A Two-Step Weighted Bootstrap Framework
Open Access DepositedRobust Prediction Transportability under Covariate Shift
Researchers are often interested in transporting a prediction model or a causal relationship to a new population with a different covariate distribution. Weighting methods are commonly used to correct for sample selection bias and mitigate the covariate shift problem. However, when and under what conditions weighting is appropriate remains underexplored. Although covariate shift has been extensively studied in both prediction modeling and causal inference, often referred to as sample selection bias, these areas are typically treated separately, despite sharing important conceptual similarities. In this dissertation, we first elucidate the connections with overlap weight and compare the key differences between weighting methods in causal inference and in semi-supervised prediction, focusing on their goals, underlying assumptions, and data-generating mechanisms. We then address the practical challenge of insufficient population overlap, which often leads to unstable or ineffective weighting in prediction transportability. To overcome this, we propose a two-step procedure combining importance sampling and double bootstrap techniques, to improve predictive performance under covariate shift even in limited-overlap scenarios. Building on this method, we further develop a novel approach for measuring population overlap that incorporates modeling information from both the propensity score estimation and the outcome model. This measure provides a more informative assessment of overlap quality than existing purely empirical metrics, offering practitioners guidance on when weighting is likely to succeed. Through comprehensive simulations with source and target samples generated under distinct mechanisms, we evaluate various weighting strategies, including no weights, standard propensity score weights, and the proposed two-step weights, across different degrees of covariate shift, overlap, and model misspecification. We find that when overlap is low, weighting methods do not improve predictive accuracy, while in moderate or high-overlap settings, our proposed method performs comparably to standard approaches under correct model specification and shows significant improvements under misspecification. Finally, we discuss practical considerations for selecting appropriate weighting methods and demonstrate how our new overlap measure can inform these decisions, ultimately providing a robust framework for prediction transportability under covariate shift.
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