The Construct Of MCP Statistic In Adaptive Group Sequential Design And Its Use In Sample Size Re-estimation

ObjectivesTo construct a new statistic named MCP in adaptive group sequential design, which can control the whole type I error of the study under the pre-specified a, and to apply the MCP statistic to sample size re-estimation.Methods(1) Based on the statistical theory that the p-value Pkfrom the sub-sample at the kth stage is conditionally or unconditionally uniformly distributed on [0,1] under Ho, the distribution of MCP statistic was derived by use of transform method which was based on Jacobi determinant. Meanwhile, calculating method of the p-value of the whole study and the confidence interval of the test parameter were also derived.(2) Monte Carlo simulation was used to study the property of MCP statistic by comparing it with MSP and MPP statistic.Results(1) The T1statistic of MCP was uniformly distributed on [0,1] under Ho; The T2statistic of MCP yielded with the sub-probability density function/(t2)=fα1β1f(t1, t2)dt2dt1under Ho; The joint distribution of (T1,T2)was not influenced by sample size re-adjustment during interim analysis, thus the whole type I error of the study was perfectly controlled by use of MCP statistic; The p-value calculated based on stage-wise ordering was consistent with the result of hypothesis test; If the trial stopped after the interim analysis,then the confidence interval of θ was the set:{θ|1-F(F-1(1-p1)-(?)≥α1)};Tf the trial stopped until the second stage was finished,then the confidence interval of θ was the set:(2)The conditional power of MCP at the interim analysis was cP=1-The re-estimated sample size was n2=The conditional type I error of MCP at the interim analysis was Under the condition that fα1β1A*(p1)dp1=fα1β1A(p1)dp1,the two-stage adaptive group sequential design could be extended to multi-stage,which enabled multi-re-estimating pf sample size.(3)The Monte Carlo simulation showed that:the whole type I error of the study could be perf_ectly controlled by use of MCP statistic；The conditional power of MCP near the area of P1=0had the trend of approaching that of MSP, thus no over-high conditional power like MPP would happen；Compared with MSP,MCP had a wider "inner wedge",which made MCP had less probability to commit type II error in the interim analysis.In a reasonable range of re-estimated sample size,the re-estimated sample size of MCP is between that of MSP and MPP.ConclusionsMCP had similar operating characters as MSP and MPP.The property of MCP in sample size re-estimation was between that of MSP and MPP in most occasions. Moreover,MCP remedied the drawbacks of MSP and MPP. Thus,MCP was more suitable to be used in the sample size re-estimation of adaptive group sequential design and had great value in practical applications.The innovation points of this paper were(1)the distribution and properties of MCP statistic were derived theoretically and thus formula references for calculating stop boundaries and re-estimated sample size were provided；(2)operating characters of MCP,MSP and MPP are showed by Monte Carlo simulation and practical guidance for choosing statistic when designing a clinical trial were provided.