Estimation of complex carryover effects in crossover designs with repeated measures

It has been argued that the models used to analyze data from crossover designs are not appropriate when simple carryover effects are assumed. In this paper, the estimability conditions of the carryover effects are found, and a theoretical result that supports them, additionally, two simulation examples are developed in a non-linear dose-response for a repeated measures crossover trial in two designs: the traditional AB/BA design and a Williams square. Both show that a semiparametric model can detect complex carryover effects and that this estimation improves the precision of treatment effect estimators. We concluded that when there are at least five replicates in each observation period per individual, semiparametric statistical models provide a good estimator of the treatment effect and reduce bias with respect to models that assume either, the absence of carryover or simplex carryover effects. In addition, an application of the methodology is shown and the richness in analysis that is gained by being able to estimate complex carryover effects is evident.