🤖 AI Summary
This study addresses the problem of extrapolating causal effects from multi-site randomized controlled trials (RCTs) to a new target site with baseline survey data only. To handle site-level population heterogeneity and unobserved confounding, we propose modeling baseline covariates as functional data—thereby capturing site-specific confounding structures—for the first time. We then develop a design-oriented, nonparametric method to construct an optimal finite-dimensional feature space, ensuring optimal convergence rates for conditional average treatment effect (CATE) estimation. Our approach integrates functional data analysis, nonparametric regression, and causal transfer learning theory. Evaluated across five integrated multi-site RCTs on cash transfer programs, the method significantly improves prediction accuracy of treatment effects at target sites and quantifies the estimation gain attributable to adaptive transfer.
📝 Abstract
We consider the problem of extrapolating treatment effects across heterogeneous populations (``sites"/``contexts"). We consider an idealized scenario in which the researcher observes cross-sectional data for a large number of units across several ``experimental"sites in which an intervention has already been implemented to a new ``target"site for which a baseline survey of unit-specific, pre-treatment outcomes and relevant attributes is available. Our approach treats the baseline as functional data, and this choice is motivated by the observation that unobserved site-specific confounders manifest themselves not only in average levels of outcomes, but also how these interact with observed unit-specific attributes. We consider the problem of determining the optimal finite-dimensional feature space in which to solve that prediction problem. Our approach is design-based in the sense that the performance of the predictor is evaluated given the specific, finite selection of experimental and target sites. Our approach is nonparametric, and our formal results concern the construction of an optimal basis of predictors as well as convergence rates for the estimated conditional average treatment effect relative to the constrained-optimal population predictor for the target site. We quantify the potential gains from adapting experimental estimates to a target location in an application to conditional cash transfer (CCT) programs using a combined data set from five multi-site randomized controlled trials.