Improved two‐stage group sequential procedures for testing a secondary endpoint after the primary endpoint achieves significance

In two‐stage group sequential trials with a primary and a secondary endpoint, the overall type I error rate for the primary endpoint is often controlled by an α‐level boundary, such as an O'Brien‐Fleming or Pocock boundary. Following a hierarchical testing sequence, the secondary endpoint is tested only if the primary endpoint achieves statistical significance either at an interim analysis or at the final analysis. To control the type I error rate for the secondary endpoint, this is tested using a Bonferroni procedure or any α‐level group sequential method. In comparison with marginal testing, there is an overall power loss for the test of the secondary endpoint since a claim of a positive result depends on the significance of the primary endpoint in the hierarchical testing sequence. We propose two group sequential testing procedures with improved secondary power: the improved Bonferroni procedure and the improved Pocock procedure. The proposed procedures use the correlation between the interim and final statistics for the secondary endpoint while applying graphical approaches to transfer the significance level from the primary endpoint to the secondary endpoint. The procedures control the familywise error rate (FWER) strongly by construction and this is confirmed via simulation. We also compare the proposed procedures with other commonly used group sequential procedures in terms of control of the FWER and the power of rejecting the secondary hypothesis. An example is provided to illustrate the procedures.     

Challenges and Opportunities to Use Biowaivers to Compare Generics in China

Biowaivers for class I drugs according to the biopharmaceutics classification system (BCS) were first introduced in 2000. The in vitro equivalence can be used to document bioequivalence between products. This study compared the in vitro dissolution behavior of two BCS class I drugs, amoxicillin and metronidazole, which are sold in China. Identifying a reference product on the Chinese domestic market was impossible. Three 250-mg and two 500-mg amoxicillin capsules and four metronidazole tablet products were tested. None of the amoxicillin products and three of the four metronidazole tablets were found to be equivalent to each other when the same strengths were compared. The bioequivalence of products that fail the in vitro test can be established via in vivo clinical studies which are expensive and time consuming. Establishing nationally or globally accepted reference products may provide regulatory agencies with an efficient mechanism approving high quality generics.     

我国仿制药人体生物等效性临床试验研究室建设的现状与发展路径

我国开展仿制药一致性评价最主要的困难之一是临床试验资源不足,解决办法是考虑将生物等效性临床试验资格认定调整为备案 管理。因此,对备案的医疗机构建设生物等效性试验研究室是一个潜在的挑战。文章分析了国内当前具备生物等效性 / I期临床资质的 机构、分布、承担项目能力及生物等效性临床试验机构、药物分析实验室和合同研究组织之间的关系等,对仿制药生物等效性临床试验 研究室的建设内容和规模展开讨论,供业内及监管部门参考。     

Adaptive two-stage analysis of genetic association in case-control designs

We study a two-stage analysis of genetic association for case-control studies. In the first stage, we compare Hardy-Weinberg disequilibrium coefficients between cases and controls and, in the second stage, we apply the Cochran- Armitage trend test. The two analyses are statistically independent when Hardy-Weinberg equilibrium holds in the population, so all the samples are used in both stages. The significance level in the first stage is adaptively determined based on its conditional power. Given the level in the first stage, the level for the second stage analysis is determined with the overall Type I error being asymptotically controlled. For finite sample sizes, a parametric bootstrap method is used to control the overall Type I error rate. This two-stage analysis is often more powerful than the Cochran-Armitage trend test alone for a large association study. The new approach is applied to SNPs from a real study.     

An adaptive two-stage design with treatment selection using the conditional error function approach

As an approach to combining the phase II dose finding trial and phase III pivotal trials, we propose a two-stage adaptive design that selects the best among several treatments in the first stage and tests significance of the selected treatment in the second stage. The approach controls the type I error defined as the probability of selecting a treatment and claiming its significance when the selected treatment is indifferent from placebo, as considered in Bischoff and Miller (2005). Our approach uses the conditional error function and allows determining the conditional type I error function for the second stage based on information observed at the first stage in a similar way to that for an ordinary adaptive design without treatment selection. We examine properties such as expected sample size and stage-2 power of this design with a given type I error and a maximum stage-2 sample size under different hypothesis configurations. We also propose a method to find the optimal conditional error function of a simple parametric form to improve the performance of the design and have derived optimal designs under some hypothesis configurations. Application of this approach is illustrated by a hypothetical example.     

