Semiparametric Analysis of Covariance Model for a Crossover Design with Carryover Effects

We postulate a semiparametric mixed analysis of the covariance model for a crossover design with carryover effects. The model is estimated via a hybrid of restricted maximum likelihood estimation and smoothing splines regression embedded into the backfitting algorithm. To mitigate heterogeneity in experimental settings common in clinical trials, responses are adjusted using a nonparametric function of the covariates. A bootstrap-based test for random treatment effect using the adjusted responses is also proposed. Simulation studies indicate that the bootstrap-based test for variance components is correctly sized. The test is also powerful and is relatively robust to the magnitude of variance in the alternative hypothesis. Furthermore, the test is advantageous over classical analysis of covariance in the presence of design and measurement issues in experiments.