臺灣博碩士論文加值系統

本論文的研究動機來自一筆孟加拉的生育資料 (Bangladesh Demographic and Health Survey, 簡稱 BDHS)。為研究生育的間隔時間，由至少生育兩胎的婦女取樣。我們對這筆資料進行基本分析時，發現有些資訊可能帶有偏誤，我們將之歸類為右截切的問題。我們進行了模擬實驗，探究截切所造成的影響，並透過反轉時間軸的方式成功調整右截切的偏誤。最後我們將此方法應用在資料分析，先前的偏誤已不復見，亦看出婦女生育的間隔時間的世代差異。

This thesis was motivated by a real dataset published in Bangladesh Demographic and Health Survey (BDHS) about women’s birth and other health information in Bangladesh. To study serial birth intervals, we only selected women who gave at least two births which however created bias in the sampling procedure. We formulate the problem under the framework of right truncation and analyze its effect via simulations. By applying the reverse-time technique, we can correct the truncation bias. The modified method is then applied to analyze the data. The new result shows that younger and older generations do reveal some difference in their first birth intervals.

CONTENTS
摘要 I
ABSTRACT II
致謝 III
LIST OF TABLES V
LIST OF FIGURES V
CHAPTER I : INTRODUCTION 1
1.1 MOTIVATION 1
1.2 PROBLEM FORMULATION 2
1.2.1 Notations ignoring the clustering structure 2
1.2.2 Sampling constraint and its influence 4
1.3 THESIS OUTLINE 5
CHAPTER 2 PRELIMINARY DATA ANALYSIS 7
2.1 DESCRIPTIVE STATISTICS OF DBHS DATA 7
2.2 CHILD MARRIAGE AND CHILD MOTHERS 8
2.3 CHARACTERISTICS OF WOMEN AND CHILDREN IN THE SAMPLE 9
CHAPTER 3 LITERATURE REVIEW 10
3.1 PARAMETRIC MODELS FOR SURVIVAL DATA IN PRESENCE OF CURE 10
3.2 RANDOM-EFFECT PARAMETRIC MODELING FOR CLUSTERING STRUCTURE DATA 11
3.3 RECURRENCE GAP-TIME DATA 12
3.4 TRUNCATION 13
CHAPTER 4 MAIN RESULTS 16
4.1 DATA ANALYSIS FOR GAP TIMES – IGNORING TRUNCATION 16
4.2 DATA GENERATION ALGORITHM 17
4.3 SIMULATION ANALYSIS FOR STUDYING THE TRUNCATION EFFECT 19
4.4 SIMULATION STUDY – ADJUSTMENT FOR RIGHT TRUNCATION 21
4.5 DATA ANALYSIS - ADJUSTMENT FOR RIGHT TRUNCATION 22
CHAPTER 5 CONCLUSION 23
REFERENCES 24
APPENDIX I : TABLES 25
APPENDIX II : FIGURES 26


LIST OF TABLES
TABLE 2.1: ECONOMIC RANKS OF SIX DIVISIONS BASED ON THREE METHODS 25
TABLE 2.2 : DESCRIPTIVE STATISTICS OF SIX DIVISIONS 25


LIST OF FIGURES
FIGURE 1.1 : DATA STRUCTURE 2
FIGURE 1.2 : BIRTH PROCESS OF A WOMAN 3
FIGURE 1.3 : BIAS OF RIGHT TRUNCATION 5
FIGURE 1.4 : TRENDS FOR BANGLADESH WOMEN’S USE OF CONTRACEPTION 5
FIGURE 2.1 : WEALTH CONDITIONS OF SIX REGIONS IN BANGLADESH E 26
FIGURE 2.2 : ECONOMIC RANKS OF SIX DIVISIONS BASED ON THREE METHODS 26
FIGURE 2.3 : MEAN-SD SCATTER PLOT OF WIFE/HOUSEHOLD FOR SIX REGIONS 27
FIGURE 2.4 : MEAN-SD SCATTER PLOT OF CHILDREN/WIFE FOR SIX REGIONS 27
FIGURE 2.5 : HISTOGRAM OF AGE AT FIRST-BIRTH 28
FIGURE 2.6 : WOMEN’S AGES AT FIRST-BIRTH FOR 5 GENERATION GROUPS 28
FIGURE 2.7 : HISTOGRAM OF U 29
FIGURE 2.8 : HISTOGRAM OF CHILDREN’S BIRTH YEARS 29
FIGURE 3.1 : GOMPERTZ CURVES WITH FIXED 30
FIGURE 3.2 : GOMPERTZ CURVES WITH FIXED 30
FIGURE 3.3 : FOUR-PARAMETER LOG-LOGISTIC CURVES 31
FIGURE 3.4 : NOTATIONS FOR BANGLADESH BIRTH DATA 31
FIGURE 3.5 : TRUNCATION ADJUSTMENT PROPOSED BY LYNDEN-BELL 32
FIGURE 4.1 : SECOND GAP TIME ESTIMATION GIVEN T1 32
FIGURE 4.2 : SURVIVAL CURVE OF T1 BASED ON MOM’S FIRST BIRTH AGE 33
FIGURE 4.3 : SURVIVAL CURVE OF T1 BASED ON MOM’S AGE ON 2007 33
FIGURE 4.4 : SURVIVAL CURVE OF C 34
FIGURE 4.5 : RESTRICTED SIMULATION AGE 34
FIGURE 4.6 : SURVIVAL CURVE OF SIMULATION T2 35
FIGURE 4.7 : CURE RATE OF SIMULATION T2 35
FIGURE 4.8 : SURVIVAL CURVES OF T1 BASED ON TRUNCATED DATA 36
FIGURE 4.9 : SURVIVAL CURVES OF T1 BASED ON UN-TRUNCATED DATA 36
FIGURE 4.10 : SURVIVAL CURVES OF T1 FOR YOUNG GENERATION 37
FIGURE 4.11 : SURVIVAL CURVES OF T1 FOR MIDDLE (LEFT) AND OLD (RIGHT) GENERATIONS 37
FIGURE 4.12 : ADJUSTMENT OF TRUNCATION EFFECT FOR SIMULATION DATA 38
FIGURE 4.13 : ADJUSTMENT OF TRUNCATION EFFECT FOR DBHS DATA 39

CHIEN-LIN SU (2015). Statistical Analysis for Clustered Survival data with a Hierarchical Structure or in Presence of Cure. Un-publish Ph.D. thesis.

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Klein, J. P., & Moeschberger, M. L. (2005). Survival analysis: techniques for censored and truncated data. Springer Science & Business Media.