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Causal Generalization of Continuous Treatment Effects under Covariate Shift

arXiv 2608.19383 ↗First posted 19 Aug 2026stat.ME stat.MLcited by 0

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Abstract (arXiv)

Average dose-response functions are widely used to summarize causal effects of continuous treatments, but most existing methods assume that the observed sample represents the target population. We study a covariate-shift setting in which covariates, treatment, and outcome are observed in a labelled source sample, while only covariates are observed in the target sample. We develop a two-sample local polynomial regression framework based on pseudo-outcomes that use source outcomes to address confounding and target covariates to define the population of interest. We further propose a source-to-target extension of distance covariance optimal weighting (DCOW), designed to remove treatment-covariate dependence in the source sample while aligning the weighted source covariate distribution with the target population. A central theoretical contribution is a weight-level analysis of this optimization-based procedure: we show that the population criterion identifies the oracle source-to-target weights and that approximate empirical minimizers, including exact minimizers as a special case, converge uniformly to these weights under regularity conditions. We also establish consistency and asymptotic normality of the resulting estimator. Simulations show that the proposed method improves target dose-response estimation relative to DCOW, generalized-propensity-score weighting, entropy balancing, and unweighted alternatives. We illustrate the method in a county-level analysis of PM2.5 exposure and subsequent heart-disease mortality using a source-target validation design.

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References · 17

  1. 2017OSQP: An Operator Splitting Solver for Quadratic Programscited by 161
  2. 2020An Introduction to Proximal Causal Learningcited by 95
  3. 2018Confounding-Robust Policy Improvementcited by 76
  4. 2015Nonparametric methods for doubly robust estimation of continuous treatment effectscited by 64
  5. 2021A Review of Generalizability and Transportabilitycited by 37
  6. 2020Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curvescited by 36
  7. 2017Minimal Dispersion Approximately Balancing Weights: Asymptotic Properties and Practical Considerationscited by 18
  8. 2020Entropy Balancing for Continuous Treatmentscited by 12
  9. 2020Energy Balancing of Covariate Distributionscited by 9
  10. 2021End-to-End Balancing for Causal Continuous Treatment-Effect Estimationcited by 9
  11. 2020Nonparametric Estimation of Population Average Dose-Response Curves using Entropy Balancing Weights for Continuous Exposurescited by 8
  12. 2018Matching on Generalized Propensity Scores with Continuous Exposurescited by 7
5 more
  1. 2022Debiased inference for a covariate-adjusted regression functioncited by 5
  2. 2021Independence weights for causal inference with continuous treatmentscited by 4
  3. 2021Robust Sample Weighting to Facilitate Individualized Treatment Rule Learning for a Target Populationcited by 3
  4. 2022A nonparametric doubly robust test for a continuous treatment effectcited by 3
  5. 2026Estimating Continuous Treatment Effects with Two-Stage Kernel Ridge Regressioncited by 1

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