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Model averaging for estimating treatment effects

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Abstract

The estimation of treatment effects on the response variable is often a primary goal in empirical investigations in disciplines such as medicine, economics and marketing. Typically, the investigator would select one model from a multitude of models and estimate the treatment effects based on this single winning model. In this paper, we consider an alternative model averaging approach, where estimates of treatment effects are obtained from not one single model but a weighted ensemble of models. We develop a weight choice method based on a minimisation of the approximate risk under squared error loss of the model average estimator of the conditional treatment effects. We prove that the model average estimator resulting from this criterion has an optimal asymptotic property. The results of a simulation study show that the proposed approach is superior to various existing model selection and averaging methods in a large region of the parameter space in finite samples. The proposed method is applied to a data set on HIV treatment.

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Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

The authors are grateful to Drs. Craig Rolling and Yuhong Yang for providing their codes for the computation of the TECV estimates and to Dr. Yuhong Yang for several helpful discussions. This paper has benefitted from the suggestions and comments of two referees. All remaining errors are ours.

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Authors and Affiliations

  1. School of Statistics, Capital University of Economics and Business, 121 Zhangjialukou, Huaxiang Fengtai District, Beijing, 100070, China

    Zhihao Zhao

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 55 Zhongguancun East Road, Haidian District, Beijing, 100190, China

    Xinyu Zhang

  3. School of Mathematical Sciences, Capital Normal University, 105 West Third Ring Road North, Haidian District, Beijing, 100048, China

    Guohua Zou

  4. Department of Management Sciences, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Kowloon, Hong Kong, China

    Alan T. K. Wan & Geoffrey K. F. Tso

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  1. Zhihao Zhao
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  2. Xinyu Zhang
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  3. Guohua Zou
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  4. Alan T. K. Wan
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  5. Geoffrey K. F. Tso
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Correspondence to Xinyu Zhang.

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Zhao’s work was supported by Capital University of Economics and Business: The Fundamental Research Funds for Beijing Universities (Grant No. XRZ2021042) and Youth Academic Innovation Team Construction project of Capital University of Economics and Business (Grant No. QNTD202303). Zhang’s work was partially supported by the National Natural Science Foundation of China (Grant Nos. (71925007, 72091212 and 12288201) and the CAS Project for Young Scientists in Basic Research (YSBR-008). Zou’s work was partially supported by the National Natural Science Foundation of China (Grant Nos. 11971323, 12031016). Wan’s work was supported by the Hong Kong Research Grants Council (Grant No. 11500419) and the National Natural Science Foundation of China (Grant No. 71973116).

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Zhao, Z., Zhang, X., Zou, G. et al. Model averaging for estimating treatment effects. Ann Inst Stat Math 76, 73–92 (2024). https://doi.org/10.1007/s10463-023-00876-4

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  • DOI: https://doi.org/10.1007/s10463-023-00876-4

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