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A powerful tool for the analysis of nonrandomized observational studies has been the potential outcomes model. Utilization of this framework allows analysts to estimate average treatment effects. This article considers the situation in which high-dimensional covariates are present and revisits the standard assumptions made in causal inference. We show that by employing a flexible Gaussian process framework, the assumption of strict overlap leads to very restrictive assumptions about the distribution of covariates, results for which can be characterized using classical results from Gaussian random measures as well as reproducing kernel Hilbert space theory. In addition, we propose a strategy for data-adaptive causal effect estimation that does not rely on the strict overlap assumption. These findings reveal under a focused framework the stringency that accompanies the use of the treatment positivity assumption in high-dimensional settings.
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More robust estimation of average treatment effects using kernel optimal matching in an observational study of spine surgical interventions
Inverse probability of treatment weighting (IPTW), which has been used to estimate average treatment effects (ATE) using observational data, tenuously relies on the positivity assumption and the correct specification of the treatment assignment model, both of which are problematic assumptions in many observational studies. Various methods have been proposed to overcome these challenges, including truncation, covariate‐balancing propensity scores, and stable balancing weights. Motivated by an observational study in spine surgery, in which positivity is violated and the true treatment assignment model is unknown, we present the use of optimal balancing by kernel optimal matching (KOM) to estimate ATE. By uniformly controlling the conditional mean squared error of a weighted estimator over a class of models, KOM simultaneously mitigates issues of possible misspecification of the treatment assignment model and is able to handle practical violations of the positivity assumption, as shown in our simulation study. Using data from a clinical registry, we apply KOM to compare two spine surgical interventions and demonstrate how the result matches the conclusions of clinical trials that IPTW estimates spuriously refute.
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- Award ID(s):
- 1740822
- PAR ID:
- 10452668
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Statistics in Medicine
- Volume:
- 40
- Issue:
- 10
- ISSN:
- 0277-6715
- Format(s):
- Medium: X Size: p. 2305-2320
- Size(s):
- p. 2305-2320
- Sponsoring Org:
- National Science Foundation
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