The Study Of Blinded Sample Size Re-Estimation With Survival Data

BackgroundThe calculation of an appropriate sample size is a key problem in the planning phase of a clinical trial,which often depends upon certain nuisance parameters.In traditional fixed design,researchers estimate the values of those nuisance parameters based on the experts’ suggestion and data from previous similar researches,then figure out the sample size.And the sample size is invariable in the process of the trial.However,when the information about the key parameter is deficient or the conditions of clinical trials are quite different,the values of nuisance parameters are hard to be accurately estimated.As a consequence,the sample size would be inaccurate.If the estimated sample size is much larger than the true one,it would offend moral principles and result in waste.On the contrary,if the estimated sample size is much smaller,the trial would be underpowered and would be disable to find out efficient drugs or treatments.Adaptive design is proposed to address the problem,in which sample size re-estimation is permitted to be conducted depending upon the observed data during the interim.Survival data is a common data type in clinical trials,but in the interim analysis the survival data is censored with a great percentage,which brings up a huge challenge for sample size re-estimation.The unblinding method means that treatment allocations are unmasked during the analysis in the interim,which would damage the validity and integrity of the trial.The purpose of our study is to explore a blinded method to reestimate the sample size for survival data.Objective and MethodsThis study presumed that survival time follows distinct patterns,exponential distributions or Weibull distributions.In the interim,we use an imputation method to impute the obtained survival data with a high censored rate.Then adjusted EM algorithm is applied for the integrated data to re-estimate the nuisance parameter,with which a reestimated sample size is calculated sequentially.Monte Carlo simulations are employed to test the accuracy and stability of the method.Supposed a two-arm clinical trial based on log-rank test,and the allocation rate of subjects in two groups is 1:1.In advance of the trial,a hunting zone is ascertained based on the pre-specified parameter.The parameters in the hunting zone are refered to as imputed parameters.In the interim,integrate the censored data with the parameters in the hunting zone.Apply adjusted EM algorithm for the integrated data,then a number of reestimated values of parameters are obtained.Pick out the best reestimated value,whose difference is minimum with the imputed parameter,as the reestimated value of true parameter.The process amends the problem that estimated values of EM algorithm depend on the initial values,which is referred to as adjusted EM algorithm.At last,compute the reestimated sample size based on the reestimated parameters.Set two series of interim time-points,and contrast the result of each point.Plan 1 is based on the additional follow-up time t,I1 is at the time-point T0(entry period),I2 is T0+0.25 t,I3 is T0+0.5t,and I4 is T0+0.75 t.Plan 2 is based on the number of events E,I1 is at the time-point T0,I2 e is 0.25 E,I3e is 0.5E,and I4 e is 0.75 E.The simulation is performed 1000 times for each scenario,and compute the mean and standard deviation of reestimated sample size to evaluate the accuracy and the stability of the new method.In the meantime,apply log-rank test for 10000 times with the reestimated sample size to calculate the type I error and empirical power.Results and ConclusionThis paper presents a method to reestimate the sample size of the survival trial,which follows exponential distributions or Weibull distributions.The main conclusions are summarized as follows.When survival data follows exponential distributions and the hazard ratio is assumed,a hunting zone M10 ? 0.5M10 is specified based upon the median survival time of the control group M10.By comparing the reestimated sample size at different interims under different hazard ratios,we find out that when the hunting zone contains the true parameter at interims as I2,I3,I4,I3 e,I4e,the reestimated sample size ?N is precise and the variation is stable.In practice,the cost of trials increases as interim analysis postpones.So it is appropriate to conduct interim analysis at I2 or I3 e under similar conditions.The interim analysis should be adjusted if the conditions are quite different from the setting of our study.When survival data follows Weibull distributions,the shape parameter γ would be reestimated at interim analysis.Specify a hunting zone of γ based on previous experiences,the rules are displayed as follows.If the hazard rate decreases over time,the hunting zone is 0.5 to 1.If the hazard rate increases over time,the hunting zone is1 to2.If the hazard rate is stable over time,the hunting zone is 0.5 to 1.5.When hunting zones include the true parameter,the reestimated sample size is close to the true sample size.Slight changes of γ can cause large fluctuations of sample size,so the variance of reestimated sample size is large.As a result,it is appropriate to conduct interim analysis at I1 under similar conditions.If conditions vary widely,the interim analysis could be adjusted by new simulations.