

β R2

β R2

β R2

β R2

20-29 years

Age -0.02

0.10

-

0.10

-

0.09

-

0.03

Family income 0.11 -0.74 2.19 * 1.53Level of education 0.92 *** -5.62 *** 6.34 *** 1.78Area of residence -0.37 4.33 0.55 0.26Perception of dental health -1.41 *** 9.71 *** 12.08 *** 6.14 ***Dental examination within 1 yr 0.95 *** -8.72 *** -3.46 -8.02 ***

30-39 years

Age -0.11 ***

0.07

-

0.08

-

0.07

-

0.04

Family income 0.00a 0.22 2.06 * 1.72 *Level of education 0.60 *** -5.27 *** 3.49 ** 0.98Area of residence -0.01 0.05 -2.84 -2.00Perception of dental health -1.14 *** 9.34 *** 11.18 *** 8.41 ***Dental examination within 1 yr 0.82 *** -7.06 *** -0.37 -4.29 **

40-49 years

Age 0.04

0.08

-

0.13

-

0.17

-

0.14

Family income 0.04 0.06 2.19 ** 1.29Level of education 0.16 -0.16 3.92 *** 3.94 ***Area of residence -0.19 2.32 -4.25 * -1.91Perception of dental health -1.25 *** 12.07 *** 15.08 *** 14.29 ***Dental examination within 1 yr 0.71 *** -5.60 *** -0.81 -2.63

50-59 years

Age 0.11 **

0.08

-

0.13

-

0.22

-

0.19

Family income 0.14 -0.36 1.18 0.70Level of education 0.06 1.13 4.82 *** 5.04 ***Area of residence 0.21 -1.33 -7.31 *** -6.78 ***Perception of dental health -1.54 *** 12.02 *** 14.83 *** 14.29 ***Dental examination within 1 yr 0.10 -1.36 1.15 -0.22

60-69 years

Age 0.10 *

0.05

-

0.10

-

0.14

-

0.12

Family income -0.07 0.26 2.03 ** 1.89 **Level of education -0.09 2.13 ** 4.89 *** 4.48 ***Area of residence 1.59 *** -6.01 *** -7.47 *** -6.86 ***Perception of dental health -1.22 *** 9.93 *** 10.66 *** 10.12 ***Dental examination within 1 yr 0.03 -2.69 -1.25 -1.94

70-79 years

Age 0.29 ***

0.05

-

0.06

-

0.09

-

0.08

Family income -0.37 1.50 2.07 * 2.19 **Level of education -0.35 5.70 *** 7.63 *** 7.35 ***Area of residence 1.39 ** -4.32 * -6.07 ** -5.13 **Perception of dental health -0.86 *** 7.56 *** 6.78 *** 6.49 ***Dental examination within 1 yr -1.30 ** 2.77 5.90 ** 5.45 **

β: Beta coefficients; R2: R square; Significance level: *P < 0.05, **P < 0.01, ***P<0.001

aValue of 0.004

was rounded off the numbers to two decimal places

69

4. Discussion

Dental caries and periodontal diseases, the most common oral disease, are

preventable by positively motivate patient to keep their oral hygiene in good

condition and to receive an appropriate preventive treatments will most likely to

help maintain a good oral health for one's life. Lifestyle choices which reflects

having a good oral health are under patient's control, unlike family history and

use of medications. The dental professional provides the information through the

health education to assist the patient in order to choose healthy lifestyle. However,

this approach may only be effective to a very small number of patients if the

education simply consists of information only. The important thing is to motivate

patients and they need an accurate information to make a change in their

behavior. Especially from adult's point of view, they should know the importance

of why understanding the new information or a changed behavior is needed for

them before the learning takes in place. Adults should be ready to learn and

perceive the benefit they will obtain in their life (Harris et al., 2009). The tooth

healthspan curves were developed to provide a comprehensive information about

dental health status in Korean adult population. They can provide health

information which can be understood in easy way at personal level. Moreover, the

indices are focused on health rather than disease.

In KNHANES, filled surface and missing surface are recorded separately

according to the cause of tissue damage to assess proper statistical analysis for

caries; code 3 for filled surface as a result of caries, code 7 for filled surface due

to any other reason, code 4 for missing surface as a result of caries and code 5

for missing surface due to any other reason. The surface which is recorded as 3

and 7 was simplified to health related filled surface and recorded as 4 and 5 was

simplified to health related missing surface when the alternative indices of dental

70

health were calculated because it is proper way to describe dental health status.

This approach has some limitation because only dentition status was used rather

than the other tissue such as alveolar bone, soft tissue to present oral health and

caries was considered as a disease only. However advance was made because it

focus on the health and function.

The tooth healthspan curves was developed by applying methodology used in

growth chart. The growth chart is a reference for diagnosis. The criteria for short

stature is under 3 percentile or outside of -2 standard deviation of the distribution

of the population. The use of growth chart have been expanded to diagnose

overweight and to monitor obesity (Story et al., 2002). Nader et al. (2006) reported

that the children who is in upper 85 percentile in BMI curve at age of 24, 36, 54

months old are likely to be overweight when they become 12 years-old. According

to American health promotion guideline, it is recommended for 2-3 years old to

have their BMI measured and to have a dietary counseling. Moreover, the

methodology of growth curve is used to develop model of blood pressure

distribution in child. The tooth healthspan curves are expected to be used to

provide accurate information to individuals about their health and to suggest

indices which is necessary for diagnosis criteria in clinical and public health

setting.

