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Peer-reviewedCC BYStatistics in medicine

Two-Stage Estimation for Causal Inference Involving Semi-Continuous Exposures.

  • Xiaoya Wang1
  • Richard J Cook1
  • Yeying Zhu1
  • Tugba Akkaya-Hocagil2
  • R Colin Carter3
  • Sandra W Jacobson4
  • Joseph L Jacobson4
  • Louise M Ryan5
5 affiliations
  1. 1Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada.
  2. 2Department of Biostatistics, School of Medicine, Ankara University, Ankara, Turkey.
  3. 3Departments of Emergency Medicine and Pediatrics, Columbia University, New York, New York, USA.
  4. 4Department of Psychiatry and Behavioral Neurosciences, Wayne State University, Detroit, Michigan, USA.
  5. 5School of Mathematical and Physical Sciences, University of Technology Sydney, Ultimo, New South Wales, Australia.
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Abstract

Methods for causal inference are well developed for binary and continuous exposures, but in many settings, the exposure has a substantial mass at zero-such exposures are called semi-continuous. We propose a general causal framework for such semi-continuous exposures, together with a two-stage estimation strategy. A two-part propensity structure is introduced for the semi-continuous exposure, with one component for exposure status (exposed vs unexposed) and another for the exposure level among those exposed, and incorporates both into a marginal structural model that disentangles the effects of exposure status and dose. The two-stage procedure sequentially targets the causal dose-response among exposed individuals and the causal effect of exposure status at a reference dose, allowing flexibility in the choice of propensity score methods in the second stage. We establish consistency and asymptotic normality for the resulting estimators, and characterize their limiting values under misspecification of the propensity score models. Simulation studies evaluate finite sample performance and robustness, and an application to a study of prenatal alcohol exposure and child cognition demonstrates how the proposed methods can be used to address a range of scientific questions about both exposure status and exposure intensity.

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Cite

BibTeXRIS
BibTeX
@article{wang2026twostage,
  title = {{Two-Stage Estimation for Causal Inference Involving Semi-Continuous Exposures.}},
  author = {Xiaoya Wang and Richard J Cook and Yeying Zhu and Tugba Akkaya-Hocagil and R Colin Carter and Sandra W Jacobson and Joseph L Jacobson and Louise M Ryan},
  journal = {Statistics in medicine},
  year = {2026},
  month = oct,
  doi = {10.1002/sim.70800},
  url = {https://europepmc.org/article/MED/42951587},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Two-Stage Estimation for Causal Inference Involving Semi-Continuous Exposures.
AU  - Xiaoya Wang
AU  - Richard J Cook
AU  - Yeying Zhu
AU  - Tugba Akkaya-Hocagil
AU  - R Colin Carter
AU  - Sandra W Jacobson
AU  - Joseph L Jacobson
AU  - Louise M Ryan
PY  - 2026
DA  - 2026/10/28
JO  - Statistics in medicine
DO  - 10.1002/sim.70800
UR  - https://europepmc.org/article/MED/42951587
AB  - Methods for causal inference are well developed for binary and continuous exposures, but in many settings, the exposure has a substantial mass at zero-such exposures are called semi-continuous. We propose a general causal framework for such semi-continuous exposures, together with a two-stage estimation strategy. A two-part propensity structure is introduced for the semi-continuous exposure, with one component for exposure status (exposed vs unexposed) and another for the exposure level among those exposed, and incorporates both into a marginal structural model that disentangles the effects of exposure status and dose. The two-stage procedure sequentially targets the causal dose-response among exposed individuals and the causal effect of exposure status at a reference dose, allowing flexibility in the choice of propensity score methods in the second stage. We establish consistency and asymptotic normality for the resulting estimators, and characterize their limiting values under misspecification of the propensity score models. Simulation studies evaluate finite sample performance and robustness, and an application to a study of prenatal alcohol exposure and child cognition demonstrates how the proposed methods can be used to address a range of scientific questions about both exposure status and exposure intensity.
SN  - 0277-6715
SN  - 1097-0258
ER  -