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Finite-sample improved confidence intervals based on the estimating equation theory for the modified Poisson and least-squares regressions

  • Hisashi Noma ORCID logo EMAIL logo and Masahiko Gosho
Published/Copyright: July 17, 2025
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Epidemiologic Methods
From the journal Epidemiologic Methods Volume 14 Issue 1

Abstract

Objectives

In clinical and epidemiological studies, the modified Poisson and least-squares regression analyses for binary outcomes have been used as standard multivariate analysis methods to provide risk ratio and risk difference estimates. However, their ordinary Wald-type confidence intervals can suffer from finite-sample biases in the robust variance estimators, and the coverage probabilities of true effect measures are substantially below the nominal level (usually 95 %). To address this issue, new accurate inference methods are needed.

Methods

We propose two accurate inference methods based on the estimating equation theory for these regression models. A remarkable advantage of these regression models is that the correct models to be estimated are known, that is, conventional binomial regression models with log and identity links. Using this modeling information, we first derive the quasi-score statistics, whose robust variances are estimated using the correct model information, and then propose a confidence interval based on the regression coefficient test using χ 2-approximation. To further improve the large sample approximation, we propose adapting a parametric bootstrap method to estimate the sample distribution of the quasi-score statistics using the correct model information. In addition, we developed an R package, rqlm (https://doi.org/10.32614/CRAN.package.rqlm), that can implement the new methods via simple commands.

Results

In extensive simulation studies, the coverage probabilities of the two new methods clearly outperformed the ordinary Wald-type confidence interval when the regression function assumptions were correctly specified, especially in small and moderate sample settings. We also illustrated the proposed methods by applying them to an epidemiological study of epilepsy. The proposed methods provided wider confidence intervals, reflecting statistical uncertainty.

Conclusions

The current standard Wald-type confidence intervals may provide misleading evidence. Erroneous evidence can potentially influence clinical practice, public health, and policymaking. These possibly inaccurate results should be circumvented using effective statistical methods. These new inference methods would provide more accurate evidence for future medical studies.

Keywords: epidemiologic regression; generalized linear model; quasi-likelihood; estimating equation; bootstrap
Corresponding author: Hisashi Noma, Department of Interdisciplinary Statistical Mathematics, The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan; and The Graduate Institute for Advanced Studies, The Graduate University for Advanced Studies (SOKENDAI), Tokyo, Japan, E-mail: 

Funding source: Japan Society for the Promotion of Science

Award Identifier / Grant number: JP23K11931, JP22H03554, JP24K21306, and JP23H03063

Acknowledgments

The authors would like to thank Dr. Y. Arai (Tottori University) for permission to use the valuable data and K. Nakazono (The Institute of Statistical Mathematics) for his helpful comments on the earlier draft.

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: The authors state no conflict of interest.

  6. Research funding: This study was supported by Grants-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (grant numbers: JP23K11931, JP22H03554, JP24K21306, and JP23H03063).

  7. Data availability: Supplementary Materials are available online at Epidemiologic Methods online and an R package for implementing the proposed methods is available at CRAN (https://cran.r-project.org/web/packages/rqlm).

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Supplementary Material

This article contains supplementary material (https://doi.org/10.1515/em-2024-0030).

Received: 2024-11-26
Accepted: 2025-06-18
Published Online: 2025-07-17

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/em-2024-0030
Keywords for this article
epidemiologic regression; generalized linear model; quasi-likelihood; estimating equation; bootstrap

Articles in the same Issue

  1. Causal mediation analysis for difference-in-difference design and panel data
  2. Research Articles
  3. Sensitivity analysis for unmeasured confounding for a joint effect with an application to survey data
  4. Investigating the association between school substance programs and student substance use: accounting for informative cluster size
  5. The quantiles of extreme differences matrix for evaluating discriminant validity
  6. Finite-sample improved confidence intervals based on the estimating equation theory for the modified Poisson and least-squares regressions
  7. What if dependent causes of death were independent?
  8. Bot invasion: protecting the integrity of online surveys against spamming
  9. A study of a stochastic model and extinction phenomenon of meningitis epidemic
  10. Understanding the impact of media and latency in information response on the disease propagation: a mathematical model and analysis
  11. Time-varying reproductive number estimation for practical application in structured populations
  12. Perspective
  13. Should we still use pointwise confidence intervals for the Kaplan–Meier estimator?
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