Study On Sample Size Calculation Based On Proportional Hazards Mixture Cure Model

With the advancement of medicine and the improvement of medical technology,many diseases can be cured,or patients can no longer get sick for a long time.Cure factors should be given full attention in the design of survival trials.This article mainly studies the method of determining the sample size in a survival test with a certain cure rate.Scholars have fully studied the determination methods and comparison of advantages and disadvantages of discrete covariates and continuous covariates,but they have not been considered or compared together.In this paper,the method proposed by Zhan et al.(2019)with continuous covariates(denoted as Ewell method)and the method proposed by Xiong and Wu(2017)with discrete covariates(denoted as XW method)are linked together for the first time through the setting of equal covariate variances,so that the calculation method of sample size can be flexibly selected through the connection of covariate variances.The sample size calculation formulas of the two methods are obtained under weighted log-rank test and the martingale theory of counting process.Based on the proportional hazards mixture cure model,firstly,the sample size and relative bias of the Ewell method and the XW method are simulated when various parameters are considered,such as the accrual patterns of the test patient,accrual time,follow-up time and hazard ratio,etc.Then,based on the e1684 data set and the metastatic castration sensitive prostate cancer data set,the R language function "smcure" is used to estimate the cure rate and hazard ratio in the actual data set,and the sample sizes of the two methods are compared.The results of data simulation and case analysis show that the Ewell method is better overall,which provides a good idea for the sample size design of the survival test.Under specific parameter selection or model setting,through binary discretization or continuity methods,and the setting of equal variances,the calculation methods of discrete covariates and continuous covariates can be selected based on the best,which improves the efficiency of clinical trials and saves costs and makes the statistical effect more significant.