For the curve fitting at the specific age, 400 to 500 of sample size are needed to

appropriately precise the empirical percentiles (Guo et al., 2000). Although data

from the KNHANES for five years were pooled because data collected for one

year in KNHANES series did not have enough observations to construct growth

charts, some age groups did not have enough observations. 18.00-21.99 years old

and 78.00-81.99 years old age group were pooled with 4 years interval and

22.00-79.99 years old were pooled with 2 years interval. For both end of the

curves, 16.00-17.99 and 82.00-89.99 years old were included because they were

71

necessary for smoothing the value at 20 and 80 years old. 8 years interval was

used to make 82.00-89.99 years old age group because there were insignificant

amount of observations made over 80 years old especially in male elderly

(Supplement table 1-2).

Smoothing procedure is needed to make percentile curve useful in clinical setting

because the connected line of estimated empirical percentiles is irregular. Various

model are known to smooth curves. Yoshino et al. (2006) used moving average

method which is widely used in time series analysis and Jeong (2011) used cubic

spline method which is a 3-order polynomial model type. For weight-for-age,

length-for-age, and head circumference-for-age, birth to 36 months, a 3-parameter

linear models were fit to empirical percentile points for weight, length and head

circumference at midpoints of age intervals. The 3-parameter linear models were

proven valid to describe change of body measures from birth to 36 months.

Two-step smoothing curve was applied to weight-for-age in older children and

adolescent (2-20 years old) and BMI-for-age because there is no model known for

describing BMI-for-age (Kuczmarski et al., 2002). In the first step of smoothing

weight-for-age and BMI-for-age for older children, locally weighted regression

(LWR) was used. Polynomial regression was used in the second step of

smoothing for weight-for-age and BMI-for-age. Actual smoothing is occurred in

LWR and the results of second stage smoothing are almost identical to result of

first stage smoothing (Figure 5, 7, 9, 11, 13, 15). Polynomial regression has many

parameters to estimate and higher order term such as age to the seventh power

result in low efficiency and robustness. Developing the valid model for the tooth

healthspan curves such as 3-parameter linear model used in growth curve is

needed for future research.

A modified LMS procedure was used to the smoothed percentile curves.

Maintaining the original distribution of percentile curves and providing a way to

72

estimate percentiles are advantage to using modified LMS method (Kuczmarski et

al., 2002). The validity of estimation was dropped because the skewness of dental

health indices was bigger than of body measures. To overcome the problem, the

estimates of L, M, and S, values are calculated in two groups; over 50 percentiles

and under 45 percentiles assuming sampled population of two groups came from

different distribution. Explanation of this is reasonable because there are distinct

inequality in oral health and clearly high risk group. However the estimates of L,

M, and S, values for male of lower percentile did not make smooth curve in FST

index and PT index (Figure 19, 21). The reason for this is most likely due to the

stability of empirical percentile for male was lower than for women. In the future,

including more observations produced by KNHANES would improve the model.

Because the LMS values were calculated by solving equations that used the

values for percentiles ranging from the 5th to the 95th, any use of the LMS

values to calculate z-scores below -1.6 (5.48 percentile) or above 1.6 (94.52

percentile) should be done with an awareness of the limitations.

It is important to select proper indices to measure health of population in public

health program. Historically, reducing dental caries have been the goal of dental

public health program and DMFT index was used as a primary index. However,

with increased in life expectancies and improvement on observation in oral health

is causing the elderly to experience a higher retention rate of teeth and

maintaining restorations which is result of dental caries, and this became an

important factor as well as reducing dental caries. The focus is changing from

occurring disease to preserve tissue. DMFT index has limitation because it

measure disease as opposed to health.

Sheiham et al. (1987) recommended FST index as an alternative index for dental

health rather than DMFT index. Because the explained variance in FST was 28%

and was superior than DMFT index of which explained variance was only 10%

73

among skilled manual workers and their wives index by calculating linear

regressions on a 300 pairs of study population consist of skilled manual workers

and their wives. He used age, dental history, regular dental visit and satisfaction

with dental appearance as the explanatory variables. Marcenes and Sheiham (1993)

construct three models of linear regression for fathers, mothers and for children

separately. Their explanatory variables explained a greater percentage of the

variance for FST than for DMFT. Especially the results were clear in models of

adults rather than of children. In this study the oral health related variables used

in Benigeri et al. (1998) were selected to compare DMFT index and the percentile

of three alternative indices of dental health; ST index, FST index and PT index.

Age, family income, level of education, area of residence, perception of dental

health and dental examination within 1 year explained a larger proportions of

DMFT index and percentile of ST index in younger generation. In contrast the

proportion of explanation was high in older ages for percentile of FST index and

PT index. The percentile of FST index was explained well in most of age groups

and up to three times higher proportion was explained in 50's than DMFT index

(Table 30, 31).

