Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series A, Pt. 3, 722--739

A HOLISTIC ANALYSIS OF POISSON DATA WITH APPLICATION TO A TRIAL OF SELENIUM AND CANCER DEATHS

By

DENNIS V. LINDLEY

SUMMARY. We consider a comparative trial of a new treatment against a standard, where the data are Poisson. The novelty is that the likelihood for the data is placed in the scientific context and the model incorporates both data uncertainty and initial uncertainty about the parameters. Both estimation and hypothesis-testing are discussed. The analysis is applied to a clinical trial of the effect of selenium on cancer deaths. Several assumptions have been made to simplify the analysis; in a final section it is shown how these might be relaxed.

DEDICATION.Dev Basu's work was marked by profound simplicity; he would take a deep problem and analyse it with outstanding clarity, revealing a solution that was correct and, above all, had that great virtue of simplicity. In offering this paper as a tribute to the memory of one of the finest statisticians it has been my good fortune to meet, I have tried to take a simple problem and analyse it in its complicated, real-world context, in the hope that the offered solution will have a few of the features that he would have produced.

*AMS (1991) subject classification}. *Primary 62F15; secondary 62P10, 62P30.

*Key words and phrases. *Reliability, clinical trials, Poisson, exponential, negative binomial, $F$-distribution, Bayes factor, elimination of nuisance parameters, likelihood, $\chi^2$-distribution, estimation, hypothesis tests, conjugate distributions.