Semiparametric and nonparametric modeling for effect modification in matched studies

This study describes a new graphical method for assessing and characterizing e$ect modi%cation by a matching covariate in matched case–control studies. This method to understand e$ect modi%cation is based on a semiparametric model using a varying coe2cient model. The method allows for nonparametric relationships between e$ect modi%cation and other covariates, or can be useful in suggesting parametric models. This method can be applied to examining e$ect modi%cation by any ordered categorical or continuous covariates for which cases have been matched with controls. The method applies to e$ect modi%cation when causality might be reasonably assumed. An example from veterinary medicine is used to demonstrate our approach. The simulation results show that this method, when based on linear, quadratic and nonparametric e$ect modi%cation, can be more powerful than both a parametric multiplicative model %t and a fully nonparametric generalized additive model %t. c © 2003 Elsevier B.V. All rights reserved.