Sample Size Studies In Clinical Trials

Phase Ⅲ clinical trials are confirmatory studies,so sample size calculation is a critical step.Fisher information is used in conjunction with Brownian motion in the sequential design of clinical trials.However,there is no literature that specifically applies Fisher information to the sample size calculation of clinical trials.This paper mainly focuses on the fixed sample size design and group sequential design in clinical trials,using Fisher information to give a sample size formula framework,and calculate the sample size formulas for 0-1 distribution and exponential distribution,and conduct simulation and data analysis on the sample size results.The full text is divided into five chapters.The first chapter is the introduction,which introduces the research background of clinical trials and sample size calculation and the research status at home and abroad,and finally introduces the innovations and main research contents of this paper.The second chapter is preparatory knowledge,introducing Fisher information,survival analysis model,log-rank test and cox proportional hazards model.The third chapter firstly gives the sample size formula frame in fixed sample size design,and then gives the sample size formulas of three estimation methods of 0-1 distribution and the formula of the number of events of exponential distribution.The validity of the sample size formulas of the two distributions is verified by simulation experiments.Data analysis was performed on the sample size results of the two distributions.The results show that the sample size differences of the three estimation methods of the 0-1 distribution also increase with the increase of the ratio R of the sample sizes;when the incidence rate was higher or lower,the relationships between the three sample sizes were significantly different;the sample size results and simulation of exponential distribution derived in this paper are different from those of Schoenfeld’s classical sample size formula when the ratio of sample size is R=1 and R≠1.The fourth chapter presents the statistical principle of group sequential design and the frame of sample size formula,and introduces several classical interim analysis methods.Then,the sample size formulas of the three estimation methods of 0-1 distribution and the event number formula of exponential distribution are given.Simulation experiments were carried out to verify the validity of the sample size formulas for the two distributions.Data were analyzed for the interim analysis method and the sample size formula for the two distributions.The results show that the seven classic interim analysis methods have different characteristics and are suitable for different types of clinical trials;the effect of incidence on the expected sample size of 0-1 distribution in the sequential design is consistent with that in the fixed sample size design;the expected sample size of 0-1 distribution and exponential distribution is significantly smaller than that of fixed sample size design,which shows the advantages of sequential group design.The fifth chapter summarizes the content of the whole paper and gives the conclusion,and discusses the future research direction.