The problem of estimating the average treatment effects is important when evaluating the effectiveness of medical treatments or social intervention policies. Most of the existing methods for estimating the average treatment effect rely on some parametric assumptions about the propensity score model or the outcome regression model one way or the other. In reality, both models are prone to misspecification, which can have undue influence on the estimated average treatment effect. We propose an alternative robust approach to estimating the average treatment effect based on observational data in the challenging situation when neither a plausible parametric outcome model nor a reliable parametric propensity score model is available. Our estimator can be considered as a robust extension of the popular class of propensity score weighted estimators. This approach has the advantage of being robust, flexible, data adaptive, and it can handle many covariates simultaneously. Adopting a dimension reduction approach, we estimate the propensity score weights semiparametrically by using a non-parametric link function to relate the treatment assignment indicator to a low-dimensional structure of the covariates which are formed typically by several linear combinations of the covariates. We develop a class of consistent estimators for the average treatment effect and study their theoretical properties. We demonstrate the robust performance of the estimators on simulated data and a real data example of investigating the effect of maternal smoking on babies’ birth weight.
Randomized controlled trials (RCT’s) allow researchers to estimate causal effects in an experimental sample with minimal identifying assumptions. However, to generalize or transport a causal effect from an RCT to a target population, researchers must adjust for a set of treatment effect moderators. In practice, it is impossible to know whether the set of moderators has been properly accounted for. I propose a two parameter sensitivity analysis for generalizing or transporting experimental results using weighted estimators. The contributions in the article are threefold. First, I show that the sensitivity parameters are scale-invariant and standardized, and introduce an estimation approach for researchers to account for both bias in their estimates from omitting a moderator, as well as potential changes to their inference. Second, I propose several tools researchers can use to perform sensitivity analysis: (1) numerical measures to summarize the uncertainty in an estimated effect to omitted moderators; (2) graphical summary tools to visualize the sensitivity in estimated effects; and (3) a formal benchmarking approach for researchers to estimate potential sensitivity parameter values using existing data. Finally, I demonstrate that the proposed framework can be easily extended to the class of doubly robust, augmented weighted estimators.
more » « less- NSF-PAR ID:
- 10495256
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Journal of the Royal Statistical Society Series A: Statistics in Society
- ISSN:
- 0964-1998
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract We consider how to merge a limited amount of data from a randomized controlled trial (RCT) into a much larger set of data from an observational data base (ODB), to estimate an average causal treatment effect. Our methods are based on stratification. The strata are defined in terms of effect moderators as well as propensity scores estimated in the ODB. Data from the RCT are placed into the strata they would have occupied, had they been in the ODB instead. We assume that treatment differences are comparable in the two data sources. Our first “spiked‐in” method simply inserts the RCT data into their corresponding ODB strata. We also consider a data‐driven convex combination of the ODB and RCT treatment effect estimates within each stratum. Using the delta method and simulations, we identify a bias problem with the spiked‐in estimator that is ameliorated by the convex combination estimator. We apply our methods to data from the Women's Health Initiative, a study of thousands of postmenopausal women which has both observational and experimental data on hormone therapy (HT). Using half of the RCT to define a gold standard, we find that a version of the spiked‐in estimator yields lower‐MSE estimates of the causal impact of HT on coronary heart disease than would be achieved using either a small RCT or the observational component on its own.
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