Comparisons For Calculating Confidence Intervals Of Rate Differences In Clinical Trials With Both Rates Of 100%

Background:In medical research field,an extreme situation may be happened that the event rates of two groups are both 100%or 0%,such as the excellent and good rate of CT image system,the success rate of joint replacement,and the cerebrospinal fluid leak out rate of meninx paster etc..The rate difference between two groups in these cases is 0.Traditional approximately normal and exact methods could not estimate confidence intervals of rate difference since they are not able to estimate the standard deviation of rate difference.To resolve this issue,three methods were proposed by scholar successively,namely Miettinen-Nurminen Method(M-N),Newcombe-Wilson Score Method(N-W)and continuity correction Newcombe-Wilson Score Method(N-W_C).The question that which one could perform better among the three methods needs to be verified.Objective:To explore the methods which are used to calculate rate difference confidence intervals in case the event rates of two groups are both 100%,the Monte Carlo simulation method will be utilized to compare the statistical performance of three methods for rate difference confidence intervals estimation.Hence it can provide the basis for the selection of statistical analysis methods of rate difference confidence interval in clinical trials.Method:Firstly,the three methods M-N,N-W,and N-W_C,which are used to calculate rate difference confidence intervals in case the event rates of two groups are both 100%,would be introduced.The Monte Carlo method was used to simulate the binomial distribution,and the simulation parameters were set as following:the test level was two-side 0.05;the non-inferiority margin was fixed at 5%;the overall rate of the control group was set from 98%to 99.9%by 0.1%.The overall rate of the treatment group was 98%to 99.9%.The statistical performance of the test method was evaluated by the Type ? error rate and the power of test.All statistical calculations were implemented using SAS9.4 software programming.Results:Based on the Wald method to estimate the sample size,the Type ? error rates of M-N method,N-W method and N-W_C method are below 2.5%,lower than pre-specified 5%;for the M-N method and N-W method,when the event rate is between 98%and 98.5%,the test power can reach greater than 50%,when the event rate is between 98.6%-99%,the test power will be reduced from 46.4%to 28.5%;for the N-W_C method,the test power is up to 53.5%,when the event rate is greater than 98.5%the test power is below 26.9%.Based on the Newcombe method,the rates of Type ? error of three methods are less than 1.5%,which is lower than the pre-specified 5%;for M-N method and N-W_C method,the rates of Type ? error will be reduced with the increasing of event rates,when the event rate is 98%,the rates of Type ? errors are 1.3%and 1.1%respectively.The rate of Type ? error of N-W method fluctuated with the changing of event rate,the Type ? errors are below 1.5%basically.From the simulation results of test power(1-?),using the Newcombe sample size design,the test power of M-N method can achieve to 50%when the event rate is in 98%-98.8%,while the test power will be reduced from 50%to 7.4%when the event rate exceeds 98.8%;the trends of test power of N-W method and N-W_C method are quite different:the test power of N-W C method is basically below 50%when the event rate is in 98%-100%;for N-W method,the test power fluctuates in the range of 50%-70%when the event rate is in 98%-99.5%,once the event rate reaches to 99.5%,the test power is greater than 80%.Based on the sample size design by Wald and Newcombe methods,the rates of Type ? error of three methods are close to the pre-specified 5%when the event rate is between 98%and 99%,but once the event rate exceeds 99%,the rates of Type ? error of three methods will be greater than 5%.When the event rate is 99.9%,the rate of Type ? error of N-M method can reach to 9.5%,and the other two methods can reach to 8.3%.In the simulation results of test power(1-?),the test power of M-N method is in the vicinity of 80%(ranging from 73.4%to 84.3%)when the event rate is in 98%-99%;for the N-W method,the test power is in the range of 73.4%-80.2%when the event rate is less than 98.8%,and the power will reduce from 80.2%to 62.3%once the event rate is greater than 98.8%.the trend of test power of N-W_C method(ranging from 62.3%to 83.3%)is consistent with the M-N method when the event rate is in 98%-99%..When the event rate exceeds 99%,the trends of test power of the three methods are significantly different:for M-N method and N-W_C method,the test powers are gradually decreased to 14.2%,which is much lower than the requirement of power in clinical trial;however,the test power of N-W method is gradually increased,and the test powers are 84.3%,94.3%,and 99.8%when the event rates are 99%,99.5%,and 99.9%respectively.Conclusions:When the sample size was designed based on the Wald method and the Newcombe scoring method,and the rate difference confidence interval was calculated using the corresponding analysis method,the Type ? error and test power could meet the requirements of clinical trials when the event rate was in 98%-99%;however,when the event rate is greater than 99%,the three methods are likely to appear Type I error expansion or under test power,the existing methods still need to be further improved.