Personalized treatment selection using data from crossover designs with carry-over effects

In this work, we propose a semiparametric method for estimating the optimal treatment for a given patient based on individual covariate information for that patient when data from a crossover design are available. Here, we assume there are carry-over effects for patients switching from one treatment to another. For the K treatment (K ≥ 2) scenario, we show that nonparametric estimation of carry-over effects can have the undesirable property that comparison of treatment means can only be done using independent outcome measurements from different groups of patients rather than using available joint measurements for each patient. To overcome this barrier, we compare probabilities of outcome variable of each treatment dominating outcome variables for all other treatments conditional on patient-specific scores constructed from patient covariates. We suggest single-index models as appropriate models connecting outcome variables to covariates and our empirical investigations show that frequencies of correct treatment assignments are highly accurate. The proposed method is also rather robust against departures from a single-index model structure. We also conduct a real data analysis to show the applicability of the proposed procedure.