1
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Yan Y, Ren M. Consistent inverse probability of treatment weighted estimation of the average treatment effect with mismeasured time-dependent confounders. Stat Med 2023; 42:517-535. [PMID: 36513267 DOI: 10.1002/sim.9629] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2021] [Revised: 11/17/2022] [Accepted: 12/02/2022] [Indexed: 12/15/2022]
Abstract
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.
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Affiliation(s)
- Ying Yan
- School of Mathematics, Sun Yat-sen University, Guangzhou, China
| | - Mingchen Ren
- Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada
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2
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Yi GY, Chen LP. Estimation of the average treatment effect with variable selection and measurement error simultaneously addressed for potential confounders. Stat Methods Med Res 2023; 32:691-711. [PMID: 36694932 PMCID: PMC10119903 DOI: 10.1177/09622802221146308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
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.
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Affiliation(s)
- Grace Y Yi
- Department of Statistical and Actuarial Sciences, 6221University of Western Ontario, London, Canada.,Department of Computer Science, 6221University of Western Ontario, London, Canada
| | - Li-Pang Chen
- Department of Statistical and Actuarial Sciences, 6221University of Western Ontario, London, Canada.,Department of Statistics, 34913National Chengchi University, Taipei, Taiwan
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3
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Abrahamowicz M, Beauchamp ME, Moura CS, Bernatsky S, Ferreira Guerra S, Danieli C. Adapting SIMEX to correct for bias due to interval-censored outcomes in survival analysis with time-varying exposure. Biom J 2022; 64:1467-1485. [PMID: 36065586 DOI: 10.1002/bimj.202100013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2021] [Revised: 05/16/2022] [Accepted: 05/28/2022] [Indexed: 12/14/2022]
Abstract
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.
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Affiliation(s)
- Michal Abrahamowicz
- Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, QC, Canada.,Centre for Outcomes Research and Evaluation, Research Institute of the McGill University Health Centre, Montreal, QC, Canada
| | - Marie-Eve Beauchamp
- Centre for Outcomes Research and Evaluation, Research Institute of the McGill University Health Centre, Montreal, QC, Canada
| | - Cristiano Soares Moura
- Centre for Outcomes Research and Evaluation, Research Institute of the McGill University Health Centre, Montreal, QC, Canada
| | - Sasha Bernatsky
- Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, QC, Canada.,Centre for Outcomes Research and Evaluation, Research Institute of the McGill University Health Centre, Montreal, QC, Canada
| | - Steve Ferreira Guerra
- Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, QC, Canada
| | - Coraline Danieli
- Centre for Outcomes Research and Evaluation, Research Institute of the McGill University Health Centre, Montreal, QC, Canada
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4
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Liu J, Li W. A semiparametric method for evaluating causal effects in the presence of error-prone covariates. Biom J 2021; 63:1202-1222. [PMID: 34357652 DOI: 10.1002/bimj.202000069] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2020] [Revised: 02/18/2021] [Accepted: 03/10/2021] [Indexed: 11/12/2022]
Abstract
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.
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Affiliation(s)
- Jianxuan Liu
- Department of Mathematics, Syracuse University, Syracuse, NY, USA.,Center for Policy Research, Maxwell School of Citizenship and Public Affairs, Syracuse University, Syracuse, NY, USA
| | - Wei Li
- Department of Mathematics, Syracuse University, Syracuse, NY, USA
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5
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Hoque MR, Aviña‐Zubieta JA, De Vera MA, Qian Y, Esdaile JM, Xie H. Impact of Antimalarial Adherence on Mortality among Patients with Newly Diagnosed Systemic Lupus Erythematosus: A Population‐based Cohort Study. Arthritis Care Res (Hoboken) 2021; 74:1089-1097. [DOI: 10.1002/acr.24550] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2020] [Revised: 12/08/2020] [Accepted: 12/22/2020] [Indexed: 11/07/2022]
Affiliation(s)
- M Rashedul Hoque
- Arthritis Research Canada Richmond Canada British Columbia
- Faculty of Health Sciences Simon Fraser University Burnaby Canada British Columbia
| | - J Antonio Aviña‐Zubieta
- Arthritis Research Canada Richmond Canada British Columbia
- Division of Rheumatology Department of Medicine University of British Columbia Vancouver Canada
| | - Mary A De Vera
- Arthritis Research Canada Richmond Canada British Columbia
- Faculty of Pharmaceutical Sciences University of British Columbia Vancouver Canada
| | - Yi Qian
- Sauder School of Business University of British Columbia Vancouver Canada
| | - John M Esdaile
- Arthritis Research Canada Richmond Canada British Columbia
- Division of Rheumatology Department of Medicine University of British Columbia Vancouver Canada
| | - Hui Xie
- Arthritis Research Canada Richmond Canada British Columbia
- Faculty of Health Sciences Simon Fraser University Burnaby Canada British Columbia
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6
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Goetghebeur E, le Cessie S, De Stavola B, Moodie EEM, Waernbaum I. Formulating causal questions and principled statistical answers. Stat Med 2020; 39:4922-4948. [PMID: 32964526 PMCID: PMC7756489 DOI: 10.1002/sim.8741] [Citation(s) in RCA: 31] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2019] [Revised: 05/10/2020] [Accepted: 08/05/2020] [Indexed: 12/13/2022]
Abstract
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.
