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Evaluation of alternative confidence intervals to address non‐inferiority through the stratified difference between proportions

The confidence interval (CI) for the difference between two proportions has been an important and active research topic, especially in the context of non‐inferiority hypothesis testing. Issues concerning the Type 1 error rate, power, coverage rate and aberrations have been extensively studied for non‐stratified cases. However, stratified confidence intervals are frequently used in non‐inferiority trials and similar settings. In this paper, several methods for stratified confidence intervals for the difference between two proportions, including existing methods and novel extensions from unstratified CIs, are evaluated across different scenarios. When sparsity across the strata is not a concern, adding imputed observations to the stratification analysis can strengthen Type‐1 error control without substantial loss of power. When sparseness of data is a concern, most of the evaluated methods fail to control Type‐1 error; the modified stratified t‐test CI is an exception. We recommend the modified stratified t‐test CI as the most useful and flexible method across the respective scenarios; the modified stratified Wald CI may be useful in settings where sparsity is unlikely. These findings substantially contribute to the application of stratified CIs for non‐inferiority testing of differences between two proportions.