Sample Size Determination With Co-primary Endpoints In Non-inferiority Clinical Trials

Objective:In recent years,it has been recognized that a primary endpoint is not sufficient for evaluation of clinical trial efficacy of some diseases,and multiple possible related indicators are needed to fully reflect the effects of the intervention.In many clinical areas,such as oncology,infectious diseases,cardiovascular disease and other clinical trials,the use of co-primary endpoints has become a common design feature.The decision frame of the co-primary endpoinst requires that each endpoint needs to be statistically significant in order to reject the null hypothesis,accept the alternative hypothesis,and conclude that the trial is a positive conclusion in term of statistical inference.The Sample size determination with co-primary endpoints in superiority clinical trials has been relatively mature.But there is little research in non-inferiority clinical trails.This article aims to explore the sample size determination that protects overall power with co-primary endpoints in non-inferiority clinical trials with correlative continuity co-primary endpoints and binary co-primary endpoints from the statistical statistics of the difference and ratio,respectively.Methods:Based on the sample size determination in superiority clinical trials with correlative continuity co-primary endpoints and binary co-primary endpoints from the statistical statistics of the difference and ratio,respectively.By redefining the relevant parameters,sample size determination that protects overall power with co-primary endpoints in non-inferiority clinical trials was proposed.Method for estimating the sample size of correlative continuity co-primary endpoints and binary co-primary endpoints was set under different correlation coefficients,different effect sizes,different non-inferiority margins and different types of error levels.The estimated sample size results were verified under a certain global power(such as 80%)setting by Monte-Carlo simulation techniques.Results: The sample size determination of correlative continuity co-primary endpoints and binary co-primary endpoints in non-inferiority clinical trials in this study can ensure a pre-set global power in the decision-making framework defined by the co-primary endpoins.For the case where the continuous co-primary endpoints which effect is the difference of means,the sample size decreases with the increase of the correlation coefficient when the number of end points,the type I error level,the global power and the effect size parameters are constant.When the standard effect size difference between the endpoints is large,the sample size mainly depends on the smaller standard effect size and is less affected by the relationship of the correlation coefficient.For the case where the continuous co-primary endpoints which effect is the ratio of means,the sample size increases as the coefficient of variation increases,and decreases as the correlation coefficient increases.Under the same conditions,the ratio of means is used as the effect size could save the sample size compared with the difference between the means.The sample size estimation results for the binary co-primary endpoints also shows similar behavior patterns.Conclusions:The formula constructed in this article has a strict statistical theoretical basis and can protect the overall power better.It can provide methodological support for the sample size determination that protects overall power in non-inferiority clinical trials with correlative continuity co-primary endpoints and binary co-primary endpointsThe method in this study is with strong practical value.