Cox Model Analysis with the Dependently Left Truncated Data

A truncated sample consists of realizations of a pair of random variables (L, T) subject to the constraint that L ≤T. The major study interest with a truncated sample is to find the marginal distributions of L and T. Many studies have been done with the assumption that L and T are independent. We introduce a new way to specify a Cox model for a truncated sample, assuming that the truncation time is a predictor of T, and this causes the dependence between L and T. We develop an algorithm to obtain the adjusted risk sets and use the Kaplan-Meier estimator to estimate the Marginal distribution of L. We further extend our method to more practical situation, in which the Cox model includes other covariates associated with T. Simulation studies have been conducted to investigate the performances of the Cox model and the new estimators. INDEX WORDS: Truncation time, Dependent, Marginal distribution, Cox regression model, Kaplan-Meier method, Bootstrap method COX MODEL ANALYSIS WITH THE DEPENDENTLY LEFT TRUNCATED DATA