Assessing Poisson variation of intestinal tumour multiplicity in mice carrying a Robertsonian translocation

Summary.  Tumour multiplicity is a frequently measured phenotype in animal studies of cancer biology. Poisson variation of this measurement represents a biological and statistical reference point that is usually violated, even in highly controlled experiments, owing to sources of variation in the stochastic process of tumour formation. A recent experiment on murine intestinal tumours presented conditions which seem to generate Poisson-distributed tumour counts. If valid, this would support a claim about mechanisms by which the adenomatous polyposis coli gene is inactivated during tumour initiation. In considering hypothesis testing strategies, model choice and Bayesian approaches, we quantify the positive evidence favouring Poisson variation in this experiment. Statistical techniques used include likelihood ratio testing, the Bayes and Akaike information criteria, negative binomial modelling, reversible jump Markov chain Monte Carlo methods and posterior predictive checking. The posterior approximation that is based on the Bayes information criterion is found to be quite accurate in this small n case-study.