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Several simple, intuitive, explicitly computable estimation procedures for relative risk with interval-censored data are proposed. These procedures are the modified versions of relative risk estimators for right-censored data developed by Peto, Pike, and Andersen. Simulation study is conducted to demonstrate the performances of the proposed estimators.

Several tests for comparing k groups of interval-censored data based on Turnbull's estimator of a survival function are compared by a Monte Carlo simulation study. The tests under consideration include the IWD test proposed by Petroni and Wolfe, the score test derived by Finkelstein, and a logrank type test suggested by Sun. With a large sample size and in a two-sample comparison, simulation results suggest that the IWD test is applicable for early and crossing hazard difference alternatives, whereas Finkelstein's score test, Sun's test and the logrank test are slightly more powerful than the IWD tests under late hazard difference alternatives. The IWD test is designed for the two-sample testing problem. With a large sample size and in a k-sample comparison, Finkelstein's score test is slightly better than the other tests under a proportional hazards model, while Sun's test and the logrank test are slightly better than the score test under early and crossing hazard difference alternatives. However, none of the test statistics is uniformly better than the others for the alternatives considered in this paper with both non-overlapping and overlapping interval-censored data. Copyright © 2001 John Wiley & Sons, Ltd.

Several tests for comparing kgroups of interval‐censored data based on Turnbull's estimator of a survival function are compared by a Monte Carlo simulation study. The tests under consideration include the IWD test proposed by Petroni and Wolfe, the score test derived by Finkelstein, and a logrank type test suggested by Sun. With a large sample size and in a two‐sample comparison, simulation results suggest that the IWD test is applicable for early and crossing hazard difference alternatives, whereas Finkelstein's score test, Sun's test and the logrank test are slightly more powerful than the IWD tests under late hazard difference alternatives. The IWD test is designed for the two‐sample testing problem. With a large sample size and in a k‐sample comparison, Finkelstein's score test is slightly better than the other tests under a proportional hazards model, while Sun's test and the logrank test are slightly better than the score test under early and crossing hazard difference alternatives. However, none of the test statistics is uniformly better than the others for the alternatives considered in this paper with both non‐overlapping and overlapping interval‐censored data. Copyright © 2001 John Wiley & Sons, Ltd.