The tooth healthspan curves were constructed using cross sectional data rather

than longitudinal data. Therefore the assumption that the individual stick to his

present percentile for life would be needed when using the curves for prediction. It

is known that previous caries experience the strongest predictor of future caries

development (Powell, 1998) and caries appear to be occurring at a relatively

constant rate throughout the lifetime in recent longitudinal study (Broadbent et al.,

2008). Individual who was in lower percentile in his earlier age is likely to stay in

the lower percentile especially when he does not change the oral health related

factors such as environmental condition, behavioral choices and quality or use of

health services. Although the cross sectional data has possibility to be used for

74

prediction, the revised curve using longitudinal study still needs to achieve

prediction curve and velocity plot. The Korean Birth Cohort Study to establish the

reference standard of growth and to setup the methods for chronic diseases

prevention in children and adolescence was conducted (KCDC, 2011).

Unfortunately, there appear to be few longitudinal reports of oral health status

from childhood through to adulthood. Most published work has featured either

children and adolescents or older people reporting on caries experience. The

healthy tooth life span curves developed in this study use representative data for

Korean adult population and can be useful until the longitudinal study of high

quality is designed and conducted.

The result of this research can be meaningful when it is used in clinical and

public health settings. To facilitate the use of the curves, plain manual language

for measuring dental health index, reference chart, guideline, and percentile

calculator should be developed. This is also important because the validation in

practice is needed to revise dental health curve.

75

5. Conclusion

This study constructed statistical models for health tooth healthspan curves

using representative national survey data, advanced statistical smoothing

procedures, and LMS technique. Moreover, the indices developed were compared to

DMFT index to investigate their usefulness. The results are listed as follows.

1. The sex-specific smoothed percentile curves for ST index-for-age, FST

index-for-age, and PT index-for-age were constructed. The smoothed percentile

curves were closely matched to empirical percentile curves.

2. The parameters lambda, sigma, and mu were estimated to enable computation

of exact z-score and percentiles for every single values for ST index, FST index,

and PT index.

3. The explained proportion of variance was highest as of 10% in male and

female in their 20's and was decreased to only 5% in 80’s male and female by

age when the dependent variable was DMFT and explanatory variables were age,

family income, level of education, area of residence, perception of dental health and

dental examination within 1 year in multiple linear regression. Otherwise, the

explained proportion of variance were 9-26% and greater than any other indices

when the dependent variable was the percentile of FST index for male. The

explanatory variables were family income, level of education, area of residence,

perception of dental health and dental examination within 1 year in multiple linear

regression. For female, the explained proportion of variance were 8-10%, greater

than any other indices in 20’s and 30’s when the dependent variable were ST

index and the explained proportion of variance were 14-17%, greater than any

other indices in 40's to 70's when the dependent variables were FST index.

76

The study resulted in construction of tooth healthspan curves with sex and age

group of specific estimated parameter L, M, and S to calculate exact z-score and

percent in continuous manner. Moreover the percentiles of FST index were

explained better than DMFT index especially in elderly population. The tooth

healthspan curves provide comprehensive information in intuitive way. The curves

can be used to provide highly accurate information for individual and expected to

be a practical tool in clinical and public health setting providing diagnosis

reference and to reach appropriate goal.

77

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80

Supplement

Supplement table 1. Unweighted sample size for health tooth healthspan curves byage, and data source: Male

Age Midpoint age KNHANES IV KNHANES V Total

Total 7,606 5,514 13,120

16-17.99 years 17 275 186 461

18-19.99 years†

19 210 136 346

20-21.99 years‡

21 106 59 165

22-23.99 years†

23 175 122 297

24-25.99 years‡

25 178 109 287

26-27.99 years†

27 231 131 362

28-29.99 years†

29 192 120 312

30-31.99 years†

31 232 133 365

32-33.99 years 33 228 167 395

34-35.99 years 35 301 178 479

36-37.99 years 37 320 241 561

38-39.99 years 39 334 229 563

40-41.99 years 41 325 220 545

42-43.99 years 43 268 219 487

44-45.99 years 45 269 187 456

46-47.99 years 47 287 189 476

48-49.99 years 49 291 163 454

50-51.99 years 51 281 193 474

52-53.99 years 53 259 206 465

54-55.99 years 55 234 198 432

56-57.99 years 57 223 195 418

58-59.99 years 59 221 187 408

60-61.99 years 61 263 181 444

62-63.99 years 63 232 219 451

64-65.99 years†

65 227 153 380

66-67.99 years 67 227 191 418

68-69.99 years 69 241 188 429

70-71.99 years 71 228 169 397

72-73.99 years†

73 197 181 378

74-75.99 years†

75 177 151 328

76-77.99 years‡

77 127 113 240

78-79.99 years‡

79 90 72 162

80-81.99 years‡

81 68 47 115

82-83.99 years‡

83 38 35 73

84-85.99 years‡

85 23 21 44

86-87.99 years‡

87 14 15 29

88-89.99 years‡

89 14 10 24†Age group less than 400 of subjects,

‡Age group less than 300 of subjects

81

Supplement table 2. Unweighted sample size for health tooth healthspan curves byage, and data source: Female

