Inverse probability weighting estimation has been popularly used to consistently estimate the average treatment effect. Its validity, however, is challenged by the presence of error-prone variables. In this paper, we explore the inverse probability weighting estimation with mismeasured outcome variables. We study the impact of measurement error for both continuous and discrete outcome variables and reveal interesting consequences of the naive analysis which ignores measurement error. When a continuous outcome variable is mismeasured under an additive measurement error model, the naive analysis may still yield a consistent estimator; when the outcome is binary, we derive the asymptotic bias in a closed-form. Furthermore, we develop consistent estimation procedures for practical scenarios where either validation data or replicates are available. With validation data, we propose an efficient method for estimation of average treatment effect; the efficiency gain is substantial relative to usual methods of using validation data. To provide protection against model misspecification, we further propose a doubly robust estimator which is consistent even when either the treatment model or the outcome model is misspecified. Simulation studies are reported to assess the performance of the proposed methods. An application to a smoking cessation dataset is presented.

The inverse probability weighted Cox model is frequently used to estimate the marginal hazard ratio. Its validity requires a crucial condition that the propensity score model be correctly specified. To provide protection against misspecification of the propensity score model, we propose a weighted estimation method rooted in the empirical likelihood theory. The proposed estimator is multiply robust in that it is guaranteed to be consistent when a set of postulated propensity score models contains a correctly specified model. Our simulation studies demonstrate satisfactory finite sample performance of the proposed method in terms of consistency and efficiency. We apply the proposed method to compare the risk of postoperative hospitalization between sleeve gastrectomy and Roux‐en‐Y gastric bypass using data from a large medical claims and billing database. We further extend the development to multisite studies to enable each site to postulate multiple site‐specific propensity score models.

Inverse-probability-of-treatment weighted (IPTW) estimation has been widely used to consistently estimate the causal parameters in marginal structural models, with timedependent confounding effects adjusted for. Just like other causal inference methods, the validity of IPTW estimation typically requires the crucial condition that all variables are precisely measured. However, this condition, is often violated in practice due to various reasons. It has been well documented that ignoring measurement error often leads to biased inference results. In this paper, we consider the IPTW estimation of the causal parameters in marginal structural models in the presence of error-contaminated and time-dependent confounders. We explore several methods to correct for the effects of measurement error on the estimation of causal parameters. Numerical studies are reported to assess the finite sample performance of the proposed methods. K E Y W O R D Scausal inference, inverse-probability-of-treatment weighting, logistic regression model, marginal structural model, measurement error, time-dependent confounding