Conditional and exact tests in crossover trials

Generalized linear models are developed for crossover trials with no carryover effects and fixed subject effects. A general multinominal model for the distribution of data is considered. This subsumes both binary and categorical data. Conditional inferences eliminate subject effects by conditioning on their sufficient statistics. For normal data, least-squares analysis is exact with identical treatment inferences from unconditional and conditional analyses. For Poisson data, unconditional and conditional analyses are also identical, but for multinomial data this is not the case and the unconditional analysis is invalid. For multinomial data, asymptotic tests of both treatment effects and goodness of fit are unreliable with small samples. Procedures for exact tests are developed to overcome such problems, using enumeration, random sampling, and a hybrid of importance sampling and enumeration. A four-period binary crossover trial is used to illustrate an exact test of treatment effects by a two-stage sampling procedure based on a factorization of the conditional distribution of the sufficient statistics. An exact test of goodness of fit on the same data illustrates a two-stage scheme mixing importance sampling and enumeration.