In this paper we propose a generalized rank test based on discrete interval-censored failure time data to determine whether two lifetime populations come from the same distribution. It reduces to the Logrank test or Wilcoxon test when one has exact or right-censored data. Simulation shows that the proposed test performs pretty satisfactory. An example is presented to demonstrate how the proposed test can be applied in AIDS study.

In Part 1 of this paper, we adapt Turnbull¡¦s algorithm to estimate the distribution function of univariate interval-censored and truncated failure time data. We also propose four non-parametric tests to test whether two groups of the data come from the same distribution. The powers of proposed test statistics are compared by simulation under different distributions. The proposed tests are then used to analyze an AIDS study. In Part 2, for bivariate interval-censored data, we propose some models of how to generate the data and several methods to measure the correlation between the two variates. We also propose several nonparametric tests to determine whether the two variates are mutually independent or whether they have the same distribution. We demonstrate the performance of these tests by simulation and give an application to AIDS study¡]ACTG 181¡^.