A Compound Model of Multiple Treatment Selection with Applications to Marginal Structural Modeling

Methods of causal inference are used to estimate treatment effectiveness for non-randomized study designs. The propensity score (i.e., the probability that a subject receives the study treatment conditioned on a set of variables related to treatment and/or outcome) is often used with matching or sample weighting techniques to, ideally, eliminate bias in the estimates of treatment effect due to treatment decisions. If multiple treatments are available, the propensity score is a function of the adjustment set and the set of possible treatments. This paper develops a compound model that separates the treatment decision into a binary decision: treat or dont treat; and a potential treatment decision: choose the treatment that would be given if the subject is treated. It is applicable if the treatment set is finite, treatments are given at one time point, and the outcome is observed at a fixed time point. This representation can reduce bias when not all treatments are available to all patients. Multiple treatment stabilized marginal structural weights were calculated with this approach, and the method was applied to an observational study to evaluate the effectiveness of different neutralizing monoclonal antibodies to treat infection with various severe acute respiratory syndrome coronavirus 2 variants.