Age Midpoint age KNHANES IV KNHANES V Total

Total 10,157 7,236 17,393

16-17.99 years 17 267 185 452

18-19.99 years†

19 211 142 353

20-21.99 years†

21 193 103 296

22-23.99 years†

23 201 127 328

24-25.99 years†

25 209 170 379

26-27.99 years 27 276 161 437

28-29.99 years 29 289 199 488

30-31.99 years 31 339 227 566

32-33.99 years 33 367 210 577

34-35.99 years 35 437 305 742

36-37.99 years 37 410 303 713

38-39.99 years 39 432 322 754

40-41.99 years 41 402 288 690

42-43.99 years 43 380 230 610

44-45.99 years 45 340 199 539

46-47.99 years 47 362 258 620

48-49.99 years 49 399 244 643

50-51.99 years 51 380 311 691

52-53.99 years 53 387 288 675

54-55.99 years 55 287 275 562

56-57.99 years 57 281 243 524

58-59.99 years 59 291 236 527

60-61.99 years 61 332 205 537

62-63.99 years 63 273 258 531

64-65.99 years 65 264 205 469

66-67.99 years 67 339 197 536

68-69.99 years 69 340 247 587

70-71.99 years 71 292 225 517

72-73.99 years 73 285 209 494

74-75.99 years†

75 226 164 390

76-77.99 years†

77 218 161 379

78-79.99 years‡

79 144 117 261

80-81.99 years‡

81 114 95 209

82-83.99 years‡

83 84 56 140

84-85.99 years‡

85 47 29 76

86-87.99 years‡

87 44 27 71

88-89.99 years‡

89 15 15 30†Age group less than 400 of subjects,

‡Age group less than 300 of subjects

82

Supplement table 3. Observed mean, standard deviation, and selected percentiles forDMFT index by age: Male

Age Midpointage N Mean SD

Percentiles

10th

25th

50th

75th

90th

18.00-22.99 20 511 4.87 190.56 0 1 5 8 11

23.00-24.99 23 297 5.46 219.31 0 2 5 8 11

25.00-26.99 25 287 5.53 204.03 0 3 5 8 12

27.00-28.99 27 362 5.63 210.11 0 2 5 8 12

29.00-30.99 29 312 5.02 197.90 0 2 4 8 10

31.00-32.99 31 365 5.13 186.46 0 2 5 8 11

33.00-34.99 33 395 4.42 177.26 0 1 4 7 9

35.00-36.99 35 479 4.53 163.21 0 1 4 7 10

37.00-38.99 37 561 4.06 140.38 0 1 3 7 9

39.00-40.99 39 563 4.04 141.06 0 1 3 7 9

41.00-42.99 41 545 4.18 147.04 0 1 3 7 9

43.00-44.99 43 487 4.09 157.69 0 1 3 6 9

45.00-46.99 45 456 3.77 138.92 0 1 3 6 9

47.00-48.99 47 476 3.87 146.72 0 1 3 6 9

49.00-50.99 49 454 3.69 146.37 0 1 3 5 8

51.00-51.99 51 474 3.96 156.95 0 1 3 6 9

53.00-54.99 53 465 4.19 150.28 0 1 4 6 9

55.00-56.99 55 432 4.78 169.32 0 1 4 7 11

57.00-58.99 57 418 4.85 158.10 0 1 4 7 11

59.00-60.99 59 408 5.58 172.22 0 2 5 8 13

61.00-62.99 61 444 6.20 164.52 0 2 5 9 15

63.00-64.99 63 451 5.63 158.30 0 2 4 8 13

65.00-66.99 65 380 7.25 172.84 0 2 6 11 16

67.00-68.99 67 418 7.17 166.32 1 2 6 11 16

69.00-70.99 69 429 7.59 178.36 0 3 6 11 16

71.00-72.99 71 397 8.10 166.65 0 3 7 13 16

73.00-74.99 73 378 7.55 159.56 0 2 6 12 16

75.00-76.99 75 328 9.07 181.96 0 3 8 14 16

77.00-79.99 77 240 9.94 200.01 0 4 10 16 18

80.00-81.99 80 277 9.63 191.28 0 3 10 15 17

83

Supplement table 4. Observed mean, standard deviation, and selected percentiles forDMFT index by age: Female


