A Bayesian Analysis of Categorical and Count Pharmacodynamic Data

These types of measures are not as easily modelled as the continuous case and therefore require careful consideration. We have used a utility function approach in a decision analysis framework to define the therapeutic window for noncontinuous efficacy and toxicity measures.

The data that were analyzed relate to a drug for the treatment/reduction of incontinence. Data were available from a longitudinal, forced dose-escalating clinical trial comparing two formulations of a drug and placebo. The currently available formulation is an immediate release formulation, while the newly developed formulation of the drug is an extended release formulation. The efficacy measure was the number of incontinence episodes in a seven day period. The toxicity measure used was an ordinal categorical variable based on the degree of dry mouth reported with the categories being defined as: 0 = no dry mouth, 1 = mild, 2 = moderate, 3 = severe dry mouth. Due to the design of the study, dose was completely confounded with time. Since there was a placebo group, it was possible to check for any time effect in the data.

The BUGS (Bayesian Inference Using Gibbs Sampling) 0.6 software was used to carry out the Bayesian analysis. Generalized linear mixed effects models were used to model the efficacy and toxicity independently. A log linear model was used for the efficacy data and a proportional odds model for the toxicity data. The purpose of this analysis was to define a utility function based on the efficacy and toxicity data of the two formulations. Based on the analysis, the extended formulation is predicted to have a wider therapeutic window. A sensitivity analysis was also carried out which showed that, although the bounds on the therapeutic window changed, the new extended release formulation is predicted to have wider therapeutic index than immediate release.