A class of two-sample test statistics for stochastically ordered distribution functions with interval censored data.

A new family of non-parametric two-sample tests for discrete interval censored data is proposed. This new class is an extension of the concepts developed by Pepe and Fleming (1989) for right censored data. The class of statistics is based upon an integrated weighted difference in survival functions and is sensitive against the alternative of stochastic ordering. Turnbull's (1976) estimator of the survival function is employed. Asymptotic distribution theory is developed yielding approximate test procedures for the null hypothesis. The choice of appropriate weight functions, to ensure the stability of the statistic, is investigated. With uncensored data, the procedure reduces to the z-test. Simulation studies were performed to evaluate the size and power of the test procedure. Qualitative comparisons were made between the new test statistic and the likelihood ratio test for interval censored data, and the z-test and logrank test for complete data. The use of transformations of time were also investigated since the proposed statistics are not based on ranks. Results from the simulation studies indicate that for interval censored data the WTD procedure is superior to the likelihood ratio test under a broad range of stochastically ordered alternatives. For crossing hazards alternatives, the WTD procedure can be superior to the logrank test, based on uncensored data. For sample sizes ranging from 20 to 50 with moderate censoring, the size of the test is close to the nominal size and the test has good power.PhDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/105258/1/9116268.pdfDescription of 9116268.pdf : Restricted to UM users only