Adaptive strategies in designing the simultaneous global drug development program

Many methods have been proposed to account for the potential impact of ethnic/regional factors when extrapolating results from multiregional clinical trials (MRCTs) to targeted ethnic (TE) patients, i.e., “bridging.” Most of them either focused on TE patients in the MRCT (i.e., internal bridging) or a separate local clinical trial (LCT) (i.e., external bridging). Huang et al. (2012) integrated both bridging concepts in their method for the Simultaneous Global Drug Development Program (SGDDP) which designs both the MRCT and the LCT prospectively and combines patients in both trials by ethnic origin, i.e., TE vs. non-TE (NTE). The weighted Z test was used to combine information from TE and NTE patients to test with statistical rigor whether a new treatment is effective in the TE population. Practically, the MRCT is often completed before the LCT. Thus to increase the power for the SGDDP and/or obtain more informative data in TE patients, we may use the final results from the MRCT to re-evaluate initial assumptions (e.g., effect sizes, variances, weight), and modify the LCT accordingly. We discuss various adaptive strategies for the LCT such as sample size reassessment, population enrichment, endpoint change, and dose adjustment. As an example, we extend a popular adaptive design method to re-estimate the sample size for the LCT, and illustrate it for a normally distributed endpoint.     

Design and sample size considerations for simultaneous global drug development program

Due to the potential impact of ethnic factors on clinical outcomes, the global registration of a new treatment is challenging. China and Japan often require local trials in addition to a multiregional clinical trial (MRCT) to support the efficacy and safety claim of the treatment. The impact of ethnic factors on the treatment effect has been intensively investigated and discussed from different perspectives. However, most current methods are focusing on the assessment of the consistency or similarity of the treatment effect between different ethnic groups in exploratory nature. In this article, we propose a new method for the design and sample size consideration for a simultaneous global drug development program (SGDDP) using weighted z-tests. In the proposed method, to test the efficacy of a new treatment for the targeted ethnic (TE) group, a weighted test that combines the information collected from both the TE group and the nontargeted ethnic (NTE) group is used. The influence of ethnic factors and local medical practice on the treatment effect is accounted for by down-weighting the information collected from NTE group in the combined test statistic. This design controls rigorously the overall false positive rate for the program at a given level. The sample sizes needed for the TE group in an SGDDP for three most commonly used efficacy endpoints, continuous, binary, and time-to-event, are then calculated.     

肿瘤药物临床试验中成组序贯设计的统计学考虑

成组序贯设计因其拥有较少的病例样本数和较早终止试验的可能性成为肿瘤药物临床试验设计方法的较好选择。如何科学有效地设计和应用成组序贯设计,本文通过Monte Carlo试验模拟,探讨肿瘤药物临床试验中成组序贯设计的期中分析次数、实施时间以及α消耗函数选取等问题,为读者系统指明如何去规划一次成组序贯试验以及如何确定其最优的试验参数。模拟结果表明,成组序贯设计以时间点2∶1∶1折半划分的三次期中分析为好,其期望样本含量仅为420.53。Lan-Demets的五种α消耗函数中,1.5次幂和2次幂的α消耗函数拥有最小期望样本含量约393例,相对于O＇Brien-Fleming设计和Po-cock设计在整体上更显优势。     

Self-designing trial combined with classical group sequential monitoring

At the interim analyses of a clinical trial, it is appealing to modify the originally planned sample size in order to achieve an adequate power to detect a meaningful treatment effect. We propose a flexible sequential monitoring scheme through combining the self-designing and classical group sequential methods. The maximum sample size does not have to be specified in advance and one efficacy interim analysis is conducted for the purpose of possible early termination after the first block of data is observed. At the interim analysis for efficacy, the usual sufficient test statistic is used and the type I error rate is adjusted to maintain the overall nominal level. At the final analysis, the test is constructed from a weighted average of the blockwise test statistics based on the sequentially collected data. The weight function at each stage is determined by the observed data prior to that stage. The futility stopping rule allows the trial to be terminated when there is no beneficial treatment effect. We conduct simulation studies to evaluate the performance of the proposed design.     

