Research On The Design Performance And Effect Estimation Of Targeted Clinical Trial

Background and objectThe pharmaceutical industry has achieved substantial progress in drug’s molecular mechanism in the past few decades. However, research on the targeted therapy drugs, which have good efficacy, progressed slowly. The targeted clinical trial increases rapidly after the completion of the Human Genome Project. Proper design and evaluation of the targeted clinical trial plays a key role in the development of the targeted therapy drugs.The design of targeted clinical trial can be classified into three groups based on whether to use the study drug pharmacology therapeutic targets as inclusion and exclusion criteria. They are enrichment design, all-randomized design and strategic-randomized design. So far, simulation studies to evaluate the design of targeted clinical trial mainly use continuous data and two-sample rate data as the primary endpoint. However, most of the targeted therapies are developed for tumor research, which often use survival data as the primary clinical endpoints, such as progression-free survival (PFS) and overall survival (OS). Due to the specialty of censoring for survival data, the statistical performance of the four designs of targeted clinical trial was unclear. Therefore, the first simulation study was conducted to assess the statistical performance of the four design methods to survival censoring data, which could guide the proper choice the targeted clinical trial design. In addition, it is difficult to obtain a100%positive predictive value due to the imperfect diagnosis of disease target for the enrichment design of targeted clinical trials. Therefore it cannot be guaranteed that every participant has the disease target. Someone, who actually does not have the disease target, may get a positive result and get enrolled into the study. So the false positive phenomenon commonly occurs when we enroll the patients. If we assume that the endpoint is a continuous variable, the expected difference of the sample means based on the conventional method follows E(YT-YC)=γ(μT+-μC+)+(1-γ)(μT--μc-) Where μi+、μi-are the means of test and control groups for the patients with or without the molecular target and y is the PPV of the diagnostic method for the target (i=T, C). It contains two components. The first component is the treatment effect in patients with a positive diagnosis truly having the molecular target, and the second components is the treatment effect in patients with a positive diagnosis but in fact without the molecular target. If the treatment effect in patients without the molecular target is smaller than that of patients with the molecular target, the difference in the sample means obtained by the conventional method underestimates the treatment effect of the drug in patients with the molecular target. As a result, the bias will lead to inaccurate estimate of drug effect. Jen-Pei Liu proposed a method based on the EM algorithm and parametric bootstrap re-sampling process to adjust the bias caused by the imperfect diagnostic test. The second simulation study aims to verify the feasibility and applicable situations of this method by a simulation study to compare the statistical performance between the method which Liu proposed and the traditional method by the relative bias and the95%confidence interval coverage probability of the estimators for the treatment effects.Methods The first study was conducted to investigate the relationship between sample size and statistical power of three commonly used targeted clinical trial design methods under pre-set simulation conditions by Monte Carlo simulation techniques using SAS9.2statistical analysis system. The second simulation study is conducted to compare the bias and the95%CI coverage probability of the estimators for the treatment effects of enrichment design targeted clinical trial between the method based on the EM algorithm and parametric bootstrap re-sampling process which Liu proposed and the traditional method. The detail steps are as follows:The detail steps for investigating the relationship between sample size and statistical power of three commonly used targeted clinical trial design methods are as follows:Step1, set parameters and the type of simulated data; Step2, calculate the parameter values of the uniform distribution of censored data under different parametric conditions of setting distributions; Step3, in accordance with the set of parameter values and simulation data distribution type, generate2000survival time random samples including censored data; Step4, calculate the proportion of various design methods under different sample sizes to reject the null hypothesis when the two-side test level a=0.05, or we called it as power.When the relationship between sample size for screening and power of enrichment design is investigated, the difference of the basic steps of the simulation is: before the implementation of the above steps, a random sample was generated from the Bernoulli distribution with probability P+λsens+(1-P+)(1-λspec) and the sample size isnse. nseindicates the sample size for screening and the number of the value of1indicates the sample size for randomization. Then, follow the steps of above simulation study.The detail steps for investigating statistical performance of the method based on the EM algorithm and parametric bootstrap re-sampling process which proposed by Jen-Pei Liu are as follows:Step1, set parameters; Step2, generate a random variable Xi from the Bernoulli distribution with probability PV+which indicate the positive predictive value of the diagnostic method for the target, and Xi is an indicator variable with value of1for the patients truly with the target and value of0for the patients truly without the target. Then Xi are randomized in a1:1ratio to test group or control group; Step3, the random samples are generated from normal distribution with setting parameters according to the real status