An approach for parametric survival ANOVA with application to Weibull distribution

Motivated by the serious Type-I error issues of widely used Cox-PH method in survival analysis, this article introduces an approach one can take in deriving superior parametric tests based on distributions such as the gamma, lognormal, and Weibull. Some of the data available from such distributions are allowed to be censored, as usually the case in dealing with lifetime distributions. Since the classical approach fails to provide reasonable procedures to test the equality of means of a number of Weibull populations, beyond the two populations case, we will show how to apply the generalized inference approach to do so in a novel manner. The approach should work in other scale invariant distributions, such as the gamma and lognormal. The approach is illustrated with the Weibull distributions, taking advantage of the fact that the original data from continuous distributions can be transformed into normally distributed data leading to exact generalized test variables.