A new class of generalized log rank tests for interval-censored failure time data

This paper discusses nonparametric comparison of survival functions when one observes only interval-censored failure time data (Peto and Peto, 1972, Sun, 2006 and Zhao et al., 2008). For the problem, a few procedures have been proposed in the literature. However, most of the existing test procedures determine the test results or pp-values based on ad hoc methods or the permutation approach. Furthermore for the test procedures whose asymptotic distributions have been derived, the results are only for the null hypothesis. In other words, no nonparametric test procedure exists that has a known asymptotic distribution under the alternative hypothesis and thus can be employed to carry out the power and test size calculation. In this paper, a new class of generalized log-rank tests is proposed and their asymptotic distributions are derived under both null and alternative hypotheses. A simulation study is conducted to assess their performance for finite sample situations and an illustrative example is provided.