Estimating Additive Interaction Effect in Stratified Two-Phase Case-Control Design

There is considerable interest in epidemiology to estimate an additive interaction effect between two risk factors in case-control studies. An additive interaction is defined as the differential reduction in absolute risk associated with one factor between different levels of the other factor. A stratified two-phase case-control design is commonly used in epidemiology to reduce the cost of assembling covariates. It is crucial to obtain valid estimates of the model parameters by accounting for the underlying stratification scheme to obtain accurate and precise estimates of additive interaction effects. The aim of this paper is to examine the properties of different methods for estimating model parameters and additive interaction effects under a stratified two-phase case-control design.

Using simulations, we investigate the properties of three existing methods, namely stratum-specific offset, inverse-probability weighting, and multiple imputation for estimating model parameters and additive interaction effects. We also illustrate these properties using data from two published epidemiology studies.

Simulation studies show that the multiple imputation method performs well when both the true and analysis models are additive (i.e., does not include multiplicative interaction terms) but does not provide a discernible advantage over the offset method when the analysis models are non-additive (i.e., includes multiplicative interaction terms). The offset method exhibits the best overall properties when the analysis model contains multiplicative interaction effects.

When estimating additive interaction between risk factors in stratified two-phase case-control studies, we recommend estimating model parameters using multiple imputation when the analysis model is additive, and we recommend the offset method when the analysis model is non-additive.