Percentiles

10th

25th

50th

75th

90th

18.00-22.99 20 649 6.11 168.91 1 3 6 9 12

23.00-24.99 23 328 6.35 159.94 1 4 6 9 11

25.00-26.99 25 379 6.97 167.83 2 4 7 9 13

27.00-28.99 27 437 6.77 165.70 1 4 7 10 12

29.00-30.99 29 488 6.64 165.02 1 4 7 9 12

31.00-32.99 31 566 6.45 147.62 1 3 7 9 12

33.00-34.99 33 577 6.11 134.64 1 3 6 9 11

35.00-36.99 35 742 5.84 132.22 1 2 6 8 11

37.00-38.99 37 713 5.49 130.64 0 2 5 8 11

39.00-40.99 39 754 5.42 130.34 0 2 5 8 11

41.00-42.99 41 690 5.61 133.30 1 2 6 8 10

43.00-44.99 43 610 5.63 136.03 1 3 5 8 11

45.00-46.99 45 539 5.75 142.69 0 3 6 8 11

47.00-48.99 47 620 6.04 145.86 1 3 6 9 11

49.00-50.99 49 643 5.71 143.97 1 3 5 8 11

51.00-51.99 51 691 6.10 146.39 1 3 6 9 12

53.00-54.99 53 675 6.33 146.41 1 3 6 9 12

55.00-56.99 55 562 6.73 152.95 1 3 6 10 13

57.00-58.99 57 524 7.20 159.69 1 3 7 10 13

59.00-60.99 59 527 6.77 150.23 1 3 6 9 13

61.00-62.99 61 537 7.49 156.11 1 4 7 10 14

63.00-64.99 63 531 7.72 162.74 1 4 7 11 15

65.00-66.99 65 469 7.81 155.02 2 4 7 11 16

67.00-68.99 67 536 8.45 155.94 1 4 8 12 16

69.00-70.99 69 587 8.21 167.29 1 4 7 12 16

71.00-72.99 71 517 9.24 164.89 1 4 9 14 16

73.00-74.99 73 494 9.35 173.55 1 4 8 14 17

75.00-76.99 75 390 10.18 195.25 0 5 10 15 18

77.00-79.99 77 379 10.57 211.97 0 5 10 16 20

80.00-81.99 80 470 11.32 237.90 0 5 12 16 23

84

Supplement table 5. Observed mean, standard deviation, and selected percentiles forST index by age: Male


Percentiles

10th

25th

50th

75th

90th

18.00-22.99 20 511 22.75 201.62 16 20 23 27 28

23.00-24.99 23 297 22.06 238.58 15 20 23 25 28

25.00-26.99 25 287 21.96 221.65 15 20 23 25 27

27.00-28.99 27 362 21.91 223.63 15 19 23 26 28

29.00-30.99 29 312 22.46 215.97 16 20 23 26 28

31.00-32.99 31 365 22.15 207.25 16 19 23 26 28

33.00-34.99 33 395 22.86 203.78 16 20 24 26 28

35.00-36.99 35 479 22.65 188.30 16 20 24 26 28

37.00-38.99 37 561 23.01 161.44 17 20 24 26 28

39.00-40.99 39 563 22.62 179.02 16 20 23 26 28

41.00-42.99 41 545 22.13 198.41 15 19 23 26 28

43.00-44.99 43 487 21.73 213.48 14 19 23 26 28

45.00-46.99 45 456 22.05 205.43 15 19 23 26 28

47.00-48.99 47 476 21.77 223.36 15 19 23 26 28

49.00-50.99 49 454 21.5 237.85 14 19 23 26 28

51.00-51.99 51 474 21.12 233.22 14 18 22 25 28

53.00-54.99 53 465 19.66 264.73 11 16 21 25 27

55.00-56.99 55 432 18.42 282.24 7 14 20 24 26

57.00-58.99 57 418 16.86 293.79 3 10 19 24 27

59.00-60.99 59 408 15.81 296.17 3 10 17 23 26

61.00-62.99 61 444 15.34 252.29 0 9 17 22 25

63.00-64.99 63 451 15.73 267.56 1 9 18 23 26

65.00-66.99 65 380 13.60 248.94 0 6 15 20 24

67.00-68.99 67 418 13.24 254.26 0 4 14 21 25

69.00-70.99 69 429 11.33 239.13 0 3 10 18 24

71.00-72.99 71 397 10.76 230.68 0 2 10 18 22

73.00-74.99 73 378 10.88 224.65 0 2 11 18 23

75.00-76.99 75 328 9.19 223.53 0 0 8 16 22

77.00-79.99 77 240 7.02 214.16 0 0 5 12 21

80.00-81.99 80 277 7.22 209.44 0 0 5 12 18

85

Supplement table 6. Observed mean, standard deviation, and selected percentiles forST index by age: Female


