Analyzing counts, durations, and recurrences in clinical trials

In 1985 the (Byar and Blackard, Urology, Vol. X, 556-561, 1978) data set on bladder cancer became available to researchers. Since then, a number of studies have made use of it. However, none of these has fully utilized all of the data nor have they developed a methodology in which it is possible to estimate models of the number of recurrences and durations that are consistent with each other. The purpose of this research is to determine which, if any, of the two drugs used in the trial, pyridoxine and theotepa, were effective and, by example, illustrate procedures that could be useful in the analysis of other clinical trial data sets. First, the number of recurrences is modeled as a count using the Poisson and negative binomial distributions with covariates. Then Poisson models are tested on the durations. Finally, durations and tumor counts per recurrence are fitted to more general autoregressive Wiebull and negative binomial distributions, respectively. Poisson models for durations are rejected in favor of the more general autoregressive models. The data on durations and tumor counts are shown to be more reliable from an inference point of view than the data on the number of recurrences. The data on durations and tumor counts show quite conclusively that both drugs are effective in treating bladder cancer, a result that differs from what others have found.