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Instrumental Variable Analysis in Epidemiologic Studies: An tica Anal eu yt c ic a a m A r c a Uddin et al., Pharm Anal Acta 2015, 6:4 t h a P Pharmaceutica DOI: 10.4172/2153-2435.1000353 Analytica Acta ISSN: 2153-2435 Review Article Open Access Instrumental Variable Analysis in Epidemiologic Studies: An Overview of the Estimation Methods Uddin MJ1, Groenwold RH1,2, Ton de Boer1, Belitser SV1, Roes KC2 and Klungel OH1,2* 1Devision of Pharmacoepidemiology and Clinical Pharmacology, Utrecht Institute for Pharmaceutical Sciences, University of Utrecht, Utrecht, The Netherlands 2Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Utrecht, The Netherlands Abstract Instrumental variables (IV)analysis seems an attractive method to control for unmeasured confounding in observational epidemiological studies. Here, we provide an overview of the estimation methods of IVanalysis and indicate their possible advantages and limitations.We found that two-stage least squares is the method of first choice if exposure and outcome are both continuous and show a linear relation. In case of a nonlinear relation, two-stage residual inclusion may be a suitable alternative. In settings with binary outcomes as well as nonlinear relations between exposure and outcome, generalized method of moments (GMM), structural mean models (SMM), and bivariate probit models perform well, yet GMM and SMM are generally more robust. The standard errors of the IVestimate can be estimated using a robust or bootstrap method. All estimation methods are prone to bias when the IVassumptions are violated. Researchers should be aware of the underlying assumptions of the estimation methods as well as the key assumptions of the IVwhen interpreting the exposure effects estimated through IV analysis. Keywords: Instrumental variables; Estimation method; Unobserved confounders should on average be equally distributed among different confounding; Epidemiology; Statistical methods; Observational levels of the IV(similar to a randomized trial). These assumptions are studies; Causal inference illustrated in Figure 1. Along with these basic assumptions, there are other assumptions (i.e., homogeneous treatment effects, monotonicity) Introduction that are needed for point identification of IVestimates [14,19]. Instrumental variable (IV) analysis has primarily been used in Notation economics and social science research, as a tool for causal inference, but has begun to appear in epidemiologic research over the last decade Throughout this article, we use the following notation: Y denotes to control for unmeasured confounding [1-6]. An IV is a variable that the outcome, X denotes exposure, and Z denotes the IV. C and U can be considered to mimic the treatment assignment process in a denote the (one or more) observed and unobserved confounding randomized study [7-10]. IVanalysis generally involves in a two-stage variables, respectively. X denotes the predicted value of exposure. βˆ modelling approach to estimate the exposure effects. In the first stage, Finally, IV indicates the IV estimator, i.e., the estimator of the causal the effect of the IVon exposure is estimated, whereas in the second relation between exposure and outcome. stage, outcomes are compared in terms of predicted exposure rather Estimation method of IVanalysis than the actual exposure [11]. To value the estimates obtained through IVanalysis, it is important to understand the underlying methodology Ratio estimator (RE) of the estimation methods in the IV analysis. In a study with a single binary IV, the RE (also called Wald [25] or Over the last decade several reviews of IVanalysis were published, grouping estimator) can be applied and which is expressed as: covering various aspects including the key assumptions, estimating yy− βˆ = 10 (1) parameters, possible IVs, estimation methods, reporting of the results, IV xx− and the use of IVs in comparative effectiveness research [3,4,12-23]. 10 EY[| Z=−= 1][| EY Z 0] We summarized these reviews in Table 1. However, none of these βˆ = (2) IV ==−== articles included all possible estimation methods of IVanalysis. Hence, pX( 1| Z 1) pX ( 1| Z 0) we aimed to provide an overview of the estimation methods and to pY(1|1)(1|0)==−== Z pY Z βˆ = indicate their possible advantages and limitations. After a general IV pX(==−== 1| Z 1) pX ( 1| Z 0) (3) introduction to the assumptions underlying IVanalysis, we will describe the methods that have been used in IVstudies in medical research. Instrumental variables *Corresponding author: Klungel OH, Division of Pharmacoepidemiology and Clinical Pharmacology, University of Utrecht, Utrecht, Netherlands, Tel: The IV is an observed variable, which is related to exposure and only +31685384692, Fax +31-30 253 9166; E-mail: [email protected] related to the