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

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.