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

Consistent inverse probability of treatment weighted estimation of the average treatment effect with mismeasured time-dependent confounders

In longitudinal studies, the inverse probability of treatment weighted (IPTW) method is commonly employed to estimate the effect of time-dependent treatments on an outcome of interest. However, it has been documented that when the confounders are subject to measurement error, the naive IPTW method which simply ignores measurement error leads to biased treatment effect estimation. In the existing literature, there is a lack of measurement error correction methods that fully remove measurement error effect and produce consistent treatment effect estimation. In this article, we develop a novel consistent IPTW estimation procedure for longitudinal studies. The key step of the proposed method is to use the observed data to construct a corrected function that is unbiased of the unknown IPTW function. Simulation studies reveal that the proposed method outperforms the existing consistent and approximate measurement error correction methods for IPTW estimation of the average treatment effect. Finally, we apply the proposed method to analyze a real dataset.

Estimation of the average treatment effect with variable selection and measurement error simultaneously addressed for potential confounders

In the framework of causal inference, the inverse probability weighting estimation method and its variants have been commonly employed to estimate the average treatment effect. Such methods, however, are challenged by the presence of irrelevant pre-treatment variables and measurement error. Ignoring these features and naively applying the usual inverse probability weighting estimation procedures may typically yield biased inference results. In this article, we develop an inference method for estimating the average treatment effect with those features taken into account. We establish theoretical properties for the resulting estimator and carry out numerical studies to assess the finite sample performance of the proposed estimator.

Adapting SIMEX to correct for bias due to interval-censored outcomes in survival analysis with time-varying exposure

Many clinical and epidemiological applications of survival analysis focus on interval-censored events that can be ascertained only at discrete times of clinic visits. This implies that the values of time-varying covariates are not correctly aligned with the true, unknown event times, inducing a bias in the estimated associations. To address this issue, we adapted the simulation-extrapolation (SIMEX) methodology, based on assessing how the estimates change with the artificially increased time between clinic visits. We propose diagnostics to choose the extrapolating function. In simulations, the SIMEX-corrected estimates reduced considerably the bias to the null and generally yielded a better bias/variance trade-off than conventional estimates. In a real-life pharmacoepidemiological application, the proposed method increased by 27% the excess hazard of the estimated association between a time-varying exposure, representing the 2-year cumulative duration of past use of a hypertensive medication, and the hazard of nonmelanoma skin cancer (interval-censored events). These simulation-based and real-life results suggest that the proposed SIMEX-based correction may help improve the accuracy of estimated associations between time-varying exposures and the hazard of interval-censored events in large cohort studies where the events are recorded only at relatively sparse times of clinic visits/assessments. However, these advantages may be less certain for smaller studies and/or weak associations.

A semiparametric method for evaluating causal effects in the presence of error-prone covariates

The goal of most empirical studies in social sciences and medical research is to determine whether an alteration in an intervention or a treatment will cause a change in the desired outcome response. Unlike randomized designs, establishing the causal relationship based on observational studies is a challenging problem because the ceteris paribus condition is violated. When the covariates of interest are measured with errors, evaluating the causal effects becomes a thorny issue. We propose a semiparametric method to establish the causal relationship, which yields a consistent estimator of the average causal effect. The method we proposed results in locally efficient estimators of the covariate effects. We study their theoretical properties and demonstrate their finite sample performance on simulated data. We further apply the proposed method to the Stroke Recovery in Underserved Populations (SRUP) study by the National Institute on Aging.