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Affiliation(s)
- Els Goetghebeur
- Department of Applied Mathematics, Computer Science and StatisticsGhent UniversityGhentBelgium
- Department of Medical Epidemiology and BiostatisticsKarolinska InstitutetStockholmSweden
| | - Saskia le Cessie
- Department of Clinical Epidemiology/Biomedical Data SciencesLeiden University Medical CenterLeidenThe Netherlands
| | - Bianca De Stavola
- Great Ormond Street Institute of Child HealthUniversity College LondonLondonUK
| | - Erica EM Moodie
- Division of BiostatisticsMcGill UniversityMontrealQuebecCanada
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7
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Nab L, Groenwold RHH, van Smeden M, Keogh RH. Quantitative Bias Analysis for a Misclassified Confounder: A Comparison Between Marginal Structural Models and Conditional Models for Point Treatments. Epidemiology 2020; 31:796-805. [PMID: 32826524 PMCID: PMC7523582 DOI: 10.1097/ede.0000000000001239] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2019] [Accepted: 07/17/2020] [Indexed: 11/25/2022]
Abstract
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.
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Affiliation(s)
- Linda Nab
- From the Department of Clinical Epidemiology, Leiden University Medical Center, Leiden, The Netherlands
| | - Rolf H H Groenwold
- From the Department of Clinical Epidemiology, Leiden University Medical Center, Leiden, The Netherlands
- Department of Biomedical Data Sciences, Leiden University Medical Center, Leiden, The Netherlands
| | - Maarten van Smeden
- From the Department of Clinical Epidemiology, Leiden University Medical Center, Leiden, The Netherlands
| | - Ruth H Keogh
- Department of Medical Statistics, London School of Hygiene and Tropical Medicine, London, United Kingdom
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8
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Shu D, Yi GY. Inverse‐probability‐of‐treatment weighted estimation of causal parameters in the presence of error‐contaminated and time‐dependent confounders. Biom J 2019; 61:1507-1525. [DOI: 10.1002/bimj.201600228] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2016] [Revised: 03/19/2019] [Accepted: 06/19/2019] [Indexed: 11/09/2022]
Affiliation(s)
- Di Shu
- Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterloo Ontario Canada
| | - Grace Y. Yi
- Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterloo Ontario Canada
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9
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Kyle RP, Moodie EEM, Klein MB, Abrahamowicz M. Evaluating Flexible Modeling of Continuous Covariates in Inverse-Weighted Estimators. Am J Epidemiol 2019; 188:1181-1191. [PMID: 30649165 DOI: 10.1093/aje/kwz004] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2017] [Revised: 12/27/2018] [Accepted: 01/07/2019] [Indexed: 12/14/2022] Open
Abstract
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.
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Affiliation(s)
- Ryan P Kyle
- Department of Epidemiology, Biostatistics and Occupational Health, Faculty of Medicine, McGill University, Montréal, Québec, Canada
| | - Erica E M Moodie
- Department of Epidemiology, Biostatistics and Occupational Health, Faculty of Medicine, McGill University, Montréal, Québec, Canada
| | - Marina B Klein
- Department of Epidemiology, Biostatistics and Occupational Health, Faculty of Medicine, McGill University, Montréal, Québec, Canada
- Department of Medicine, Division of Infectious Diseases and Division of Immunodeficiency, Royal Victoria Hospital, McGill University Health Centre, Montréal, Québec, Canada
| | - Michał Abrahamowicz
- Department of Epidemiology, Biostatistics and Occupational Health, Faculty of Medicine, McGill University, Montréal, Québec, Canada
- Division of Clinical Epidemiology, McGill University Health Centre, Montréal, Québec, Canada
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10
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Shu D, Yi GY. Weighted causal inference methods with mismeasured covariates and misclassified outcomes. Stat Med 2019; 38:1835-1854. [DOI: 10.1002/sim.8073] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2018] [Revised: 10/26/2018] [Accepted: 11/19/2018] [Indexed: 11/08/2022]
Affiliation(s)
- Di Shu
- Department of Statistics and Actuarial ScienceUniversity of Waterloo Waterloo Ontario Canada
| | - Grace Y. Yi
- Department of Statistics and Actuarial ScienceUniversity of Waterloo Waterloo Ontario Canada
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11
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Estimation of Causal Effect Measures in the Presence of Measurement Error in Confounders. STATISTICS IN BIOSCIENCES 2018. [DOI: 10.1007/s12561-018-9213-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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12
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Lesko CR, Edwards JK, Cole SR, Moore RD, Lau B. When to Censor? Am J Epidemiol 2018; 187:623-632. [PMID: 29020256 DOI: 10.1093/aje/kwx281] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2016] [Accepted: 07/14/2017] [Indexed: 12/16/2022] Open
Abstract
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.
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Affiliation(s)
- Catherine R Lesko
- Department of Epidemiology, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, Maryland
| | - Jessie K Edwards
- Department of Epidemiology, Gillings School of Global Public Health, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina
| | - Stephen R Cole
- Department of Epidemiology, Gillings School of Global Public Health, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina
| | - Richard D Moore
- Department of Epidemiology, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, Maryland
- Department of Medicine, School of Medicine, Johns Hopkins University, Baltimore, Maryland
| | - Bryan Lau
- Department of Epidemiology, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, Maryland
- Department of Medicine, School of Medicine, Johns Hopkins University, Baltimore, Maryland
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