Percentiles

10th

25th

50th

75th

90th

18.00-22.99 20 649 26.56 92.88 24 26 28 28 28

23.00-24.99 23 328 26.54 85.85 24 26 27 28 28

25.00-26.99 25 379 26.56 88.29 24 26 28 28 28

27.00-28.99 27 437 26.74 76.50 24 26 28 28 28

29.00-30.99 29 488 26.52 77.63 24 26 27 28 28

31.00-32.99 31 566 26.75 65.93 24 26 28 28 28

33.00-34.99 33 577 26.88 58.93 24 26 28 28 28

35.00-36.99 35 742 26.70 66.06 24 26 28 28 28

37.00-38.99 37 713 26.83 58.89 24 26 27 28 28

39.00-40.99 39 754 26.83 64.66 25 26 28 28 28

41.00-42.99 41 690 26.75 66.73 24 26 28 28 28

43.00-44.99 43 610 26.53 79.54 24 26 27 28 28

45.00-46.99 45 539 26.07 105.74 23 25 27 28 28

47.00-48.99 47 620 26.00 102.33 23 25 27 28 28

49.00-50.99 49 643 25.64 127.77 22 25 27 28 28

51.00-51.99 51 691 25.02 131.84 20 24 26 28 28

53.00-54.99 53 675 24.74 148.62 19 24 26 28 28

55.00-56.99 55 562 23.66 175.14 17 22 25 27 28

57.00-58.99 57 524 23.15 182.61 16 21 25 27 28

59.00-60.99 59 527 22.92 192.26 16 21 25 27 28

61.00-62.99 61 537 22.15 183.37 13 20 24 27 28

63.00-64.99 63 531 20.60 207.45 9 17 23 26 28

65.00-66.99 65 469 20.35 215.12 8 17 23 26 28

67.00-68.99 67 536 18.97 211.16 6 13 22 26 27

69.00-70.99 69 587 17.61 230.63 3 11 21 25 27

71.00-72.99 71 517 16.13 238.29 2 8 18 24 27

73.00-74.99 73 494 15.48 236.24 0 8 17 24 26

75.00-76.99 75 390 13.17 255.08 0 4 14 21 26

77.00-79.99 77 379 12.96 283.52 0 4 13 22 26

80.00-81.99 80 470 10.80 274.31 0 3 9 19 25

86

Supplement table 7. Observed mean, standard deviation, and selected percentiles forFST index by age: Male


Percentiles

10th

25th

50th

75th

90th

18.00-22.99 20 511 26.64 105.35 24 26 28 28 28

23.00-24.99 23 297 26.63 109.56 24 26 28 28 28

25.00-26.99 25 287 26.76 97.39 24 26 28 28 28

27.00-28.99 27 362 26.51 110.58 23 26 27 28 28

29.00-30.99 29 312 26.61 101.46 24 26 28 28 28

31.00-32.99 31 365 26.56 93.85 24 26 27 28 28

33.00-34.99 33 395 26.80 84.22 24 26 28 28 28

35.00-36.99 35 479 26.90 73.16 25 26 28 28 28

37.00-38.99 37 561 26.84 71.60 25 26 28 28 28

39.00-40.99 39 563 26.51 84.67 24 26 27 28 28

41.00-42.99 41 545 26.23 101.64 23 26 27 28 28

43.00-44.99 43 487 25.91 131.54 22 25 27 28 28

45.00-46.99 45 456 26.04 116.35 23 25 27 28 28

47.00-48.99 47 476 25.69 143.53 22 25 27 28 28

49.00-50.99 49 454 25.52 144.35 22 25 27 28 28

51.00-51.99 51 474 25.03 179.79 22 24 26 28 28

53.00-54.99 53 465 24.02 210.86 18 23 26 27 28

55.00-56.99 55 432 23.07 237.00 14 22 25 27 28

57.00-58.99 57 418 21.92 252.78 11 19 25 27 28

59.00-60.99 59 408 21.16 254.38 9 18 23 26 28

61.00-62.99 61 444 20.68 232.90 8 18 24 26 28

63.00-64.99 63 451 20.91 230.44 8 18 24 26 28

65.00-66.99 65 380 19.18 232.96 6 14 22 26 27

67.00-68.99 67 418 18.69 237.50 5 14 21 26 27

69.00-70.99 69 429 17.14 250.94 2 10 19 25 27

71.00-72.99 71 397 16.02 236.05 2 9 18 24 26

73.00-74.99 73 378 16.85 233.98 2 10 20 25 27

75.00-76.99 75 328 14.08 247.75 0 5 15 23 26

77.00-79.99 77 240 11.85 265.49 0 2 9 21 26

80.00-81.99 80 277 11.91 242.36 0 4 11 19 24

87

Supplement table 8. Observed mean, standard deviation, and selected percentiles forFST index by age: Female


