The Interim Analysis And Decision In Clinical Trials: Application Of Conditional Power

The estimates of treatment effect, individual variation and adverse reaction are always inaccurate at the beginning of a clinical trial. In an adaptive design, investigatos need to perform interim analysis in the mid-term of the trial based on acquired data. The subsequent trial may be adjusted according to the result of interim analysis.Conditional power (CPower) and predictive probability (PP) methods are defined as the probability of achieve the expected outcome based on current data, assuming the subsequent process is in consistent with the finished part. Sample size may be adjusted based on the estimated CPower and PP. And the trial may even be considered to be early terminated.In this research, we focused on conditional power method. We firstly systematically described the basic principle of conditional power and the method of sample size adjustement. Simulation studies and datasets from real clinical trials were then used to elaborate the application of conditional power, focusing on the selection of information time of interim analysis and conditional power measures. The main research contents are:1. To explore the best information time of interim analysis:We used the comparison of two sample means as the example with the sample ratio of 1:1. At the beginning of the trial, we assumed the difference between population means 0=5, standard deviationσ₁=σ₂=14. According to a two-sided significant level of 0.05 and a power of 80%, each group needed N0 individuals. If the actual difference was lower than 0, the expected power of 80% may not be achieved at the pre-determined sample size. In simulation studies, we assumed the actual difference delta=4.5,4,3.75,3.6,3.5,3.4,3.25,3,2.5,1.5 or 0, and planned an interim analysis at 1 / 4,1 / 3,1 / 2,2 / 3 or 3 / 4 information time, calculating the conditional power, respectively. The sample size would not be adjusted if Cpower was greater than or equal to 80%. Otherwise, sample size needs to be increased to N to achive a Cpower of 80%. We then evaluated the accuracy of Cpower prediction and sample size adjustment at different information time.2. To examine the distribution of conditional power:Firstly, we determined the sample size according to a power of 80% and other parameters. We performed an interim analysis at each information time (0.1-0.9), calculating the conditional power and estimating the real power. We repeated this procedure 10,000 times, and evaluated the characteristics of Cpower distribution; Secondly, by fixing the sample size, we chose different information time (0.1-0.9) and different parameters ( =5,4,3.5,3,2,0), then compared the median and mean of Cpower distribution to the real power; Thirdly, we fixed the power and set up different parameters to indentify the percentile which was most close to the real power.3. To identify a reasonable predict index of powerWe calculated a new index (inverse power, Ipower). By fixing the power of 80%,50% or 20%,we constructed the functional relation between Cpower and power, then calculated power according to Cpower and compared it to actual power.4. Case study: For illustration purpose, two real examples were discussed. The first one was from a phase III clinical trial which intended to analyze the effecacy and safety of trospium chloride in curing detrusor instability. We assumed an interim analysis was performed at the half of the trial, calculated the conditional power, and adjusted the sample size accordingly; The other one was the NHLBI type II coronary intervention study, which evaluated the efficacy of cholestyramine on the progression of CAD as assessed by angiography. The result of the study was not statistically significant. However, we estimated the additional sample size needed to achieve the expected power using the CPower method.The main results of this research are as follows:1. By comprehensively considering the representativeness of interim data and the distribution characteristics of Cpower, we suggest to choose the information time of 0.5 for an interim analysis, when Cpower is close to the real power to the most degree.2. The skewness of the distribution of CPower is associated with the actual power. If power=50%,Cpower is distributed like a U-shape; If power>50%, Cpower is left skewed while it is right skewed if power<50%.3. The Ipower calculated based on Cpower is in great consistent with the real power. It becomes more and more stable as the information time increases. The deviance can be controlled at the level of 5% after the information time of 0.5.The main conclusions of this research are:1. When using the traditional Cpower method, we suggest the interim analysis to be performed at the half of the trial; the type I error rate would not be inflated after sample size adjustment. However, as Cpower follows a U-shape distribution with large variation and may be influenced by original sample size, the deviation would be large and the power would be slightly below expectation, which deserves much caution in application.2. Whe using the Ipower method, prediction would not be affected by information time. Thus the interim analysis can be performed at the middle or late half of the trial; after sample size modification the type I error rate is well controlled and the power can achieve the expected level.