Semiparametric regression splines in matched case-control studies

We develop semiparametric methods for matched case-control studies using regression splines. Three methods are developed: 1) an approximate cross-validation scheme to estimate the smoothing parameter inherent in regression splines, as well as 2) Monte Carlo expectation maximization (MCEM) and 3) Bayesian methods to fit the regression spline model. We compare the approximate cross-validation approach, MCEM, and Bayesian approaches using simulation, showing that they appear approximately equally efficient; the approximate cross-validation method is computationally the most convenient. An example from equine epidemiology that motivated the work is used to demonstrate our approaches.