序列二元間隔時間之時間區塊交叉比的半參數估計方法

Abstract

在許多醫學研究中，時常會觀察到多元事件的資料。在長期追蹤研究下，觀察個體可能會反覆經歷多個有序多元事件的序列，舉例來說，在慢性疾病的進程，病患可能會重複發生住院與出院兩種情況。本文感興趣的是兩事件之間的二元間隔時間，例如，在醫院的住院天數與從醫院出院到再入院間的時間區間。由於每一個體可能反覆發生多個二元間隔時間的序列，此種資料稱為序列二元間隔時間資料。本研究目的為在序列二元間隔時間資料下，估計二元間隔時間之時間區塊的相關性。交叉比是一個常用的相關性測度，用來測量二元間隔時間隨時間變化的相關性。本文考慮對數交叉比與時間區塊相關的參數迴歸模式，來估計時間區塊的交叉比，並推廣Chang(2017)所考慮的三個半參數估計方法到參數迴歸函數下，估計時間區塊交叉比，以及使用倒數機率設限權重來解決誘導相依設限的問題。最後，本文利用三種不同聯合分布的蒙地卡羅模擬，來探討三種方法估計量的估計表現。

Multiple events data are frequently encountered in many medical studies. For a long-term follow-up study, subjects may experience several series of ordered multiple events alternately over time. For instance, patients may have repeated hospitalizations and discharges in the progress of chronic diseases. In the study, the time variables of interest are the bivariate gap times between bivariate events, for example, the length of stay in hospital and the time interval between the discharge from a hospital and readmission. Since each subject may have several episodes of bivariate gap times over time, such data are called the serial bivariate gap time data. The aim of the study is to estimate the time-segment association of bivariate gap times for serial bivariate gap time data. The cross ratio is a common measure to quantify the time-varying association between bivariate gap times. To estimate the time-segment cross ratios, we consider the parametric regression model which specifies an explicit relation between the log cross ratio and the time segments. Three semi-parametric estimation methods considered by Chang (2017) are extended to estimate the time-segment cross ratios via the parametric regression function, in which the inverse probability of censoring weight is used to deal with the induced dependent censoring. Finally, the performance of the estimators obtained from three estimation methods is investigated by conducting the Monte-Carlo simulations with three different joint distributions.