of target in test group and control group; Step4, calculate the estimates of the treatment effects and its95%confidence interval with the method based on the EM algorithm and parametric bootstrap re-sampling process and the traditional method respectively; Step5, repeat the above steps2,000times and calculate the relative bias and the95%confidence interval coverage probability of the estimators for the treatment effects which are estimated by using the method based on the EM algorithm and parametric bootstrap re-sampling process and the traditional method respectively.ResultsThe results of the first simulation study to investigate the relationship between sample size and power of three commonly used targeted clinical trial designs in difference situation:either the exponential distribution, Weibull distribution or Gompertz distribution is used to generate survival data, or the endpoint is a continuous variable or a binary variable, the simulation results are same. In the first case, the all-randomized design and enrichment design obtain almost the same power with the same sample size for randomization while the strategy design obtain the smallest power. However, the sample size for screening of enrichment design is larger than that of the all-randomized design for getting the same power. In the second case, if the sample sizes for randomization are same, the enrichment design gets the largest power followed by all-randomized design and the strategy design gets the smallest power. In this case, the enrichment design selected only the largest beneficial part of the subjects that target positive patients to obtain the best statistical performance, but ignores the efficacy of the test drug for target negative patients. Meanwhile, the sample size for screening of enrichment design is larger than that of the all-randomized design to get the same power. In the third case, the simulation results are similar to the results obtained in second case. If the sample sizes for randomization are the same, the enrichment design will get the largest power, followed by the all-randomized design and the strategy design. The different point is that the sample size for screening of enrichment design is smaller than that of the all-randomized design to get the same power. In the fourth case, the enrichment design still gets the largest power with the same sample size. The second is the strategy design and the last is the all-randomized design. This is the only case that the strategy design gets the larger power than the all-randomized design.The results of second simulation study to investigate statistical performance of the method based on the EM algorithm and parametric bootstrap re-sampling process:(1) The relative bias of the estimator for the treatment effects. Its value that obtained by the method based on the EM algorithm and parametric bootstrap re-sampling process decreases as the PV+、μt+and n increasing, and increases as σ increasing and is possible to achieve the desired requirement only when PV+、μT+、 n is large enough and a is small. For example, the value will be larger than1%when μT=120. The relative bias will obtain the largest value of about14.8%when n=100、PV+=0.7、a=20and μT+=120. In addition, the value of the relative bias of the estimator for the treatment effects which are estimated through the traditional method almost equal to (1-PV+)×μT-(2) The95%confidence interval coverage probability of the estimator for the treatment effects. Its value that obtained by the method based on the EM algorithm and parametric bootstrap re-sampling process is impacted by μT+and a largely. The value is farther away from95%as a increasing. Furthermore, the rules that how μT+impact the95%confidence interval coverage probability are complex.The rules can be summarized as follows when σ is determined. There are two values a and b, assuming b> a. when μT+<a, the value of the95%confidence interval coverage probability is farther away from95%as μT+increasing. When a μT+<b, the value is closer to95%as μT+increasing. When μT+> b, the value hardly changes as μT+increasing and almost equals to95%. For example, if sample size is set to be200, the PPV is set to be0.7andσ is set to be20, the95%confidence interval coverage probability will obtain the largest value of about0.5705when μT+=130. Its value equals to about0.6535whenμT+=120. WhenμT+≥140, the value is larger than0.5705and increases as theμT+increasing. There is no clear relationship between the95%confidence interval coverage probability and PV+, n. In addition, the value of the95%confidence interval coverage probability is closer to95%as μT+and n decreasing or a and PV+increasing, and its value almost equal to0when μT+is large enough. The95%confidence interval coverage probability will obtain the largest value of about0.8725when n=100、PV+=0.9、σ=20and μT+=120.Considering both the bias and95%confidence interval of the effect estimates, only under the condition that a is small and μT+is large enough, the method based on the EM algorithm and parametric bootstrap re-sampling process can get an accurate effect estimates for enrichment design. If the condition cannot be fulfilled, this method cannot get effect estimates with small bias and satisfactory95%confidence interval, which results to the inaccurate effect estimates. ConclusionsWhen there is sufficient evidence to show a clear interacted relationship between the status of the target and the drug effect and also have a reliable target diagnosis method, we recommend to use the enrichment design. If there is not a reliable target diagnosis method or it is unclear whether the therapy is beneficial for marker-negative patients as well, we recommend to use the all-randomized design.The method based on the EM algorithm and parametric bootstrap re-sampling process cannot avoid the problem of biased effect estimates in the enrichment design targeted clinical trials. Improvement of the target diagnosis methods to reduce the bias is recommended.