Exact confidence intervals for risk differences of stratified binomial proportions

Confidence intervals for risk differences are commonly used in non-inferiority trials where the primary efficacy endpoint is binary. When analyses incorporate stratification, existing methods based on asymptotic approximations may fail to provide adequate coverage, whereas developing exact confidence intervals to guarantee coverage probability remain an unresolved challenge despite its appeal. We propose an exact test of equivalence for the common risk difference by combining exact p-values from each stratum using characteristic functions and inverse Fourier transformations. Exact confidence intervals are then derived by inverting the exact test. The proposed method ensures coverage probability, which is particularly important in non-inferiority trials where under-coverage could potentially allow an inferior drug to meet the non-inferiority boundary and gain approval. The proposed method is evaluated in simulation studies and illustrated using real data from an HIV treatment trial. It represents a significant advancement in stratified binary endpoint analysis.