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Combining parametric and nonparametric models to estimate treatment effects in observational studies

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  • Daniel Daly‐Grafstein
  • Paul Gustafson

Abstract

Performing causal inference in observational studies requires we assume confounding variables are correctly adjusted for. In settings with few discrete‐valued confounders, standard models can be employed. However, as the number of confounders increases these models become less feasible as there are fewer observations available for each unique combination of confounding variables. In this paper, we propose a new model for estimating treatment effects in observational studies that incorporates both parametric and nonparametric outcome models. By conceptually splitting the data, we can combine these models while maintaining a conjugate framework, allowing us to avoid the use of Markov chain Monte Carlo (MCMC) methods. Approximations using the central limit theorem and random sampling allow our method to be scaled to high‐dimensional confounders. Through simulation studies we show our method can be competitive with benchmark models while maintaining efficient computation, and illustrate the method on a large epidemiological health survey.

Suggested Citation

  • Daniel Daly‐Grafstein & Paul Gustafson, 2023. "Combining parametric and nonparametric models to estimate treatment effects in observational studies," Biometrics, The International Biometric Society, vol. 79(3), pages 1986-1995, September.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:3:p:1986-1995
    DOI: 10.1111/biom.13776
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    References listed on IDEAS

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    1. Corwin M. Zigler & Krista Watts & Robert W. Yeh & Yun Wang & Brent A. Coull & Francesca Dominici, 2013. "Model Feedback in Bayesian Propensity Score Estimation," Biometrics, The International Biometric Society, vol. 69(1), pages 263-273, March.
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    3. Olli Saarela & David A. Stephens & Erica E. M. Moodie & Marina B. Klein, 2015. "On Bayesian estimation of marginal structural models," Biometrics, The International Biometric Society, vol. 71(2), pages 279-288, June.
    4. O. Saarela & L. R. Belzile & D. A. Stephens, 2016. "A Bayesian view of doubly robust causal inference," Biometrika, Biometrika Trust, vol. 103(3), pages 667-681.
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