Testing Homogeneity of Two Zero‐inflated Poisson Populations

Abstract

The problem of testing treatment difference in the occurrence of a safety parameter in a randomized parallel-group comparative clinical trial under the assumption that the number of occurrence follows a zero-inflated Poisson (ZIP) distribution is considered. Likelihood ratio tests (LRT) for homogeneity of two ZIP populations are derived under the hypotheses that (i) there is no difference in inflation parameters, (ii) there is no difference in non-zero means; and (iii) there is no difference in both inflation parameters and non-zero means. Approximate formulas for sample size calculation are also obtained for achieving a desired power for detecting a clinically meaningful difference under the corresponding alternative hypotheses. An example concerning the assessment of the gastrointestinal (GI) safety in terms of the number of erosion counts of a newly developed compound for the treatment of osteoarthritis and rheumatoid arthritis is given for illustration purpose.