Percentiles

10th

25th

50th

75th

90th

18.00-22.99 20 649 26.56 92.88 24 26 28 28 28

23.00-24.99 23 328 26.54 85.85 24 26 27 28 28

25.00-26.99 25 379 26.56 88.29 24 26 28 28 28

27.00-28.99 27 437 26.74 76.50 24 26 28 28 28

29.00-30.99 29 488 26.52 77.63 24 26 27 28 28

31.00-32.99 31 566 26.75 65.93 24 26 28 28 28

33.00-34.99 33 577 26.88 58.93 24 26 28 28 28

35.00-36.99 35 742 26.70 66.06 24 26 28 28 28

37.00-38.99 37 713 26.83 58.89 24 26 27 28 28

39.00-40.99 39 754 26.83 64.66 25 26 28 28 28

41.00-42.99 41 690 26.75 66.73 24 26 28 28 28

43.00-44.99 43 610 26.53 79.54 24 26 27 28 28

45.00-46.99 45 539 26.07 105.74 23 25 27 28 28

47.00-48.99 47 620 26.00 102.33 23 25 27 28 28

49.00-50.99 49 643 25.64 127.77 22 25 27 28 28

51.00-51.99 51 691 25.02 131.84 20 24 26 28 28

53.00-54.99 53 675 24.74 148.62 19 24 26 28 28

55.00-56.99 55 562 23.66 175.14 17 22 25 27 28

57.00-58.99 57 524 23.15 182.61 16 21 25 27 28

59.00-60.99 59 527 22.92 192.26 16 21 25 27 28

61.00-62.99 61 537 22.15 183.37 13 20 24 27 28

63.00-64.99 63 531 20.60 207.45 9 17 23 26 28

65.00-66.99 65 469 20.35 215.12 8 17 23 26 28

67.00-68.99 67 536 18.97 211.16 6 13 22 26 27

69.00-70.99 69 587 17.61 230.63 3 11 21 25 27

71.00-72.99 71 517 16.13 238.29 2 8 18 24 27

73.00-74.99 73 494 15.48 236.24 0 8 17 24 26

75.00-76.99 75 390 13.17 255.08 0 4 14 21 26

77.00-79.99 77 379 12.96 283.52 0 4 13 22 26

80.00-81.99 80 470 10.80 274.31 0 3 9 19 25

88

Supplement table 9. Observed mean, standard deviation, and selected percentiles forPT index by age: Male


Percentiles

10th

25th

50th

75th

90th

18.00-22.99 20 511 27.65 42.92 27 28 28 28 28

23.00-24.99 23 297 27.61 58.47 27 28 28 28 28

25.00-26.99 25 287 27.63 49.74 27 28 28 28 28

27.00-28.99 27 362 27.52 53.69 26 28 28 28 28

29.00-30.99 29 312 27.48 52.74 26 27 28 28 28

31.00-32.99 31 365 27.47 49.55 26 27 28 28 28

33.00-34.99 33 395 27.47 51.67 26 27 28 28 28

35.00-36.99 35 479 27.45 53.53 26 27 28 28 28

37.00-38.99 37 561 27.35 54.37 26 27 28 28 28

39.00-40.99 39 563 27.08 66.78 25 27 28 28 28

41.00-42.99 41 545 26.80 83.18 25 26 28 28 28

43.00-44.99 43 487 26.35 125.35 24 26 27 28 28

45.00-46.99 45 456 26.49 100.76 24 26 27 28 28

47.00-48.99 47 476 26.17 127.20 23 26 27 28 28

49.00-50.99 49 454 25.95 135.40 23 25 27 28 28

51.00-51.99 51 474 25.53 169.60 22 25 27 28 28

53.00-54.99 53 465 24.45 206.68 19 24 26 28 28

55.00-56.99 55 432 23.54 229.69 15 22 26 28 28

57.00-58.99 57 418 22.44 249.82 11 20 26 27 28

59.00-60.99 59 408 21.64 253.11 10 19 24 27 28

61.00-62.99 61 444 21.09 232.07 8 18 24 27 28

63.00-64.99 63 451 21.53 226.92 9 18 25 27 28

65.00-66.99 65 380 19.85 232.02 6 15 23 26 28

67.00-68.99 67 418 19.40 237.48 5 15 22 26 28

69.00-70.99 69 429 17.87 250.49 3 11 20 26 27

71.00-72.99 71 397 16.68 236.83 2 10 19 25 27

73.00-74.99 73 378 17.58 235.08 2 11 21 25 27

75.00-76.99 75 328 14.95 252.23 0 5 17 24 26

77.00-79.99 77 240 12.81 268.74 0 3 11 22 26

80.00-81.99 80 277 12.95 254.43 1 4 13 22 25

89

Supplement table 10. Observed mean, standard deviation, and selected percentiles forPT index by age: Female


