A two-sample test for stochastic ordering with interval-censored data

A new class of asymptotically nonparametric two-sample approximate tests for discrete interval-censored data is proposed. This class extends the family developed by Pepe and Fleming (1989, Biometrics 45, 497-507) for right-censored data and is based on an integrated weighted difference in survival function estimates. The tests are sensitive to the alternative of stochastic ordering and use Turnbull's (1976, Journal of the Royal Statistical Society, Series B 38, 290-295) estimator of the survival function. The choice of appropriate weight functions is investigated. Simulation results indicate that for interval-censored data the new procedure, with an appropriate weight function, can be more powerful than an omnibus likelihood ratio test and Mantel's (1967, Biometrics, 23, 65-78) test under a broad range of stochastically ordered alternatives. For small sample sizes (n = 50), with moderate censoring (47% and 70%), the size of the test is close to the nominal size.