我們感興趣估計罹病時間的分配函數，然而因為罹病時間難以確切掌握，這類資料經常受到設限。本篇論文中我們考慮型一區間設限資料。此種資料只提供受測者在診查時間的年齡與當時是否已經得病，這種資料常見於流行病研究中。在分析中，我們容許免疫者的存在。我們討論三種母數方法和一個無母數方法以估計罹病時間。母數方法包含最大概似估計法，與兩個非線性迴歸的方法。第四個方法考慮以 “自我一致函數” (self-consistency equation) 建構無母數的估計量。

We are interested in estimating the distribution of age of onset. However data of age onset are often censored. In genetic research, the age-onset distribution of a disease may be the penetrance function that represents the cumulative probability of developing a disease by a certain age under a specified genotype. In this thesis, we consider statistical inference based on current status data which is also called as interval censored of case I. Given current status data, we only observe the current age and whether subject has the disease or not but the exact age of onset is never observable. Such data are often seen in epidemiological studies. We consider four methods to estimate the distribution of age-onset given current status data in the presence of long-term survivors. That is, we allow some people to be immune for the disease. Parametric methods include maximum likelihood estimation and two methods based on non-linear regression techniques. At last, we construct nonparametric estimation using self-consistency equation.

Contents:
Chapter 1 Introduction 1-3
1.1 Motivation and Objectives
1.2 Outline of the Thesis
Chapter 2 Literature Review 4-7
2.1 Penetrance Function in Genetic Research
2.2 Long-Term Survivorship
Chapter 3 Inference Methods for Current
Status Data 8-24
3.1 Maximum Likelihood Estimation
3.2 Nonlinear Regression After Arc-sin
Transformation
3.3 Quasi-likelihood Estimation
3.4 Comparison of the Parametric Methods
3.5 Nonparametric Estimation
Chapter 4 Simulation Study 25-30
4.1 Simulation schemes
4.2 Simulation results when C is discrete
4.3 Simulation results when C has a
continuous uniform distribution
Chapter 5 Discussion and Conclusion 31
Reference 32-33

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