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      Variance estimation when using inverse probability of treatment weighting (IPTW) with survival analysis

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          Abstract

          Propensity score methods are used to reduce the effects of observed confounding when using observational data to estimate the effects of treatments or exposures. A popular method of using the propensity score is inverse probability of treatment weighting (IPTW). When using this method, a weight is calculated for each subject that is equal to the inverse of the probability of receiving the treatment that was actually received. These weights are then incorporated into the analyses to minimize the effects of observed confounding. Previous research has found that these methods result in unbiased estimation when estimating the effect of treatment on survival outcomes. However, conventional methods of variance estimation were shown to result in biased estimates of standard error. In this study, we conducted an extensive set of Monte Carlo simulations to examine different methods of variance estimation when using a weighted Cox proportional hazards model to estimate the effect of treatment. We considered three variance estimation methods: (i) a naïve model‐based variance estimator; (ii) a robust sandwich‐type variance estimator; and (iii) a bootstrap variance estimator. We considered estimation of both the average treatment effect and the average treatment effect in the treated. We found that the use of a bootstrap estimator resulted in approximately correct estimates of standard errors and confidence intervals with the correct coverage rates. The other estimators resulted in biased estimates of standard errors and confidence intervals with incorrect coverage rates. Our simulations were informed by a case study examining the effect of statin prescribing on mortality. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

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          Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men.

          Standard methods for survival analysis, such as the time-dependent Cox model, may produce biased effect estimates when there exist time-dependent confounders that are themselves affected by previous treatment or exposure. Marginal structural models are a new class of causal models the parameters of which are estimated through inverse-probability-of-treatment weighting; these models allow for appropriate adjustment for confounding. We describe the marginal structural Cox proportional hazards model and use it to estimate the causal effect of zidovudine on the survival of human immunodeficiency virus-positive men participating in the Multicenter AIDS Cohort Study. In this study, CD4 lymphocyte count is both a time-dependent confounder of the causal effect of zidovudine on survival and is affected by past zidovudine treatment. The crude mortality rate ratio (95% confidence interval) for zidovudine was 3.6 (3.0-4.3), which reflects the presence of confounding. After controlling for baseline CD4 count and other baseline covariates using standard methods, the mortality rate ratio decreased to 2.3 (1.9-2.8). Using a marginal structural Cox model to control further for time-dependent confounding due to CD4 count and other time-dependent covariates, the mortality rate ratio was 0.7 (95% conservative confidence interval = 0.6-1.0). We compare marginal structural models with previously proposed causal methods.
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            A critical appraisal of propensity-score matching in the medical literature between 1996 and 2003.

            Propensity-score methods are increasingly being used to reduce the impact of treatment-selection bias in the estimation of treatment effects using observational data. Commonly used propensity-score methods include covariate adjustment using the propensity score, stratification on the propensity score, and propensity-score matching. Empirical and theoretical research has demonstrated that matching on the propensity score eliminates a greater proportion of baseline differences between treated and untreated subjects than does stratification on the propensity score. However, the analysis of propensity-score-matched samples requires statistical methods appropriate for matched-pairs data. We critically evaluated 47 articles that were published between 1996 and 2003 in the medical literature and that employed propensity-score matching. We found that only two of the articles reported the balance of baseline characteristics between treated and untreated subjects in the matched sample and used correct statistical methods to assess the degree of imbalance. Thirteen (28 per cent) of the articles explicitly used statistical methods appropriate for the analysis of matched data when estimating the treatment effect and its statistical significance. Common errors included using the log-rank test to compare Kaplan-Meier survival curves in the matched sample, using Cox regression, logistic regression, chi-squared tests, t-tests, and Wilcoxon rank sum tests in the matched sample, thereby failing to account for the matched nature of the data. We provide guidelines for the analysis and reporting of studies that employ propensity-score matching. Copyright (c) 2007 John Wiley & Sons, Ltd.
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              Stratification and weighting via the propensity score in estimation of causal treatment effects: a comparative study.

              Estimation of treatment effects with causal interpretation from observational data is complicated because exposure to treatment may be confounded with subject characteristics. The propensity score, the probability of treatment exposure conditional on covariates, is the basis for two approaches to adjusting for confounding: methods based on stratification of observations by quantiles of estimated propensity scores and methods based on weighting observations by the inverse of estimated propensity scores. We review popular versions of these approaches and related methods offering improved precision, describe theoretical properties and highlight their implications for practice, and present extensive comparisons of performance that provide guidance for practical use. 2004 John Wiley & Sons, Ltd.
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                Author and article information

                Contributors
                peter.austin@ices.on.ca
                Journal
                Stat Med
                Stat Med
                10.1002/(ISSN)1097-0258
                SIM
                Statistics in Medicine
                John Wiley and Sons Inc. (Hoboken )
                0277-6715
                1097-0258
                22 August 2016
                30 December 2016
                : 35
                : 30 ( doiID: 10.1002/sim.v35.30 )
                : 5642-5655
                Affiliations
                [ 1 ]Institute for Clinical Evaluative Sciences Toronto OntarioCanada
                [ 2 ] Institute of Health Management, Policy and EvaluationUniversity of Toronto Toronto OntarioCanada
                [ 3 ] Schulich Heart Research ProgramSunnybrook Research Institute TorontoCanada
                Author notes
                [*] [* ] Correspondence to: Peter Austin, Institute for Clinical Evaluative Sciences, G106, 2075 Bayview Avenue, Toronto, Ontario M4N 3M5, Canada.



                E‐mail: peter.austin@ 123456ices.on.ca

                Article
                SIM7084 SIM-16-0202.R1
                10.1002/sim.7084
                5157758
                27549016
                ff0bceeb-7546-41c2-b0b9-0077e5126e7f
                © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

                This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or adaptations are made.

                History
                : 09 March 2016
                : 09 June 2016
                : 01 August 2016
                Page count
                Figures: 6, Tables: 2, Pages: 14, Words: 5711
                Funding
                Funded by: Ontario Ministry of Health and Long‐Term Care (MOHLTC)
                Funded by: Canadian Institutes of Health Research (CIHR)
                Award ID: MOP 86508
                Categories
                Research Article
                Research Articles
                Custom metadata
                2.0
                sim7084
                sim7084-hdr-0001
                30 December 2016
                Converter:WILEY_ML3GV2_TO_NLMPMC version:4.9.8 mode:remove_FC converted:15.12.2016

                Biostatistics
                propensity score,survival analysis,inverse probability of treatment weighting (iptw),monte carlo simulations,variance estimation,observational study

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