Formulating causal questions and principled statistical answers

Although review papers on causal inference methods are now available, there is a lack of introductory overviews on what they can render and on the guiding criteria for choosing one particular method. This tutorial gives an overview in situations where an exposure of interest is set at a chosen baseline ("point exposure") and the target outcome arises at a later time point. We first phrase relevant causal questions and make a case for being specific about the possible exposure levels involved and the populations for which the question is relevant. Using the potential outcomes framework, we describe principled definitions of causal effects and of estimation approaches classified according to whether they invoke the no unmeasured confounding assumption (including outcome regression and propensity score-based methods) or an instrumental variable with added assumptions. We mainly focus on continuous outcomes and causal average treatment effects. We discuss interpretation, challenges, and potential pitfalls and illustrate application using a "simulation learner," that mimics the effect of various breastfeeding interventions on a child's later development. This involves a typical simulation component with generated exposure, covariate, and outcome data inspired by a randomized intervention study. The simulation learner further generates various (linked) exposure types with a set of possible values per observation unit, from which observed as well as potential outcome data are generated. It thus provides true values of several causal effects. R code for data generation and analysis is available on www.ofcaus.org, where SAS and Stata code for analysis is also provided.

Quantitative Bias Analysis for a Misclassified Confounder: A Comparison Between Marginal Structural Models and Conditional Models for Point Treatments

Observational data are increasingly used with the aim of estimating causal effects of treatments, through careful control for confounding. Marginal structural models estimated using inverse probability weighting (MSMs-IPW), like other methods to control for confounding, assume that confounding variables are measured without error. The average treatment effect in an MSM-IPW may however be biased when a confounding variable is error prone. Using the potential outcome framework, we derive expressions for the bias due to confounder misclassification in analyses that aim to estimate the average treatment effect using an marginal structural model estimated using inverse probability weighting (MSM-IPW). We compare this bias with the bias due to confounder misclassification in analyses based on a conditional regression model. Focus is on a point-treatment study with a continuous outcome. Compared with bias in the average treatment effect in a conditional model, the bias in an MSM-IPW can be different in magnitude but is equal in sign. Also, we use a simulation study to investigate the finite sample performance of MSM-IPW and conditional models when a confounding variable is misclassified. Simulation results indicate that confidence intervals of the treatment effect obtained from MSM-IPW are generally wider, and coverage of the true treatment effect is higher compared with a conditional model, ranging from overcoverage if there is no confounder misclassification to undercoverage when there is confounder misclassification. Further, we illustrate in a study of blood pressure-lowering therapy, how the bias expressions can be used to inform a quantitative bias analysis to study the impact of confounder misclassification, supported by an online tool.

Evaluating Flexible Modeling of Continuous Covariates in Inverse-Weighted Estimators

Correct specification of the exposure model is essential for unbiased estimation in marginal structural models with inverse-probability-of-treatment weights. However, although flexible modeling is commonplace when estimating effects of continuous covariates in outcome models, its use is less frequent in estimation of inverse probability weights. Using simulations, we assess the accuracy of the treatment effect estimates and covariate balance obtained with different exposure model specifications when the true relationship between a continuous, possibly time-varying covariate Lt and the logit of the probability of exposure is nonlinear. Specifically, we compare 4 approaches to modeling the effect of Lt when estimating inverse probability weights: a linear function, the covariate-balancing propensity score, and 2 easy-to-implement flexible methods that relax the assumption of linearity: cubic regression splines and fractional polynomials. Using data from 2 empirical studies, we compare linear exposure models with flexible exposure models to estimate the effect of sustained virological response to hepatitis C virus treatment on the progression of liver fibrosis. Our simulation results demonstrate that ignoring important nonlinear relationships when fitting the exposure model may provide poorer covariate balance and induce substantial bias in the estimated exposure-outcome associations. Analysts should routinely consider flexible modeling of continuous covariates when estimating inverse-probability-of-treatment weights.

When to Censor?

Loss to follow-up is an endemic feature of time-to-event analyses that precludes observation of the event of interest. To our knowledge, in typical cohort studies with encounters occurring at regular or irregular intervals, there is no consensus on how to handle person-time between participants' last study encounter and the point at which they meet a definition of loss to follow-up. We demonstrate, using simulation and an example, that when the event of interest is captured outside of a study encounter (e.g., in a registry), person-time should be censored when the study-defined criterion for loss to follow-up is met (e.g., 1 year after last encounter), rather than at the last study encounter. Conversely, when the event of interest must be measured within the context of a study encounter (e.g., a biomarker value), person-time should be censored at the last study encounter. An inappropriate censoring scheme has the potential to result in substantial bias that may not be easily corrected.