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Statistical inferences for missing response problems based on modified empirical likelihood

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Abstract

In this paper, we advance the application of empirical likelihood (EL) for missing response problems. Inspired by remedies for the shortcomings of EL for parameter hypothesis testing, we modify the EL approach used for statistical inference on the mean response when the response is subject to missing behavior. We propose consistent mean estimators, and associated confidence intervals. We extend the approach to estimate the average treatment effect in causal inference settings. We detail the analogous estimators for average treatment effect, prove their consistency, and example their use in estimating the average effect of smoking on renal function of the patients with atherosclerotic renal-artery stenosis and elevated blood pressure, chronic kidney disease, or both. Our proposed estimators outperform the historical mean estimators under missing responses and causal inference settings in terms of simulated relative RMSE and coverage probability on average.

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Data accessibility

The rest of the simulation data can be found in the supplementing materials. Access to CORAL data is upon request to MS. Pamela S. Brewster, pamela.brewster@utoledo.edu, and Dr. Christopher J. Cooper, christopher.cooper@utoledo.edu.

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Acknowledgements

Dr. Sima Sharghi would like to acknowledge and thank the important part that Dr. Sally Thurston from University of Rochester has played for completion of this paper. Working under supervision of Dr. Thurston, supported by T32ES007271 NIEHS grant provided the means for completion of this research paper. The authors thank MS. Pamela S. Brewster, and Dr. Christopher J. Cooper from University of Toledo for generously allowing the use of the CORAL data. The authors are also very grateful for the anonymous reviewers and their comments. Their comments has shaped the paper to be more cohesive and clear.

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Authors and Affiliations

  1. Department of Biostatistics and Computational Biology, University of Rochester, New York, USA

    Sima Sharghi

  2. Welltower Inc, Ohio, USA

    Kevin Stoll

  3. Department of Mathematics and Statistics, Bowling Green State University, Ohio, USA

    Wei Ning

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  1. Sima Sharghi
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  2. Kevin Stoll
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  3. Wei Ning
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Correspondence to Sima Sharghi.

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Sharghi, S., Stoll, K. & Ning, W. Statistical inferences for missing response problems based on modified empirical likelihood. Stat Papers (2024). https://doi.org/10.1007/s00362-024-01553-1

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