治癒模式之半母數迴歸分析

Abstract

本論文針對存活資料，考慮“不受感染體質”(nonsusceptibility)者之存在，在混合模式架構下提出半母數迴歸分析方法。我們採用邏輯斯模式分析解釋變數與“發病與否”的關係。針對受感染體質者之“潛在發病時間”，我們探討兩類迴歸模式之推論問題。第一類模式包含常見的加速失敗模式和位移模式，我們利用計數程序之機率性質以建構估計函數，並進一步提出模式選取方法。第二類為線性轉換模式，包含等比風險模式與等比勝負比模式。我們採用概似函數法做為參數估計的原則，除了分析獨立設限的情況外，並進一步提出當存在競爭風險時，如何修正模式假設與推論方法。兩個研究方向都利用 EM 的技巧，以補插法處理感染體質不確定之觀測值。我們透過模擬實驗評估所提出方法在有限樣本下之表現。

In this thesis, we consider semiparametric regression analysis for survival data in presence of non-susceptibility or cure. The mixture framework is adopted in analysis of such data. The incidence rate is assumed to follow the logistic regression model and the latency distribution is studied under two types of semiparametric regression models. One class refers to the semi-parametric linear regression model which includes the AFT and location-shift models as special cases. We propose estimating functions and also a model checking procedure based on properties of counting processes. The other class is known as transformation models which contain the proportional hazards model and proportional odds model. The likelihood principle is adopted for parameter estimation. We examine two situations of independent and dependent censoring respectively. In both research directions, the principle of EM is applied to handle uncertain susceptibility status. Simulation results are provided to examine the finite-sample properties of the proposed methods.