Percentiles

10th

25th

50th

75th

90th

18.00-22.99 20 649 27.52 45.29 26 28 28 28 28

23.00-24.99 23 328 27.43 51.43 26 28 28 28 28

25.00-26.99 25 379 27.35 59.14 25 27 28 28 28

27.00-28.99 27 437 27.43 46.37 26 27 28 28 28

29.00-30.99 29 488 27.14 61.43 25 27 28 28 28

31.00-32.99 31 566 27.28 45.89 25 27 28 28 28

33.00-34.99 33 577 27.37 41.23 26 27 28 28 28

35.00-36.99 35 742 27.24 47.03 25 27 28 28 28

37.00-38.99 37 713 27.29 45.14 26 27 28 28 28

39.00-40.99 39 754 27.25 50.96 26 27 28 28 28

41.00-42.99 41 690 27.16 49.93 25 27 28 28 28

43.00-44.99 43 610 27.01 66.33 25 27 28 28 28

45.00-46.99 45 539 26.55 93.17 24 26 27 28 28

47.00-48.99 47 620 26.38 90.92 24 26 27 28 28

49.00-50.99 49 643 26.13 108.50 23 26 27 28 28

51.00-51.99 51 691 25.46 125.11 21 25 27 28 28

53.00-54.99 53 675 25.16 143.49 21 24 27 28 28

55.00-56.99 55 562 24.06 172.79 18 23 26 28 28

57.00-58.99 57 524 23.53 177.69 16 22 25 28 28

59.00-60.99 59 527 23.27 188.64 17 22 25 27 28

61.00-62.99 61 537 22.59 176.97 15 21 25 27 28

63.00-64.99 63 531 21.05 207.08 9 18 24 27 28

65.00-66.99 65 469 20.87 213.27 8 18 24 27 28

67.00-68.99 67 536 19.49 209.32 6 15 22 26 27

69.00-70.99 69 587 18.16 232.42 3 12 21 25 27

71.00-72.99 71 517 16.65 240.81 2 9 19 25 27

73.00-74.99 73 494 16.04 238.20 0 8 18 24 27

75.00-76.99 75 390 13.80 256.20 0 4 15 22 26

77.00-79.99 77 379 13.53 288.99 0 4 14 23 26

80.00-81.99 80 470 11.62 281.85 0 3 10 20 25

90

국 문 요 약

통계적 모형을 이용한 한국인 치아 건강수명곡선 개발

건강수준의 증진은 고령화의 진행과 더불어 치아 건강의 유지 기간을 증대시키고

있다. 따라서 질병경험에 초점을 둔 우식경험영구치지수와 별개로 건강에 초점을 둔

지표를 개발할 필요성이 있다. 치아 건강수명곡선은 연령에 따른 건전영구치지수, 기

능영구치지수, 현재영구치지수의 감소를 백분위수 곡선을 활용하여 나타낸 것이다. 지

금까지 개발된 치아 건강수명곡선은 가중치 및 적절한 평활화 방법을 적용하지 않았

다. 무엇보다 모수적 모형 없이 평활화만 수행하여 정확한 수치를 제공할 수 없다는

한계를 지니고 있었다. 따라서 본 연구에서는 대표성 있는 자료를 이용하고 발전된

평활화 모형과 LMS 기법을 도입하였다. 이를 통해 치아 건강수명곡선의 통계적 모형

을 도출하고 이를 우식경험영구치지수와 비교하여 그 유용성을 확인해보고자 하였다.

대표성을 가진 단면적 건강 조사인 국민건강영양조사의 4기, 5기 1-2차년도 자료를

이용하였다. 이 중 건강 설문과 건강검진을 받은 만 16세 이상 89세 이하를 대상으로

하여 조사 설계 관련 변수, 인구학적 변수, 구강건강 관련 변수를 선별하였다. 건전영

구치지수, 기능영구치지수, 현재영구치지수의 경험적 백분위수를 성별, 연령별로 산출

하였다. 이 백분위수 곡선을 국소가중회귀와 7차 다항회귀로 평활화한 후 LMS 모형

을 평활화한 곡선에 적용하여 총 6 종류의 치아 건강수명곡선을 모형화 하였다. 개발

된 지수를 우식경험영구치지수와 비교하기 위하여 지수를 종속변수로 하고 구강건강

관련요인을 설명변수로 하는 선형회귀분석을 수행하였다. 이를 통해 다음과 같은 결

과를 얻었다.

1. 성별 건전영구치수명곡선, 성별 기능영구치수명곡선, 성별 현재영구치수명곡선을

산출하였다. 평활화한 백분위수 곡선은 경험적 백분위수 곡선을 잘 반영하였다.

91

2. 성별 건전영구치수명곡선, 성별 기능영구치수명곡선, 성별 현재영구치수명곡선에

서 모수 lambda, sigma, mu 값을 도출함으로써 특정 건강치아지수에 해당하는

z-score와 백분위수를 수치적으로 계산할 수 있도록 하였다.

3. 우식경험영구치지수를 종속변수로 하고 연령, 소득수준, 교육수준, 거주 지역, 구

강건강인지, 1년 내 구강검진 수진 여부를 독립변수로 한 다중회귀분석 결과 설명되

는 분산은 20대 남성과 여성에서 10%로 가장 높았고 연령의 증가에 따라 점점 낮아

져서 80대에서 남성과 여성에서 5%로 감소하였다. 한편 건전영구치지수, 기능영구치

지수, 현재영구치지수의 백분위수를 종속변수로 하고 소득수준, 교육수준, 거주 지역,

구강건강인지, 1년 내 구강검진 수진 여부를 독립변수로 한 다중회귀분석 결과 설명

되는 분산은 남자의 경우 모든 연령대에서 기능영구치지수의 백분위수의 경우 9-26%

로 가장 높았으며 여자의 경우 20, 30대는 건전영구치지수의 백분위수가 8-10%로 가

장 높았고 40-70대는 기능영구치지수의 백분위수가 14-17%로 가장 높았다.

대표성을 지닌 국가 검진 자료와 최신의 통계적 방법론을 적용하여 개인 수준의 건

강 정보를 수치적으로 제공할 수 있는 치아건강수명곡선을 도출하였다. 통계 모형의

모수 lambda, mu, sigma를 이용하여 단일 관측치에 대한 정확한 z-score와 백분위수

를 구할 수 있었다. 또한 고연령군에서 우식경험영구치지수에 비해 기능영구치지수의

백분위수가 구강건강 관련요인을 잘 설명하는 것을 알 수 있었다. 치아 건강수명곡선

은 직관적이며 포괄적인 정보를 제공한다. 따라서 개인에게 건강에 대한 정확한 정보

를 제공하고 임상에서의 진단 기준과 보건 사업에 필요한 지표를 제공하는 도구로서

활용할 수 있을 것이다.

핵심되는 말: 구강 건강, 국가 건강 조사, 백분위수 곡선, 우식경험영구치지수, 기능치

아지수, 변형 LMS 절차

Date post:	25-Aug-2020
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