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The surrogate index: Combining short-term proxies to estimate long-term treatment effects more rapidly and precisely

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  • Sijia Li
  • Alex Luedtke

Abstract

SummaryWe aim to make inferences about a smooth, finite-dimensional parameter by fusing together data from multiple sources. Previous works have studied the estimation of a variety of parameters in similar data fusion settings, including estimation of the average treatment effect and average reward under a policy, with the majority of them merging one historical data source with covariates, actions and rewards, and one data source of the same covariates. In this article, we consider the general case where one or more data sources align with each part of the distribution of the target population, such as the conditional distribution of the reward given actions and covariates. We describe potential gains in efficiency that can arise from fusing these data sources together in a single analysis, which we characterize by a reduction in the semiparametric efficiency bound. We also provide a general means of constructing estimators that achieve these bounds. Numerical simulations demonstrate marked improvements in efficiency from using the proposed estimators rather than their natural alternatives. Finally, we illustrate the magnitude of efficiency gains that can be realized in vaccine immunogenicity studies by fusing data from two HIV vaccine trials.

Suggested Citation

  • Sijia Li & Alex Luedtke, 2023. "The surrogate index: Combining short-term proxies to estimate long-term treatment effects more rapidly and precisely," Biometrika, Biometrika Trust, vol. 110(4), pages 1041-1054.
    • Handle: RePEc:oup:biomet:v:110:y:2023:i:4:p:1041-1054.
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