Semiparametric regression models for detecting effect modification in matched case-crossover studies

In matched case-crossover studies, it is generally accepted that covariates on which a case and associated controls are matched cannot exert a confounding effect on independent predictors included in the conditional logistic regression model because any stratum effect is removed by the conditioning on the fixed number of sets of a case and controls in the stratum. Hence, the conditional logistic regression model is not able to detect any effects associated with the matching covariates by stratum. In addition, the matching covariates may be effect modification and the methods for assessing and characterizing effect modification by matching covariates are quite limited. In this article, we propose a unified approach in its ability to detect both parametric and nonparametric relationships between the predictor and the relative risk of disease or binary outcome, as well as potential effect modifications by matching covariates. Two methods are developed using two semiparametric models: (1) the regression spline varying coefficients model and (2) the regression spline interaction model. Simulation results show that the two approaches are comparable. These methods can be used in any matched case-control study and extend to multilevel effect modification studies. We demonstrate the advantage of our approach using an epidemiological example of a 1-4 bi-directional case-crossover study of childhood aseptic meningitis associated with drinking water turbidity.