Marginal models for the analysis of crossover experiments with a categorical response.

Abstract

In many applications giving rise to repeated categorical measurements, interest often focuses on modeling the effects of covariates on the marginal probability of response. This is true for crossover experiments where primary interest is in modeling the marginal probability of response to each treatment, while simultaneously accounting for the dependence of within-subject responses and the possibility of period effects, carryover effects, and treatment-by-period interactions. It is well known that specification of a model for the marginal probabilities does not completely specify the model for the cell probabilities. Methods that have been proposed in the literature to circumvent this problem are reviewed. An alternative strategy is to provide a model for the association structure of the data, in addition to a model for the marginal probabilities. The transformation from the cell probabilities to the marginal probabilities and associations becomes one-to-one, thus facilitating the use of conventional likelihood methodology. The utility of this full likelihood approach to the analysis of marginal probabilities from crossover experiments is explored. A marginal model specified in terms of linear models for marginal logits and linear models for log-odds ratios is proposed for the analysis of binary data from two-period crossover experiments. An appealing feature of the model is that parameters have straightforward interpretations. The marginal model for the binary, two-period design is extended to handle polytomous (ordinal and nominal) responses and multiperiod designs, and accommodate within-subject, as well as between-subject, covariates measured on categorical or continuous scales. For two-period designs, the marginal model is readily inverted into a model for the cell probabilities. An alternative strategy for model fitting based on the constraint-equations specification of the model is considered for situations where model inversion is not as straightforward. Using both real and simulated data, the full likelihood approach is shown to be a useful and feasible alternative for modeling marginal probabilities of response from crossover experiments. Results of a simulation study showed that likelihood inference based on the proposed models compared favorably to the Mainland-Gart test and Prescott's test for a treatment effect, Gart's test and Prescott's test for a period effect, and the Hills-Armitage test for a treatment-by-period interaction.