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.
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This content will become publicly available on April 25, 2024
A Within-Group Approach to Ensemble Machine Learning Methods for Causal Inference in Multilevel Studies
Machine learning (ML) methods for causal inference have gained popularity due to their flexibility to predict the outcome model and the propensity score. In this article, we provide a within-group approach for ML-based causal inference methods in order to robustly estimate average treatment effects in multilevel studies when there is cluster-level unmeasured confounding. We focus on one particular ML-based causal inference method based on the targeted maximum likelihood estimation (TMLE) with an ensemble learner called SuperLearner. Through our simulation studies, we observe that training TMLE within groups of similar clusters helps remove bias from cluster-level unmeasured confounders. Also, using within-group propensity scores estimated from fixed effects logistic regression increases the robustness of the proposed within-group TMLE method. Even if the propensity scores are partially misspecified, the within-group TMLE still produces robust ATE estimates due to double robustness with flexible modeling, unlike parametric-based inverse propensity weighting methods. We demonstrate our proposed methods and conduct sensitivity analyses against the number of groups and individual-level unmeasured confounding to evaluate the effect of taking an eighth-grade algebra course on math achievement in the Early Childhood Longitudinal Study.
more » « less- NSF-PAR ID:
- 10408960
- Publisher / Repository:
- DOI PREFIX: 10.3102
- Date Published:
- Journal Name:
- Journal of Educational and Behavioral Statistics
- Volume:
- 49
- Issue:
- 1
- ISSN:
- 1076-9986
- Format(s):
- Medium: X Size: p. 61-91
- Size(s):
- ["p. 61-91"]
- Sponsoring Org:
- National Science Foundation
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Summary Comparative effectiveness research often involves evaluating the differences in the risks of an event of interest between two or more treatments using observational data. Often, the post‐treatment outcome of interest is whether the event happens within a pre‐specified time window, which leads to a binary outcome. One source of bias for estimating the causal treatment effect is the presence of confounders, which are usually controlled using propensity score‐based methods. An additional source of bias is right‐censoring, which occurs when the information on the outcome of interest is not completely available due to dropout, study termination, or treatment switch before the event of interest. We propose an inverse probability weighted regression‐based estimator that can simultaneously handle both confounding and right‐censoring, calling the method CIPWR, with the letter C highlighting the censoring component. CIPWR estimates the average treatment effects by averaging the predicted outcomes obtained from a logistic regression model that is fitted using a weighted score function. The CIPWR estimator has a double robustness property such that estimation consistency can be achieved when either the model for the outcome or the models for both treatment and censoring are correctly specified. We establish the asymptotic properties of the CIPWR estimator for conducting inference, and compare its finite sample performance with that of several alternatives through simulation studies. The methods under comparison are applied to a cohort of prostate cancer patients from an insurance claims database for comparing the adverse effects of four candidate drugs for advanced stage prostate cancer.
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For large observational studies lacking a control group (unlike randomized controlled trials, RCT), propensity scores (PS) are often the method of choice to account for pre-treatment confounding in baseline characteristics, and thereby avoid substantial bias in treatment estimation. A vast majority of PS techniques focus on average treatment effect estimation, without any clear consensus on how to account for confounders, especially in a multiple treatment setting. Furthermore, for time-to event outcomes, the analytical framework is further complicated in presence of high censoring rates (sometimes, due to non-susceptibility of study units to a disease), imbalance between treatment groups, and clustered nature of the data (where, survival outcomes appear in groups). Motivated by a right-censored kidney transplantation dataset derived from the United Network of Organ Sharing (UNOS), we investigate and compare two recent promising PS procedures, (a) the generalized boosted model (GBM), and (b) the covariate-balancing propensity score (CBPS), in an attempt to decouple the causal effects of treatments (here, study subgroups, such as hepatitis C virus (HCV) positive/negative donors, and positive/negative recipients) on time to death of kidney recipients due to kidney failure, post transplantation. For estimation, we employ a 2-step procedure which addresses various complexities observed in the UNOS database within a unified paradigm. First, to adjust for the large number of confounders on the multiple sub-groups, we fit multinomial PS models via procedures (a) and (b). In the next stage, the estimated PS is incorporated into the likelihood of a semi-parametric cure rate Cox proportional hazard frailty model via inverse probability of treatment weighting, adjusted for multi-center clustering and excess censoring, Our data analysis reveals a more informative and superior performance of the full model in terms of treatment effect estimation, over sub-models that relaxes the various features of the event time dataset.more » « less
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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.more » « less
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Abstract Structural nested mean models (SNMMs) are useful for causal inference of treatment effects in longitudinal observational studies. Most existing works assume that the data are collected at prefixed time points for all subjects, which, however, may be restrictive in practice. To deal with irregularly spaced observations, we assume a class of continuous‐time SNMMs and a martingale condition of no unmeasured confounding (NUC) to identify the causal parameters. We develop the semiparametric efficiency theory and locally efficient estimators for continuous‐time SNMMs. This task is nontrivial due to the restrictions from the NUC assumption imposed on the SNMM parameter. In the presence of ignorable censoring, we show that the complete‐case estimator is optimal among a class of weighting estimators including the inverse probability of censoring weighting estimator, and it achieves a double robustness feature in that it is consistent if at least one of the models for the potential outcome mean function and the treatment process is correctly specified. The new framework allows us to conduct causal analysis respecting the underlying continuous‐time nature of data processes. The simulation study shows that the proposed estimator outperforms existing approaches. We estimate the effect of time to initiate highly active antiretroviral therapy on the CD4 count at year 2 from the observational Acute Infection and Early Disease Research Program database.
