Test of equality of proportional hazard models with jointly censored data

This paper addresses the problem of and solutions to the equality of two samples following the same class of nonlinear models. The test statistic used is based on the partial likelihood estimate from two independent samples with proportional hazard under complete and censored samples. By assuming that the hazard function is time-dependent, we develop exact inference for the partial likelihood estimate of the ratio of two hazard rates. The results obtained are important for testing the equality of sampling distributions and evaluating parameters for the hazard models. We propose a new sequential test based on the partial likelihood estimate, followed by an efficient computational methodology for exact inferential statistics. Examples are provided to demonstrate the implementation of our statistical testing procedure.