Common risk difference and corresponding confidence interval adjusted for multiple factors – comparison of seven different methods

The U.S. Food and Drug Administration (FDA) recently emphasized the importance of covariate adjustment in the analysis of clinical trial endpoints. A prevalent technique, particularly in the analysis of dichotomous endpoints, involves calculating weighted estimates as suggested by Cochran (1954) and Mantel and Haenszel (1959). This approach entails pooling data from all summary tables stratified by relevant factors and weights assigned to each stratum based on the harmonic mean of the stratum-specific sample sizes (referred to as MH weight). However, it is worth noting that while MH weight is commonly used, it may not always yield optimal efficiency. To address this, Mehrotra and Railkar (2000) proposed 'minimum risk' weighting strategies for constructing Wald-type confidence intervals. More recently, Klingenberg (2014) introduced two score-based methods for computing confidence intervals on differences in proportions, adjusted for strata, and demonstrated their superiority over Wald-type methods. In addition, model-based techniques such as logistic regression are commonly employed for covariate adjustment, where Wald-type confidence intervals are often obtained via the Delta method. However, Wald-type intervals are prone to undercoverage, as noted by Agresti and Coull (1998). To improve this, we propose cell-wise adjustments (Agresti and Caffo 2000; Agresti and Coull 1998) along with bias-reduction techniques (Firth 1993) tailored specifically for logistic regression models. We conducted extensive simulations to compare the performance of seven methods and demonstrate that such adjustments improve the coverage of Wald-type confidence intervals.