Correcting for Measurement Error in Time-Varying Covariates in Marginal Structural Models

Abstract

Unbiased estimation of causal parameters from marginal structural models (MSMs) requires a fundamental assumption of no unmeasured confounding. Unfortunately, the time-varying covariates used to obtain inverse probability weights are often error-prone. Although substantial measurement error in important confounders is known to undermine control of confounders in conventional unweighted regression models, this issue has received comparatively limited attention in the MSM literature. Here we propose a novel application of the simulation-extrapolation (SIMEX) procedure to address measurement error in time-varying covariates, and we compare 2 approaches. The direct approach to SIMEX-based correction targets outcome model parameters, while the indirect approach corrects the weights estimated using the exposure model. We assess the performance of the proposed methods in simulations under different clinically plausible assumptions. The simulations demonstrate that measurement errors in time-dependent covariates may induce substantial bias in MSM estimators of causal effects of time-varying exposures, and that both proposed SIMEX approaches yield practically unbiased estimates in scenarios featuring low-to-moderate degrees of error. We illustrate the proposed approach in a simple analysis of the relationship between sustained virological response and liver fibrosis progression among persons infected with hepatitis C virus, while accounting for measurement error in γ-glutamyltransferase, using data collected in the Canadian Co-infection Cohort Study from 2003 to 2014.

Inverse‐probability‐of‐treatment weighted estimation of causal parameters in the presence of error‐contaminated and time‐dependent confounders

“…Similar to Kyle et al. (), we call this method the indirect SIMEX correction method, though there is a slight difference between the two approaches. When applying or to calculate the weights, we replace by while Kyle et al.…”

“…When applying or to calculate the weights, we replace by while Kyle et al. () replace by . Alternatively, the SIMEX algorithm can be applied to directly adjust for the measurement error effects on the IPTW estimation of by modifying Steps 2 and 3.…”

“…The widely used tools, including multiple imputation, regression calibration (RC), and simulation extrapolation (SIMEX), have been applied to reduce measurement error effects in causal inference (Cole, Chu, & Greenland, ; Edwards et al., ; Kyle, Moodie, Klein, & Abrahamowicz, ; Lenis, Ebnesajjad, & Stuart, ; Stürmer, Schneeweiss, Avorn, & Glynn, ; Webb‐Vargas, Rudolph, Lenis, Murakami, & Stuart, ). Regier, Moodie, and Platt () conducted simulation studies for time‐independent settings to understand the impact of measurement error in covariates on the IPTW estimation; although being limited in simulation settings, the findings are rather informative that measurement error in confounders may have various effects on the estimation of causal parameters: attenuation, augmentation, null effects, and sign reversals.…”

“…Kyle et al. () applied the SIMEX method (Cook & Stefanski, ) to reduce the measurement error effects on the IPTW estimation.…”

Weighted causal inference methods with mismeasured covariates and misclassified outcomes

“…[10][11][12][13][14] Many correction methods for dealing with measurement error have been developed for regression settings, where describing the association relationship is the focus. There has been little work on causal inference with measurement error, although this area has recently received increasing attention with some methods available to handle error-prone covariates, [15][16][17] misclassified treatment, 18,19 and mismeasured outcomes. 20,21 Measurement error and misclassification arise ubiquitously in applications and present a considerable challenge to statistical inference.…”