Self-Designing Trial Combined with Classical Group Sequential Monitoring

ABSTRACT

At the interim analyses of a clinical trial, it is appealing to modify the originally planned sample size in order to achieve an adequate power to detect a meaningful treatment effect. We propose a flexible sequential monitoring scheme through combining the self-designing and classical group sequential methods. The maximum sample size does not have to be specified in advance and one efficacy interim analysis is conducted for the purpose of possible early termination after the first block of data is observed. At the interim analysis for efficacy, the usual sufficient test statistic is used and the type I error rate is adjusted to maintain the overall nominal level. At the final analysis, the test is constructed from a weighted average of the blockwise test statistics based on the sequentially collected data. The weight function at each stage is determined by the observed data prior to that stage. The futility stopping rule allows the trial to be terminated when there is no beneficial treatment effect. We conduct simulation studies to evaluate the performance of the proposed design.     

Group Sequential Survival Trial Design and Monitoring Using the Log-Rank Test

For randomized group sequential survival trial designs with unbalanced treatment allocation, the widely used Schoenfeld formula is inaccurate, and the commonly used information time as the ratio of number of events at interim look to the number of events at the end of trial can be biased. In this article, a sample size formula for the two-sample log-rank test under the proportional hazards model is proposed that provides more accurate sample size calculation for unbalanced survival trial designs. Furthermore, a new information time is introduced for the sequential survival trials such that the new information time is more accurate than the traditional information time when the allocation of enrollments is unbalanced in groups. Finally, we demonstrate the monitoring process using the sequential conditional probability ratio test and compare it with two other well-known group sequential procedures. An example is given to illustrate unbalanced survival trial design using available software. Supplementary materials for this article are available online.     

A simple and efficient bias-reduced estimator of response probability following a group sequential phase II trial

A phase II clinical trial evaluating the rate of response of a new therapeutic treatment is often designed to have one or two interim analyses, allowing possible termination of the trial at an early stage if lack of treatment efficacy is evident. Due to the sequential nature of such a trial, the sample proportion yields biased estimation for the rate of response. In this paper we propose an estimator of response rate by subtracting the estimated bias directly from the sample proportion. The proposed estimator is simple, intuitive, and easy to compute. When the bias of the sample proportion is of concern to the investigators, the proposed estimator is an efficient alternative to other estimators in the literature in terms of bias and mean squared error.     

STOPPING BOUNDARIES ADJUSTED FOR SAMPLE SIZE REESTIMATION AND NEGATIVE STOP

We propose an approach to specify group sequential stopping boundaries adjusted for sample size reestimation and negative stop in interim analyses of a clinical trial. Sample size can be adjusted based on the observed delta at each interim to maintain the targeted power. The calculation of stopping boundaries incorporates possible changes in the type-I error due to sample size reestimation and/or negative stops; hence the overall type-I error is well controlled. This approach combines the advantages of the group sequential and sample size reestimation methods and is more efficient than either one alone. It provides flexibility in clinical trials and still maintains the integrity of these trials. When no early stop is planned, the stopping boundaries will be adjusted only for sample size reestimation. All calculations are given in closed mathematical forms and adjustments in stopping boundaries are based on the exact type-I error change. Therefore, the penalty for the type-I error inflation due to such interim conductions is kept to a minimum.     

Strategies for Including Patients Recruited During Interim Analysis of Clinical Trials

In clinical trials a periodical check of safety and efficacy data is often needed. For organizational reasons it is rarely desirable to stop a trial during such an interim analysis. Therefore, new study patients are included in the trial while the interim analysis is ongoing. Disregarding the additional information provided by these interim patients would be unsatisfactory, especially for an office of regulatory affairs. Consequently, the rules for group sequential or adaptive decisions must be adjusted to the recruitment of interim patients. In this paper, two strategies for modifying study designs to consider the analysis of interim patients are proposed.     

