A Generalized Log‐Rank‐Type Test for Comparing Survivals with Doubly Interval‐Censored Data

Abstract

In doubly interval-censored data, the survival time of interest is defined as the elapsed time between an initial event and a subsequent event, but the occurrences of both events cannot be observed exactly. Instead, only right- or interval-censored observations on the occurrence times are available. Our purpose is to develop a generalized log-rank-type test for comparing survival functions of several groups. For the same problem, Sun (The Statistical Analysis of Interval-censored Failure Time Data, Springer, New York) suggested a nonparametric test based on the estimated marginal survival functions of the two related events. We consider a new method using uniform weights, which depend only on the size of the risk set at each observed time. The proposed method does not require the estimation of marginal survival functions and furthermore can reduce to the log-rank test for right-censored data. Results from a simulation study show that our test performs well in terms of size and power. We analyze the AIDS cohort study data taken from Kim et al. (Biometrics 49, 13-22).