Study On The Methods Of Sample Size Re-Estimation For Co-Primary Outcome Data

Background:Clinical trial is the most important way to evaluate the safety and efficacy of new treatments in medical research,and sample size estimation is an essential part of clinical trials.Traditional sample size estimation methods are generally based on data from previous studies,but because the parameter information that researchers have is often insufficient,the estimation is often inaccurate.When the sample size is overestimated,it will cause unnecessary waste and increase the risk of patient exposure;when the sample size is underestimated,it will cause insufficient test power and increase the risk of trial failure.For the above problems,the group sequential design and the sample size re-estimation are often used at present.The latter is easier to understand by clinical researchers because of its intuitive results,and because it focuses on improving the success rate of promising trials,it is more in line with the needs of most researchers and has received more and more attention in recent years.But current research in this area is usually only focused on the case of one endpoint When there are two endpoints in the trial,the common method is to re-estimate the sample size separately for each endpoint,and then select the larger of the two obtained sample sizes as the final sample size.This strategy ignores the correlation between endpoints,which will inevitably lead to inaccurate sample size re-estimation.Therefore,this study attempts to improve this situation and provide a theoretical basis for relevant situations in clinical practice.Objectives:This study attempts to explore the sample size estimation method when there are two endpoints and both endpoints are significant before the overall significance is considered,and considers the situation of continuous variables,in order to make the re-estimated sample size more accurate under the premise of controlling Type I errors and maintaining the power.Methods:Under the framework of the sample size re-estimation,a new method of sample size re-estimation is constructed based on frequency theory and the Bayesian theory.(1)For the binomial distribution endpoints,based on the multivariate normal distribution theory and Bayesian theory,the corresponding joint distribution is constructed,and the conditional power and predictive probability are estimated based on the joint distribution;(2)For the bi-binomial distribution endpoints,the four outcomes under the Co-endpoints are approximately assumed to obey the tetranomial distribution,and the conditional power is calculated.Based on the bivariate logistic regeession model and using copula to construct the marginal correlation the joint distribution under the Bayesian model was established,and then the predictive probability is calculated.Finally,the proposed new method is compared with the existing methods,and its overall power,conditional power and expected sample size are evaluated through multiple simulations.Results:The simulation results show that the new estimation method(1)In the case of the null hypothesis H0,the new method proposed in this paper performs well for various parameter settings,and can keep Type I errors without inflation;(2)Based on the frequency theory,under the alternative hypothesis Hi,the new method that comprehensively considers the two endpoints can achieve a similar power as the traditional method in the promising zone,and at the same time can significantly reduce the expected sample size;(3)Based on Bayesian theory,under the alternative hypothesis H1,,the new re-estimation method for two nornally distributed endpoints can achieve higher power than the frequency method,and the sample size estimation is more accurate;However,the Bayesian method for the two binomial distribution endpoints failed to achieve the expected results and needs to be further improved.Conclusion:This study proposes a new sample size re-estimation method for two normally distributed endpoints and two binomial distribution endpoints as the main evaluation indicators.By reducing the overall expected sample size,the performance in the promising zone is greatly improved compared with traditional methods,which can help researchers obtain more effective and accurate sample size in medical clinical practice.