A Simple and Efficient Bias-Reduced Estimator of Response Probability Following a Group Sequential Phase II Trial

ABSTRACT

A phase II clinical trial evaluating the rate of response of a new therapeutic treatment is often designed to have one or two interim analyses, allowing possible termination of the trial at an early stage if lack of treatment efficacy is evident. Due to the sequential nature of such a trial, the sample proportion yields biased estimation for the rate of response. In this paper we propose an estimator of response rate by subtracting the estimated bias directly from the sample proportion. The proposed estimator is simple, intuitive, and easy to compute. When the bias of the sample proportion is of concern to the investigators, the proposed estimator is an efficient alternative to other estimators in the literature in terms of bias and mean squared error.     

Strategies for including patients recruited during interim analysis of clinical trials

In clinical trials a periodical check of safety and efficacy data is often needed. For organizational reasons it is rarely desirable to stop a trial during such an interim analysis. Therefore, new study patients are included in the trial while the interim analysis is ongoing. Disregarding the additional information provided by these interim patients would be unsatisfactory, especially for an office of regulatory affairs. Consequently, the rules for group sequential or adaptive decisions must be adjusted to the recruitment of interim patients. In this paper, two strategies for modifying study designs to consider the analysis of interim patients are proposed.     

Adaptive Group Sequential Test for Clinical Trials with Changing Patient Population

In clinical trials, a standard group sequential test with a fixed number of planned interim analyses is usually considered to assess the effect of a test treatment under study. The standard group sequential test is statistically valid under the assumption that the patient population remains unchanged from one interim analysis to another. In practice, however, this assumption is often not met because the trial may be modified after the review of the clinical data at interim. As a result, the original patient population may have changed to a similar but different patient population. In this paper, we consider changes in patient population related to some covariates of an on-going trial through a linear regression model. Under this model, we can make inference on the original target population based on additional data from the changed populations. A new group sequential test procedure that accounts for the effect of population changes is proposed. A simulation was performed to evaluate the performance of the proposed method. The results indicate that the type I error rate of the proposed test procedure is well preserved, while the type I error rate of the standard group sequential test is inflated as the population changes. Statistical powers of the proposed group sequential test are also presented.     

Adaptive group sequential test for clinical trials with changing patient population

In clinical trials, a standard group sequential test with a fixed number of planned interim analyses is usually considered to assess the effect of a test treatment under study. The standard group sequential test is statistically valid under the assumption that the patient population remains unchanged from one interim analysis to another. In practice, however, this assumption is often not met because the trial may be modified after the review of the clinical data at interim. As a result, the original patient population may have changed to a similar but different patient population. In this paper, we consider changes in patient population related to some covariates of an on-going trial through a linear regression model. Under this model, we can make inference on the original target population based on additional data from the changed populations. A new group sequential test procedure that accounts for the effect of population changes is proposed. A simulation was performed to evaluate the performance of the proposed method. The results indicate that the type I error rate of the proposed test procedure is well preserved, while the type I error rate of the standard group sequential test is inflated as the population changes. Statistical powers of the proposed group sequential test are also presented.     

Optimal Timing for Interim Analyses in Clinical Trials

In clinical trials, interim analyses are often performed before the completion of the trial. The intention is to possibly terminate the trial early or adjust the sample size. The time of conducting an interim analysis affects the probability of the early termination and the number of subjects enrolled until the interim analysis. This influences the expected total number of subjects. In this study, we examine the optimal time for conducting interim analyses with a view to minimizing the expected total sample size. It is found that regardless of the effect size, the optimal time of one interim analysis for the early termination is approximately two-thirds of the planned observations for the O'Brien–Fleming type of spending function and approximately half of the planned observations for the Pocock type when the subject enrollment is halted for the interim analysis. When the subject enrollment is continuous throughout the trial, the optimal time for the interim analysis varies according to the follow-up duration. We also consider the time for one interim analysis including the sample size adjustment in terms of minimizing the expected total sample size.     