outcome through exposure. This resembles a randomized trial, in which treatment allocation typically almost perfectly coincides Received January 06, 2015; Accepted March 08, 2015; Published March 15, 2015 with the actual treatment received and (in case of a double blind trial) treatment assignment only affects the outcome through the received Citation: Uddin MJ, Groenwold RH, Ton de Boer, Belitser SV, Roes KC, et al. (2015) Instrumental Variable Analysis in Epidemiologic Studies: An Overview of the treatment (hence the term pseudo-randomisation that is used for Estimation Methods. Pharm Anal Acta 6: 353. doi:10.4172/2153-2435.1000353 IVmethods). This implies that an IVis neither directly nor indirectly Copyright: © 2015 Uddin MJ, et al. This is an open-access article distributed under (e.g. through observed or unobserved confounders) associated with the terms of the Creative Commons Attribution License, which permits unrestricted the outcome [6,18,24]. Therefore, all observed and unobserved use, distribution, and reproduction in any medium, provided the original author and source are credited. Pharm Anal Acta ISSN: 2153-2435 PAA, an open access journal Volume 6 • Issue 4 • 1000353 Citation: Uddin MJ, Groenwold RH, Ton de Boer, Belitser SV, Roes KC, et al. (2015) Instrumental Variable Analysis in Epidemiologic Studies: An Overview of the Estimation Methods. Pharm Anal Acta 6: 353. doi:10.4172/2153-2435.1000353 Page 2 of 9 Author Publication year Journal name Title Main features -basic introduction with an empirical example International Journal of An introduction to instrumental variables for -link with randomized studies with non- Greenland 2000 Epidemiology epidemiologists compliance -estimated bound for the exposure effects -fundamental issues are described with Instrumental variables: application and Martens et al. 2006 Epidemiology several practical details using graphical limitations representation -overview of IV analysis with explanation of several key assumptions Instruments for causal inference: an Hernan and Robins 2006 Epidemiology epidemiologists dream? -highlights limitations and emphasis on estimating parameters of IV analysis -demonstrates how IV analysis arises Instrumental variables I: instrumental from an analogous but potentially Journal of Clinical variables exploit natural variation in impossible RCT design Rassen et al. 2009 Epidemiology nonexperimental data to estimate causal relationships -shows estimation of effects with an empirical example -assesses the overall relationship Instrumental variables II: instrumental between strength and imbalance of Journal of Clinical variable application—in 25 variations, the confounders between IV categories with Rassen et al. 2009 Epidemiology physician prescribing preference generally an empirical example was strong and reduced covariate imbalance -assesses several possible IVs Instrumental variable analysis for estimation -reviews commonly used IV estimation American Journal of Rassen et al. 2009 of treatment effects with dichotomous methods for binary outcome and Epidemiology outcomes compared them in empirical examples Pharmacoepidemiology Instrumental variable methods in comparative -guidance on reporting of IV analysis with Brookhart et al. 2010 and Drug Safety safety and effectiveness research an empirical example -estimation methods of IV analysis Journal of American Instrumental variable estimators for binary Clarke and Windmeijer 2010 for binary outcome with mathematical Statistical Association outcomes descriptions Use of instrumental variable in prescription drug research with -review of practice of IV analysis in Chen and Briesacher 2011 Journal of Clinical Epidemiology observational data: a systematic epidemiology review -overview of commonly used IV Instrumental variable estimation estimation methods for continuous American Journal of of causal risk ratios and causal exposure Palmer et al. 2011 Epidemiology odds ratios in Mendelian randomization -empirical example of Mendelian randomization study - review of practice of IV analysis in epidemiology -focus on target parameter (e.g. RD, OR) Issues in the reporting and -reviews methods used to estimate Davies et al. 2013 Epidemiology conduct of instrumental variable standard errors studies: a systematic review - proposes a checklist of information to be reported by studies using instrumental variables Commentary: How to report -provided flow chart for reporting of IV Swanson and Hernan 2013 Epidemiology instrumental variable analyses analyses (suggestions welcome) Pharm Anal Acta ISSN: 2153-2435 PAA, an open access journal Volume 6 • Issue 4 • 1000353 Citation: Uddin MJ, Groenwold RH, Ton de Boer, Belitser SV, Roes KC, et al. (2015) Instrumental Variable Analysis in Epidemiologic Studies: An Overview
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