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Highly robust causal semiparametric U-statistic with applications in biomedical studies

  • Anqi Yin ORCID logo , Ao Yuan EMAIL logo and Ming T. Tan EMAIL logo
Published/Copyright: November 28, 2022
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The International Journal of Biostatistics
From the journal The International Journal of Biostatistics Volume 20 Issue 1

Abstract

With our increased ability to capture large data, causal inference has received renewed attention and is playing an ever-important role in biomedicine and economics. However, one major methodological hurdle is that existing methods rely on many unverifiable model assumptions. Thus robust modeling is a critically important approach complementary to sensitivity analysis, where it compares results under various model assumptions. The more robust a method is with respect to model assumptions, the more worthy it is. The doubly robust estimator (DRE) is a significant advance in this direction. However, in practice, many outcome measures are functionals of multiple distributions, and so are the associated estimands, which can only be estimated via U-statistics. Thus most existing DREs do not apply. This article proposes a broad class of highly robust U-statistic estimators (HREs), which use semiparametric specifications for both the propensity score and outcome models in constructing the U-statistic. Thus, the HRE is more robust than the existing DREs. We derive comprehensive asymptotic properties of the proposed estimators and perform extensive simulation studies to evaluate their finite sample performance and compare them with the corresponding parametric U-statistics and the naive estimators, which show significant advantages. Then we apply the method to analyze a clinical trial from the AIDS Clinical Trials Group.

Keywords: causal effect; highly robust estimation; semiparametric model; U-statistic
Corresponding authors: Ao Yuan and Ming T. Tan, Department of Biostatistics, Bioinformatics and Biomathematics Georgetown University, Washington, DC 20057, USA, E-mail: (A. Yuan) and (M. T. Tan)

Acknowledgments

This research is part of the Ph.D. dissertation of the first author who would like to thank members of her dissertation committee for their helpful comments. This research is supported in part by NIH grant R21CA270585.

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/ijb-2022-0047). We provide additional material to support the results of this paper. This includes the proofs of Theorems and the regularity conditions, further examples, further simulation results, and a zip file with R code and datasets used for the simulations and applications.

Received: 2022-04-19
Accepted: 2022-10-31
Published Online: 2022-11-28

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijb-2022-0047
Keywords for this article
causal effect; highly robust estimation; semiparametric model; U-statistic

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. Survival analysis using deep learning with medical imaging
  4. Using a population-based Kalman estimator to model the COVID-19 epidemic in France: estimating associations between disease transmission and non-pharmaceutical interventions
  5. Approximate reciprocal relationship between two cause-specific hazard ratios in COVID-19 data with mutually exclusive events
  6. Sensitivity of estimands in clinical trials with imperfect compliance
  7. Highly robust causal semiparametric U-statistic with applications in biomedical studies
  8. Hierarchical Bayesian bootstrap for heterogeneous treatment effect estimation
  9. Penalized logistic regression with prior information for microarray gene expression classification
  10. Bayesian learners in gradient boosting for linear mixed models
  11. Unequal allocation of sample/event sizes with considerations of sampling cost for testing equality, non-inferiority/superiority, and equivalence of two Poisson rates
  12. HiPerMAb: a tool for judging the potential of small sample size biomarker pilot studies
  13. Heterogeneity in meta-analysis: a comprehensive overview
  14. On stochastic dynamic modeling of incidence data
  15. Power of testing for exposure effects under incomplete mediation
  16. Exact correction factor for estimating the OR in the presence of sparse data with a zero cell in 2 × 2 tables
  17. Right-censored partially linear regression model with error in variables: application with carotid endarterectomy dataset
  18. Assessing HIV-infected patient retention in a program of differentiated care in sub-Saharan Africa: a G-estimation approach
  19. Prediction-based variable selection for component-wise gradient boosting
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