Testing the Equality of two Survival Functions with Doubly Truncated

Abstract

Recently, several algorithms, such as Turnbull (1976) and Efron and Petrosian (1999), have been derived from the likelihood function to estimate the survival function based on doubly truncated data. However, the nonparametric methods for comparing two survival functions have not yet been developed. Therefore, this paper proposes two test statistics to test the equality of two survival functions for doubly truncated data. One is based on the integrated weighted difference between two estimated survival functions, while the other is similar in form to the usual weighted logrank test. The comparative results from a simulation study are presented and the implementation of these methods to Taiwan?€?s building lifetimes data is presented. Keywords: Doubly truncated data, survival function, self-consistent estimator