Dynamic Treatment Effect Analysis in Crossover Designs Through Repeated Measures

This paper introduces an extended model that harnesses the power of convolution operations to represent time-varying treatment and carry-over effects in a crossover study design. Unlike the traditional model, the proposed approach unifies the treatment and carry-over effects through time-varying response functions, one for each treatment. The model is not only flexible enough to accommodate a variety of treatment plans, including multiple administrations at different doses, but also allows for the inclusion of more treatment periods. The advantages of this approach are accentuated by its ability to be generalized, to avoid prior assumptions about the carry-over effect, and to maintain consistent estimation and hypothesis testing procedures. In this paper, we explore the details of hypothesis testing under this extended model, focusing in particular on the comparison of two response functions within specified intervals. The goal of this work is to improve the modeling of carry-over effects, thereby strengthening the applicability of the model to a variety of experimental settings.