Interim analyses and sequential designs in phase III studies

Recruitment of patients to a clinical trial usually occurs over a period of time, resulting in the steady accumulation of data throughout the trial's duration. Yet, according to traditional statistical methods, the sample size of the trial should be determined in advance, and data collected on all subjects before analysis proceeds. For ethical and economic reasons, the technique of sequential testing has been developed to enable the examination of data at a series of interim analyses. The aim is to stop recruitment to the study as soon as there is sufficient evidence to reach a firm conclusion. In this paper we present the advantages and disadvantages of conducting interim analyses in phase III clinical trials, together with the key steps to enable the successful implementation of sequential methods in this setting. Examples are given of completed trials, which have been carried out sequentially, and references to relevant literature and software are provided.     

Blinded sample size recalculation in clinical trials with binary composite endpoints

We consider clinical trials with a binary composite endpoint where the trial is successful when a significant result is achieved for the composite or one prespecified main component. Appropriate sample size planning is challenging in this situation, as in addition to the Type I error rate, power, and target difference the overall event rates and the correlation between the test statistics have to be defined. Reliable estimates of these quantities, however, are usually hard to obtain and therefore there is a high risk to not achieve the intended power in a fixed sample size design. In this article, we propose an internal pilot study design where the nuisance parameters are estimated in a blinded way at an interim stage and where the sample size is then revised accordingly. We investigate the characteristics of the proposed design with respect to the actual Type I error rate, power, and sample size. The application of this design is illustrated by a clinical trial example.     

A Review of: “The Statistical Analysis of Recurrent Events,by R. J. Cook and J. F. Lawless”

In a classical drop-loser (or drop-arm) design, patients are randomized into all arms (doses) and at the interim analysis, inferior arms are dropped. Therefore, compared to the traditional dose-finding design, this adaptive design can reduce the sample size by not carrying over all doses to the end of the trial or dropping the losers earlier. However, all the doses have to be explored. For unimodal (including linear or umbrella) response curves, we proposed an effective dose-finding design that allows adding arms at the interim analysis. The trial design starts with two arms, depending on the response of the two arms and the unimodality assumption; we can decide which new arms to be added. This design does not require exploring all arms (doses) to find the best responsive dose; therefore, it can further reduce the sample size from the drop-loser design by as much as 10–20%.     

Statistical Considerations for Testing Multiple Endpoints in Group Sequential or Adaptive Clinical Trials

Many clinical trials are designed with a fixed sample size or total number of events to detect a postulated size of treatment effect on a primary efficacy endpoint. When the trial is completed and the primary efficacy endpoint achieves statistical significance, formal statistical testing of other clinically important secondary endpoints often follows in order for the statistically and clinically significant results of these endpoints to be included in the label of the test pharmaceutical product. In conventional fixed designs without any interim analysis or trial extension, these endpoints are often tested in a pre-specified hierarchical order, following the closed testing principle. This testing strategy ensures a strong control of the overall type I error. However, when trials are conducted using a group-sequential design with interim analyses or can be extended using an adaptive design with an increase of sample size or total number of events, this conventional hierarchical testing strategy may violate the closure principle and the overall type I error rate may not be controlled in the strong sense.     

Design and analysis issues of multiregional clinical trials with different regional primary endpoints

One of the challenges of multiregional drug development program is to design and analyze a multiple regional clinical trial with the objective being to satisfy different regional requirements on primary endpoints. Considered in this article is a multiregional clinical trial (MRCT) designed to test for two primary endpoints. Data of a regular fixed-size well-controlled parallel arm trial are used to test for two null hypotheses in terms of two distinct yet correlated endpoints. The two hypotheses may be tested sequentially or simultaneously. Depending on the structure of the hypotheses to be tested and the understanding of type I error rate control, various scenarios of type I error rate adjustments may be applied. Furthermore, for the objective of getting approval from regional authorities for different primary endpoints, various sample size and power determinations may be applied. In this article, comparisons of different approaches are discussed systematically.