A weighting approach to causal effects and additive interaction in case-control studies: marginal structural linear odds models.

Estimates of additive interaction from case-control data are often obtained by logistic regression; such models can also be used to adjust for covariates. This approach to estimating additive interaction has come under some criticism because of possible misspecification of the logistic model: If the underlying model is linear, the logistic model will be misspecified. The authors propose an inverse probability of treatment weighting approach to causal effects and additive interaction in case-control studies. Under the assumption of no unmeasured confounding, the approach amounts to fitting a marginal structural linear odds model. The approach allows for the estimation of measures of additive interaction between dichotomous exposures, such as the relative excess risk due to interaction, using case-control data without having to rely on modeling assumptions for the outcome conditional on the exposures and covariates. Rather than using conditional models for the outcome, models are instead specified for the exposures conditional on the covariates. The approach is illustrated by assessing additive interaction between genetic and environmental factors using data from a case-control study.