Analyzing the number of "rejection episodes" in renal transplant studies

Transplantation has become the treatment of choice for many chronic and debilitating diseases. Generally, the primary endpoints in evaluating therapy are graft and patient survival time. However, an important secondary outcome is the number of "rejection episodes" experienced by study patients. This response has a distinctive statistical character. That is, it is a categorical variable since it assumes only a small number of integer values, but it is measured on a ratio-level scale since the ratio of any two values is scientifically meaningful. Historical methods for analyzing this endpoint, for example, t tests, logistic regression and Kaplan-Meier analysis, have failed to take these characteristics into account. In this study, we investigated statistical procedures for analyzing the number of rejection episodes arising during the first three months posttransplant. Data compiled by the Multiple Organ Retrieval and Exchange (MORE) of the Province of Ontario were used for this purpose. It was found that assumptions underlying normal distributional techniques were not satisfied by these data. An alternative model based on Poisson regression models was considered and was shown to provide an adequate fit.