Failure-Time Mixture Models: Yet Another Way to Establish Efficacy

We propose to use mixture survival models to establish the efficacy of the trial treatment. In particular, we consider the lognormal distribution to model the right-censored event time and a logistic regression for the incidence part of the model. The model attempts to estimate simultaneously the effects of treatments on the acceleration/deceleration of the timing of a given event and the surviving fraction—the proportion of the population for which the event may never occur. We use the SAS/IML subroutine NLPTR to obtain the maximum likelihood estimates of the model parameters. The estimates of the standard errors of the parameter estimates are computed from the inverse of the observed information matrix. We use the Cox-Snell residual plot based on the unconditional survivor function for evaluating goodness-of-fit of the model. The principal research hypothesis will be that under the trial treatment, the time-to-event will be more decelerated/accelerated compared to the control, given that the event occurs. We suggest that this methodology could be considered as a means to establish efficacy. We emphasize that there can be a substantial advantage to using mixture models even when the log-rank test is valid and significant. Data on overall survival time from a typical colorectal cancer clinical trial are used to illustrate the procedure.