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

Abstract

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.

Impact of sedation and analgesia during noninvasive positive pressure ventilation on outcome: a marginal structural model causal analysis

“…However, we included numerous measured covariates but the assumption of positivity would have not been fulfilled. The use of truncated weight would attenuate this limitation [22].…”

Missing Confounding Data in Marginal Structural Models: A Comparison of Inverse Probability Weighting and Multiple Imputation

“…More specifically, we investigate the impact of varying levels of missingness of a confounding variable, and of different assumptions regarding the nature of missingness under three missing data strategies: complete-case analysis, our inverse probability weighting method, and multiple imputation. We allow missing data only in the confounding variable, as previous research has shown that this is the only variable without which the treatment model in the MSM cannot be estimated without introducing bias in the estimate of treatment effect (Lefebvre et al, 2008). We consider only scenarios where time-dependent confounding is observed, as this is the context in which MSMs or other related approaches are necessary Petersen et al, 2006).…”

“…Note that the model for A(1) includes an additional variable, V (0), that is a risk factor for the outcome but is not a cause of the treatment being modeled. This model conditions on the available past information and is therefore both a natural and a useful model to consider, as the inclusion of predictors of the outcome in the treatment model improves the accuracy of the treatment effect estimates (Lefebvre et al, 2008).…”

The Effect of Error-in-Confounders on the Estimation of the Causal Parameter When Using Marginal Structural Models and Inverse Probability-of-Treatment Weights: A Simulation Study

“…McCaffrey et al [30] propose an inverse probability weighting correction for error-prone covariates for propensity scores that builds on the work of Pearl [31], but does not consider the MSM context. As a counter point to these approaches, it has been shown that ideal performance of effect estimators is observed when treatment weights (propensity scores) exclude covariates that serve only to predict the treatment (exposure) but not the outcome [32][33][34], thus further investigations are warranted as such data relationships are typically not known. The propensity score literature provides direction for the use of statistical learners when the data are error-free, but there are unanswered questions about the ability of statistical learners to obtain unbiased estimates or bias-reduced estimates when confounders are mismeasured.…”