Sensitivity analysis for bias due to a misclassfied confounding variable in marginal structural models

TL;DR

This paper examines how misclassification of confounding variables biases treatment effect estimates in marginal structural models, proposing a sensitivity analysis method and demonstrating its utility through simulations and a real case study.

Contribution

It introduces a novel sensitivity analysis approach for bias due to confounder misclassification in MSMs and compares its impact with conditional models.

Findings

Bias in MSMs-IPW can differ in magnitude but not in sign from conditional models.

Confidence intervals from MSMs-IPW tend to be wider with better coverage.

Simulation results highlight the importance of accounting for classification error in causal inference.

Abstract

In observational research treatment effects, the average treatment effect (ATE) estimator may be biased if a confounding variable is misclassified. We discuss the impact of classification error in a dichotomous confounding variable in analyses using marginal structural models estimated using inverse probability weighting (MSMs-IPW) and compare this with its impact in conditional regression models, focusing on a point-treatment study with a continuous outcome. Expressions were derived for the bias in the ATE estimator from a MSM-IPW and conditional model by using the potential outcome framework. Based on these expressions, we propose a sensitivity analysis to investigate and quantify the bias due to classification error in a confounding variable in MSMs-IPW. Compared to bias in the ATE estimator from a conditional model, the bias in MSM-IPW can be dissimilar in magnitude but the bias will always be equal in sign. A simulation study was conducted to study the finite sample performance of MSMs-IPW and conditional models if a confounding variable is misclassified. Simulation results showed that confidence intervals of the treatment effect obtained from MSM-IPW are generally wider and coverage of the true treatment effect is higher compared to a conditional model, ranging from over coverage if there is no classification error to smaller under coverage when there is classification error. The use of the bias expressions to inform a sensitivity analysis was demonstrated in a study of blood pressure lowering therapy. It is important to consider the potential impact of classification error in a confounding variable in studies of treatment effects and a sensitivity analysis provides an opportunity to quantify the impact of such errors on causal conclusions. An online tool for sensitivity analyses was developed: https://lindanab.shinyapps.io/SensitivityAnalysis.