Abstract Investigating the causal relationship between exposure and time-to-event outcome is an important topic in biomedical research. Previous literature has discussed the potential issues of using hazard ratio (HR) as the marginal causal effect measure due to noncollapsibility. In this article, we advocate using restricted mean survival time (RMST) difference as a marginal causal effect measure, which is collapsible and has a simple interpretation as the difference of area under survival curves over a certain time horizon. To address both measured and unmeasured confounding, a matched design with sensitivity analysis is proposed. Matching is used to pair similar treated and untreated subjects together, which is generally more robust than outcome modeling due to potential misspecifications. Our propensity score matched RMST difference estimator is shown to be asymptotically unbiased, and the corresponding variance estimator is calculated by accounting for the correlation due to matching. Simulation studies also demonstrate that our method has adequate empirical performance and outperforms several competing methods used in practice. To assess the impact of unmeasured confounding, we develop a sensitivity analysis strategy by adapting the E -value approach to matched data. We apply the proposed method to the Atherosclerosis Risk in Communities Study (ARIC) to examine the causal effect of smoking on stroke-free survival.
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Covariate-adjusted survival analyses in propensity-score matched samples: Imputing potential time-to-event outcomes
Matching on an estimated propensity score is frequently used to estimate the effects of treatments from observational data. Since the 1970s, different authors have proposed methods to combine matching at the design stage with regression adjustment at the analysis stage when estimating treatment effects for continuous outcomes. Previous work has consistently shown that the combination has generally superior statistical properties than either method by itself. In biomedical and epidemiological research, survival or time-to-event outcomes are common. We propose a method to combine regression adjustment and propensity score matching to estimate survival curves and hazard ratios based on estimating an imputed potential outcome under control for each successfully matched treated subject, which is accomplished using either an accelerated failure time parametric survival model or a Cox proportional hazard model that is fit to the matched control subjects. That is, a fitted model is then applied to the matched treated subjects to allow simulation of the missing potential outcome under control for each treated subject. Conventional survival analyses (e.g., estimation of survival curves and hazard ratios) can then be conducted using the observed outcome under treatment and the imputed outcome under control. We evaluated the repeated-sampling bias of the proposed methods using simulations. When using nearest neighbor matching, the proposed method resulted in decreased bias compared to crude analyses in the matched sample. We illustrate the method in an example prescribing beta-blockers at hospital discharge to patients hospitalized with heart failure.
more » « less- PAR ID:
- 10523102
- Publisher / Repository:
- SAGE Publications
- Date Published:
- Journal Name:
- Statistical Methods in Medical Research
- Volume:
- 29
- Issue:
- 3
- ISSN:
- 0962-2802
- Format(s):
- Medium: X Size: p. 728-751
- Size(s):
- p. 728-751
- Sponsoring Org:
- National Science Foundation
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Summary Recently there has been a surge in econometric and epidemiologic works focusing on estimating average treatment effects under various sets of assumptions. Estimation of average treatment effects in observational studies often requires adjustment for differences in pretreatment variables. Rosenbaum and Rubin have proposed the propensity score method for estimating the average treatment effect by adjusting pretreatment variables. In this paper, the empirical likelihood method is used to estimate average treatment effects on the treated under the difference-in-differences framework. The advantage of this approach is that the common marginal covariate information can be incorporated naturally to enhance the estimation of average treatment effects. Compared with other approaches in the literature, the method proposed can provide more efficient estimation. A simulation study and a real economic data analysis are presented.
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This paper concerns estimation of subgroup treatment effects with observational data. Existing propensity score methods are mostly developed for estimating overall treatment effect. Although the true propensity scores balance covariates in any subpopulations, the estimated propensity scores may result in severe imbalance in subgroup samples. Indeed, subgroup analysis amplifies a bias-variance tradeoff, whereby increasing complexity of the propensity score model may help to achieve covariate balance within subgroups, but it also increases variance. We propose a new method, the subgroup balancing propensity score, to ensure good subgroup balance as well as to control the variance inflation. For each subgroup, the subgroup balancing propensity score chooses to use either the overall sample or the subgroup (sub)sample to estimate the propensity scores for the units within that subgroup, in order to optimize a criterion accounting for a set of covariate-balancing moment conditions for both the overall sample and the subgroup samples. We develop two versions of subgroup balancing propensity score corresponding to matching and weighting, respectively. We devise a stochastic search algorithm to estimate the subgroup balancing propensity score when the number of subgroups is large. We demonstrate through simulations that the subgroup balancing propensity score improves the performance of propensity score methods in estimating subgroup treatment effects. We apply the subgroup balancing propensity score method to the Italy Survey of Household Income and Wealth (SHIW) to estimate the causal effects of having debit card on household consumption for different income groups.
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Abstract Propensity score weighting is a tool for causal inference to adjust for measured confounders in observational studies. In practice, data often present complex structures, such as clustering, which make propensity score modeling and estimation challenging. In addition, for clustered data, there may be unmeasured cluster-level covariates that are related to both the treatment assignment and outcome. When such unmeasured cluster-specific confounders exist and are omitted in the propensity score model, the subsequent propensity score adjustment may be biased. In this article, we propose a calibration technique for propensity score estimation under the latent ignorable treatment assignment mechanism, i. e., the treatment-outcome relationship is unconfounded given the observed covariates and the latent cluster-specific confounders. We impose novel balance constraints which imply exact balance of the observed confounders and the unobserved cluster-level confounders between the treatment groups. We show that the proposed calibrated propensity score weighting estimator is doubly robust in that it is consistent for the average treatment effect if either the propensity score model is correctly specified or the outcome follows a linear mixed effects model. Moreover, the proposed weighting method can be combined with sampling weights for an integrated solution to handle confounding and sampling designs for causal inference with clustered survey data. In simulation studies, we show that the proposed estimator is superior to other competitors. We estimate the effect of School Body Mass Index Screening on prevalence of overweight and obesity for elementary schools in Pennsylvania.more » « less
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Abstract It is common to conduct causal inference in matched observational studies by proceeding as though treatment assignments within matched sets are assigned uniformly at random and using this distribution as the basis for inference. This approach ignores observed discrepancies in matched sets that may be consequential for the distribution of treatment, which are succinctly captured by within-set differences in the propensity score. We address this problem via covariate-adaptive randomization inference, which modifies the permutation probabilities to vary with estimated propensity score discrepancies and avoids requirements to exclude matched pairs or model an outcome variable. We show that the test achieves type I error control arbitrarily close to the nominal level when large samples are available for propensity score estimation. We characterize the large-sample behaviour of the new randomization test for a difference-in-means estimator of a constant additive effect. We also show that existing methods of sensitivity analysis generalize effectively to covariate-adaptive randomization inference. Finally, we evaluate the empirical value of combining matching and covariate-adaptive randomization procedures using simulations and analyses of genetic damage among welders and right-heart catheterization in surgical patients.
