Confidence Intervals of Risk Ratios for the Augmented Logistic Regression with Pseudo-Observations

The augmented logistic regression proposed by Diaz-Quijano directly provides risk ratios with an augmented dataset with the pseudo-observations. However, the standard errors of regression coefficients cannot be accurately estimated using either the ordinary model variance estimator or the robust variance estimator, as neither method appropriately accounts for the pseudo-observations. In this study, we proposed two resampling strategies based on the bootstrap and jackknife methods to construct improved variance estimators for the augmented logistic regression. Both procedures can reflect the overall uncertainty of the augmented dataset involving the pseudo-observations and require only standard software, making them feasible for a wide range of clinical and epidemiological researchers. We validated these proposed methods through comprehensive simulation studies, which demonstrated that both the bootstrap- and jackknife-based variance estimators provided smaller standard error estimates and correspondingly narrower 95% confidence intervals, whereas the robust variance estimator remained biased. Additionally, we applied the proposed methods to real-world binary data, confirming their practical utility.