Sample size calculation for studies comparing binary outcomes using historical controls

In historical control trials (HCTs), the experimental therapy is compared with a control therapy that has been evaluated in a previously conducted trial. Makuch and Simon developed a sample size formula where the observations from the HC group were considered not subject to sampling variability. Many researchers have pointed out that the Makuch–Simon sample size formula does not preserve the nominal power and type I error. We develop a sample size calculation approach that properly accounts for the uncertainty in the true response rate of the HC group. We demonstrate that the empirical power and type I error, obtained over the simulated HC data, have extremely skewed distributions. We then derive a closed‐form sample size formula that enables researchers to control percentiles, instead of means, of the power and type I error accounting for the skewness of the distributions. A simulation study demonstrates that this approach preserves the operational characteristics in a more realistic scenario where the true response rate of the HC group is unknown. We also show that the controlling percentiles can be used to describe the joint behavior of the power and type I error. It provides a new perspective on the assessment of HCTs.     

A Confidence Region Approach for Assessing Equivalence in Variability of Bioavailability

The problem for assessment of equivalence in variability of bioavailability between two drug products is considered. Similar to the method for assessing bioequivalence in average bioavailability proposed by Chow and Shao (1990), an exact confidence region approach is derived when the intersubject variance is known. When the intersubject variance is unknown, a large sample approximation is considered. The proposed method for assessing equivalence of variability of bioavailability appears to be asymptotically uncorrelated with that of Chow and Shao (1990) for average bioavailability. As a result, the proposed method in conjunction with the method proposed by Chow and Shao (1990) constitutes a confidence region approach for assessing population bioequivalence. An example concerning a bioequivalence trial with 24 healthy volunteers is provided to illustrate the proposed method.     

Interval Estimation for Ratios in Bioequivalence Trials

The problem for assessment of equivalence in variability of bioavailability between two drug products is considered. An exact confidence region for the ratio between intrasubject variabilities is derived when the intersubject variance is known. When the intersubject variance is unknown, a large sample approximation is considered. The proposed method for assessing equivalence in variability of bioavailability appears to be asymptotically uncorrelated with the sample mean ratio for average bioavailabilty. As a result, the proposed method in conjunction with the sample mean ratio method can be utilized for assessing population bioequivalence. An example concerning a bioequivalence trial with 24 healthy volunteers is presented to illustrate the proposed method.     

Design and analysis of bridging studies with prior probabilities on the null and alternative hypotheses

The pharmaceutical industry and regulatory agencies are increasingly interested in conducting bridging studies in order to bring an approved drug product from the original region (eg, United States or European Union) to a new region (eg, Asian-Pacific countries). In this article, we provide a new methodology for the design and analysis of bridging studies by assuming prior knowledge on how the null and alternative hypotheses in the original, foreign study are related to the null and alternative hypotheses in the bridging study and setting the type I error for the bridging study according to the strength of the foreign-study evidence. The new methodology accounts for randomness in the foreign-study evidence and controls the average type I error of the bridging study over all possibilities of the foreign-study evidence. In addition, the new methodology increases statistical power, when compared to approaches that do not use foreign-study evidence, and it allows for the possibility of not conducting the bridging study when the foreign-study evidence is unfavorable. Finally, we conducted extensive simulation studies to demonstrate the usefulness of the proposed methodology.     

Optimal conditional error functions for the control of conditional power

Ethical considerations and the competitive environment of clinical trials usually require that any given trial have sufficient power to detect a treatment advance. If at an interim analysis the available data are used to decide whether the trial is promising enough to be continued, investigators and sponsors often wish to have a high conditional power, which is the probability to reject the null hypothesis given the interim data and the alternative of interest. Under this requirement a design with interim sample size recalculation, which keeps the overall and conditional power at a prespecified value and preserves the overall type I error rate, is a reasonable alternative to a classical group sequential design, in which the conditional power is often too small. In this article two-stage designs with control of overall and conditional power are constructed that minimize the expected sample size, either for a simple point alternative or for a random mixture of alternatives given by a prior density for the efficacy parameter. The presented optimality result applies to trials with and without an interim hypothesis test; in addition, one can account for constraints such as a minimal sample size for the second stage. The optimal designs will be illustrated with an example, and will be compared to the frequently considered method of using the conditional type I error level of a group sequential design.