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Combining Experimental and Observational Data for Identification and Estimation of Long-Term Causal Effects

Author

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  • AmirEmad Ghassami
  • Alan Yang
  • David Richardson
  • Ilya Shpitser
  • Eric Tchetgen Tchetgen

Abstract

We consider the task of identifying and estimating the causal effect of a treatment variable on a long-term outcome variable using data from an observational domain and an experimental domain. The observational domain is subject to unobserved confounding. Furthermore, subjects in the experiment are only followed for a short period of time; hence, long-term effects of treatment are unobserved but short-term effects will be observed. Therefore, data from neither domain alone suffices for causal inference about the effect of the treatment on the long-term outcome, and must be pooled in a principled way, instead. Athey et al. (2020) proposed a method for systematically combining such data for identifying the downstream causal effect in view. Their approach is based on the assumptions of internal and external validity of the experimental data, and an extra novel assumption called latent unconfoundedness. In this paper, we first review their proposed approach, and then we propose three alternative approaches for data fusion for the purpose of identifying and estimating average treatment effect as well as the effect of treatment on the treated. Our first approach is based on assuming equi-confounding bias for the short-term and long-term outcomes. Our second approach is based on a relaxed version of the equi-confounding bias assumption, where we assume the existence of an observed confounder such that the short-term and long-term potential outcome variables have the same partial additive association with that confounder. Our third approach is based on the proximal causal inference framework, in which we assume the existence of an extra variable in the system which is a proxy of the latent confounder of the treatment-outcome relation. We propose influence function-based estimation strategies for each of our data fusion frameworks and study the robustness properties of the proposed estimators.

Suggested Citation

  • AmirEmad Ghassami & Alan Yang & David Richardson & Ilya Shpitser & Eric Tchetgen Tchetgen, 2022. "Combining Experimental and Observational Data for Identification and Estimation of Long-Term Causal Effects," Papers 2201.10743, arXiv.org, revised Apr 2022.
  • Handle: RePEc:arx:papers:2201.10743
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    References listed on IDEAS

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    1. David Card, 1990. "The Impact of the Mariel Boatlift on the Miami Labor Market," ILR Review, Cornell University, ILR School, vol. 43(2), pages 245-257, January.
    2. Susan Athey & Guido W. Imbens, 2006. "Identification and Inference in Nonlinear Difference-in-Differences Models," Econometrica, Econometric Society, vol. 74(2), pages 431-497, March.
    3. Wang Miao & Zhi Geng & Eric J Tchetgen Tchetgen, 2018. "Identifying causal effects with proxy variables of an unmeasured confounder," Biometrika, Biometrika Trust, vol. 105(4), pages 987-993.
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    Cited by:

    1. Harsh Parikh & Marco Morucci & Vittorio Orlandi & Sudeepa Roy & Cynthia Rudin & Alexander Volfovsky, 2023. "A Double Machine Learning Approach to Combining Experimental and Observational Data," Papers 2307.01449, arXiv.org, revised Apr 2024.
    2. Guido Imbens & Nathan Kallus & Xiaojie Mao & Yuhao Wang, 2022. "Long-term Causal Inference Under Persistent Confounding via Data Combination," Papers 2202.07234, arXiv.org, revised Aug 2024.

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