Goodness-of-fit Tests and Minimum Power Divergence Estimators for Survival Data

Power-divergence statistics are proposed for grouped survival data. They are analogous to the power-divergence family of statistics proposed and studied in detail by Read and Cressie (1988) and Cressie and Read (1984) for contingency tables. The proposed statistics are useful for testing validity of parametric model assumptions in analyses of survival data. It is shown that these statistics have approximately chi-squared distribution under the null hypothesis. They can be used to construct parameter estimates that are consistent and asymptotically normal under usual regularity conditions. Simulation studies indicate that, with a suitable choice of the tuning parameter, the chi-squared approximation performs quite well even with small to moderate sample sizes. The approach is illustrated with a data set from the reaction control system of the Space Shuttle.