Impact of mis-specification of the treatment model on estimates from a marginal structural model

Inverse probability of treatment weighted (IPTW) estimation for marginal structural models (MSMs) requires the specification of a nuisance model describing the conditional relationship between treatment allocation and confounders. However, there is still limited information on the best strategy for building these treatment models in practice. We developed a series of simulations to systematically determine the effect of including different types of candidate variables in such models. We explored the performance of IPTW estimators across several scenarios of increasing complexity, including one designed to mimic the complexity typically seen in large pharmacoepidemiologic studies.Our results show that including pure predictors of treatment (i.e. not confounders) in treatment models can lead to estimators that are biased and highly variable, particularly in the context of small samples. The bias and mean-squared error of the MSM-based IPTW estimator increase as the complexity of the problem increases. The performance of the estimator is improved by either increasing the sample size or using only variables related to the outcome to develop the treatment model. Estimates of treatment effect based on the true model for the probability of treatment are asymptotically unbiased.We recommend including only pure risk factors and confounders in the treatment model when developing an IPTW-based MSM.