Analysis of Poisson Data in Crossover Experimental Designs

Author(s): Arvesen, J.

Journal/Book: Biometrics. 1978; 34: 421-428.

Abstract: The two-treatment, two-period crossover design is often used in clinical trials to compare treatments of acute symptoms of chronic diseases. In some cases of such diseases (e.g., angina pectoris and epilepsy) the acute symptoms are of an episodic nature, and the distribution of the number of attacks within a specified time period for a given patient appears to be approximately Poisson. The crossover design attempts to improve sensitivity by administering the two treatments to each patient, and also avoids bias due to order of administration by allocating some of the patients to one order of administration, and the remainder to the other order of administration. We derive exact conditional tests for treatment and order effects when the response variable is assumed to be Poisson distributed, analogous to those given by Gart (1969/ for binomial response. The tests are formally identical to the Fisher-Irwin exact test for independence in a 2 X 1 contingency table, the marginal totals being the total counts for the two orders of administration. Two examples of clinical trials are presented to illustrate the method, of which one concerns drugs used to alleviate the occurrence of nausea after cancer chemotherapy, and the second compares treatments for angina. Some power calculations are given. Approximate methods for analyzing three-drug crossovers, using weighted regression of the transformed counts, are presented.

Keyword(s): Clinical trials

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