Objectives: In clinical and epidemiological studies, the modified Poisson and least-squares regression analyses for binary outcomes have been standard multivariate analysis methods to provide risk ratio and risk difference estimates. However, their ordinary Wald-type confidence intervals can suffer from biases of 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 provide two accurate inference methods based on the estimating equation theory for these regression models. A remarkable advantage of these regression models is that we know the correct models to be estimated: the conventional binomial regression models with log and identity links. Utilizing this modeling information, we first derive the quasi-score statistics, whose robust variances are estimated using the correct model information, and propose a confidence interval based on the regression coefficient test using χ^2-approximation. Also, to further improve the large sample approximation, we propose adapting a parametric bootstrap method to estimate the sample distribution of the quasi-score statistic 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. We also illustrate the proposed methods via applications to an epidemiologic study of epilepsy. The proposed methods provided wider confidence intervals reflecting the statistical uncertainty. Conclusions: The current standard Wald-type confidence intervals might provide misleading evidence. If erroneous evidence is reported, it can potentially influence clinical practice, public health, and policy making. These possibly inaccurate results should be circumvented through the use of effective statistical methods. The new inference methods would provide more accurate evidence in future medical studies.

The authors have declared no competing interest.

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).

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I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).

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R package for implementing the proposed methods is available at CRAN (https://cran.r-project.org/web/packages/rqlm).