Measurement error and causal inference with instrumental variables

This work is situated in the general field of causal inference that has seen substantial international research activity over the last decade. Two important problems, which have been neglected so far form the focus of this thesis. One is concerned with the impact of measurement error on exposure. A second considers specifically binary outcomes, like success or failure, in this setting. Measurement error in exposure leads to reduced efficiency and forms a common source of bias in exposure effect estimates on outcome, in particular when the exposure effect is confounded by measured or unmeasured covariates. In the first part of the thesis, we study instrumental variable (IV) estimators for the causal effect of an arbitrary exposure. We focus in particular on the longstanding problem of developing IV estimators for the causal odds ratio. Specifically, we give an expository review of exact as well as approximate IVestimators for the causal odds ratio, that have been proposed in the biostatistical, epidemiological and econometric literature. Methods comparisons are made, both theoretically and via extensive simulation, and new insights are developed into the assumptions underlying their validity. The different estimators are used to assess the risk of gastrointestinal (GI) complications attributable to different non-steroidal anti-inflammatory drugs (instead of Cox-2 inhibitors). In the second part, we focus on IV estimators for continuous outcomes, in particular on G-estimators for the parameters indexing linear structural mean models. We assess the asymptotic bias of standard estimators in the presence of systematic exposure measurement error and develop analytic methods to correct estimators for systematic measurement error when an additional instrument for the measurement error is available. Specifically, we build on ideas from linear regression models with error in the covariates to show how an instrumental variable (IV) for the measurement error can help correct IV-based causal effect estimators for systematic error under linear structural mean models. Because simulation studies and analytic results diagnose poor performance of the proposed methods, we show how the performance can be boosted by imposing restrictions on the parameter space for the average measurement error. We apply the methods to correct for systematic error in compliance measurements on compliance adjusted analyses. In the third part of the thesis, we explore the consequences of misclassification error on a dichotomous exposure under common causal models, all being alternatives to ordinary regression adjustment for confounder control. Specifically, we focus on inverse probability of treatment weighted (IPTW) estimators for the parameters indexing marginal structural mean models and on G-estimators and propensity score adjusted estimators under semi-parametric causal models. We quantify the asymptotic bias of causal effect estimators in terms of misclassification probabilities depending on covariates and demonstrate that, perhaps contrary to intuition. all estimators are equally affected by measurement error that is independent of covariates. Finally, we extend this approach to investigate the impact of misclassification of time-varying exposures on inference for marginal structural models.

http://ift.tt/2oPKMiC