Analysis of cross-over experiments with count data in the presence of carry-over effects

This paper presents an experimental cross-over design whose response variable is a count that belongs to the Poisson distribution. The methodology is extended to data with overdispersion or subdispersion. We present the theoretical development for analysis of cases with few treatments and a few periods. In this case, we consider the log-linear link for estimation effects and the Delta method for the asymptotic inference of the estimators. When the number of periods and sequences increases, we propose an extension of the previous methodology, using the generalized linear models. In this extension, cross-over designs for count data include treatments, sequences, time effects, covariables, and any correlation structure. The most important result of the methodology is that it allows the detection of significant factors within the cross-over design when the response variable belongs to the exponential family, especially the treatment effects. Finally, we present the analysis of data obtained in a student hydration study and a simulation study. We show a comparison between the usual methods of analysis and those obtained in the present work, demonstrating the advantage over the usual methods in situations with carry-over presence.