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Abstract:
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Data from both a randomized trial (RT) and an observational study (OS) are sometimes simultaneously available for evaluating an intervention. While RT data allow for reliable estimation of average treatment effects, it may be limited in sample size and heterogeneity for estimating conditional average treatment effects (CATE). Incorporating OS data can potentially compensate for these limitations, though it risks introducing bias due to confounding by indication or treatment effect heterogeneity. We propose an approach to combining CATE estimators from each source such that it aggressively weights toward the RT estimator when bias in the OS estimator is detected. This allows the combination to be consistent for a conditional causal effect, regardless of whether the OS estimator is biased. When the bias is negligible, the estimators are combined for optimal efficiency. We show the problem can be formulated as a penalized least squares problem and consider its asymptotic properties. The method is demonstrated through simulations and an application to estimating the effects of hormone replacement therapy on the risk of coronary heart disease in data from the Women's Health Initiative.
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