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Transfer Learning for Meta-analysis Under Covariate Shift

Zilong Wang, Ali Abdeen, Turgay Ayer

Abstract

Randomized controlled trials often do not represent the populations where decisions are made, and covariate shift across studies can invalidate standard IPD meta-analysis and transport estimators. We propose a placebo-anchored transport framework that treats source-trial outcomes as abundant proxy signals and target-trial placebo outcomes as scarce, high-fidelity gold labels to calibrate baseline risk. A low-complexity (sparse) correction anchors proxy outcome models to the target population, and the anchored models are embedded in a cross-fitted doubly robust learner, yielding a Neyman-orthogonal, target-site doubly robust estimator for patient-level heterogeneous treatment effects when target treated outcomes are available. We distinguish two regimes: in connected targets (with a treated arm), the method yields target-identified effect estimates; in disconnected targets (placebo-only), it reduces to a principled screen--then--transport procedure under explicit working-model transport assumptions. Experiments on synthetic data and a semi-synthetic IHDP benchmark evaluate pointwise CATE accuracy, ATE error, ranking quality for targeting, decision-theoretic policy regret, and calibration. Across connected settings, the proposed method is best or near-best and improves substantially over proxy-only, target-only, and transport baselines at small target sample sizes; in disconnected settings, it retains strong ranking performance for targeting while pointwise accuracy depends on the strength of the working transport condition.

Transfer Learning for Meta-analysis Under Covariate Shift

Abstract

Randomized controlled trials often do not represent the populations where decisions are made, and covariate shift across studies can invalidate standard IPD meta-analysis and transport estimators. We propose a placebo-anchored transport framework that treats source-trial outcomes as abundant proxy signals and target-trial placebo outcomes as scarce, high-fidelity gold labels to calibrate baseline risk. A low-complexity (sparse) correction anchors proxy outcome models to the target population, and the anchored models are embedded in a cross-fitted doubly robust learner, yielding a Neyman-orthogonal, target-site doubly robust estimator for patient-level heterogeneous treatment effects when target treated outcomes are available. We distinguish two regimes: in connected targets (with a treated arm), the method yields target-identified effect estimates; in disconnected targets (placebo-only), it reduces to a principled screen--then--transport procedure under explicit working-model transport assumptions. Experiments on synthetic data and a semi-synthetic IHDP benchmark evaluate pointwise CATE accuracy, ATE error, ranking quality for targeting, decision-theoretic policy regret, and calibration. Across connected settings, the proposed method is best or near-best and improves substantially over proxy-only, target-only, and transport baselines at small target sample sizes; in disconnected settings, it retains strong ranking performance for targeting while pointwise accuracy depends on the strength of the working transport condition.

Paper Structure

This paper contains 61 sections, 3 theorems, 86 equations, 24 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Our Contributions
  4. Organization of this Paper
  5. Preliminaries
  6. Problem Statement
  7. Data and Proxy--Gold Setup
  8. Identification and Regularity Assumptions
  9. Proposed Framework
  10. Proposed Estimator
  11. Stage 1: Arm-Specific Transfer Learning via glmtrans
  12. Stage 2: CATE Estimation
  13. Experiments
  14. Evaluation Metrics
  15. Data-Generating Process (DGP)
  16. ...and 46 more sections

Key Result

Lemma 1

Assume the high-dimensional GLM conditions of tian2023transfer for the arm-$a$ regression (including bounded design/curvature, sparsity, and the transfer-heterogeneity condition indexed by $h$). Let $\widehat{\mu}_{a,0}$ be the glmtrans estimator using automatic source detection. Then with probabili where $n_{a,0}$ is the target arm-$a$ sample size and $n_{a,\mathcal{A}_a}$ is the total sample siz

Theorems & Definitions (5)

  • Lemma 1: Prediction error rate for glmtrans outcome regressions
  • Theorem 1: Asymptotic linearity for Option A (Proposed-CF)
  • Theorem 2: Transport error decomposition for Option B (Proposed-B)
  • proof : Proof of Theorem \ref{['thm:optA_asymp']}
  • proof : Proof of Theorem \ref{['thm:optB_decomp']}