Comparison of causal effect estimators under exposure misclassification

• Published in: Journal of statistical planning and inference Vol. 140; no. 5; pp. 1306 - 1319
• Main Authors: Babanezhad, Manoochehr, Vansteelandt, Stijn, Goetghebeur, Els
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01.05.2010; Elsevier
• Subjects: Causal inference; Exact sciences and technology; General topics; Inverse probability of treatment weighted estimator; Linear inference, regression; Marginal structural model; Mathematics; Misclassification; Probability and statistics; Propensity score; Sciences and techniques of general use; Statistics; Time-varying confounding; Causal inference; Inverse probability of treatment weighted estimator; Propensity score; Misclassification; Marginal structural model; Time-varying confounding; Estimation strategy; Error estimation; Estimator robustness; Probability distribution; Statistical simulation; Linear model; estimator; Least squares method; Marginal distribution; Inverse probability of treatment weighted; Linear regression; Probability; Statistical estimation; Bad classification; Statistical decision; Mean estimation; Statistical method; Statistical regression; Regression model; Structural model
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2009.11.015

Over the past decades, various principles for causal effect estimation have been proposed, all differing in terms of how they adjust for measured confounders: either via traditional regression adjustment, by adjusting for the expected exposure given those confounders (e.g., the propensity score), or by inversely weighting each subject's data by the likelihood of the observed exposure, given those confounders. When the exposure is measured with error, this raises the question whether these different estimation strategies might be differently affected and whether one of them is to be preferred for that reason. In this article, we investigate this by comparing inverse probability of treatment weighted (IPTW) estimators and doubly robust estimators for the exposure effect in linear marginal structural mean models (MSM) with G-estimators, propensity score (PS) adjusted estimators and ordinary least squares (OLS) estimators for the exposure effect in linear regression models. We find analytically that these estimators are equally affected when exposure misclassification is independent of the confounders, but not otherwise. Simulation studies reveal similar results for time-varying exposures and when the model of interest includes a logistic link.