Estimation of risk factor associations when the response is influenced by medication use: an imputation approach

When the outcome of interest is a quantity whose value may be altered through the use of medications, estimation of associations with this outcome is a challenging statistical problem. For participants taking medication the treated value is observed, but the underlying 'untreated' value may be the measure that is truly of interest. Problematically, those with the highest untreated values may have some of the lowest observed measurements due to the effectiveness of medications. In this paper we propose an approach in which we parametrically estimate the underlying untreated variable of interest as a function of the observed treated value, and dose and type of medication. Multiple imputation is used to incorporate the variability induced by the estimation. We show that this approach yields more realistic parameter estimates than other more traditional approaches to the problem and that study conclusions may be altered in a meaningful way by using the imputed values.