On the use and utility of the Weibull model in the analysis of survival data

In the analysis of survival data arising in clinical trials, Cox's proportional hazards regression model (or equivalently in the case of two treatment groups, the log-rank test) is firmly established as the accepted, statistical norm. The wide popularity of this model stems largely from extensive experience in its application and the fact that it is distribution free—no assumption has to be made about the underlying distribution of survival times to make inferences about relative death rates. However, if the distribution of survival times can be well approximated, parametric failure-time analyses can be useful, allowing a wider set of inferences to be made. The Weibull distribution is unique in that it is the only one that is simultaneously both proportional and accelerated so that both relative event rates and relative extension in survival time can be estimated, the latter being of clear clinical relevance. The aim of this paper is to examine the use and utility of the Weibull model in the analysis of survival data from clinical trials and, in doing so, illustrate the practical benefits of a Weibull-based analysis.