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.     

Production of acetone butanol (AB) from liquefied corn starch,a commercial substrate,using <Emphasis Type="Italic">Clostridium beijerinckii</Emphasis> coupled with product recovery by gas stripping

A potential industrial substrate (liquefied corn starch; LCS) has been employed for successful acetone butanol ethanol (ABE) production. Fermentation of LCS (60 g l⁻¹) in a batch process resulted in the production of 18.4 g l⁻¹ ABE, comparable to glucose: yeast extract based medium (control experiment, 18.6 g l⁻¹ ABE). A batch fermentation of LCS integrated with product recovery resulted in 92% utilization of sugars present in the feed. When ABE was recovered by gas stripping (to relieve inhibition) from the fed-batch reactor fed with saccharified liquefied cornstarch (SLCS), 81.3 g l⁻¹ ABE was produced compared to 18.6 g l⁻¹ (control). In this integrated system, 225.8 g l⁻¹ SLCS sugar (487 % of control) was consumed. In the absence of product removal, it is not possible for C. beijerinckii BA101 to utilize more than 46 g l⁻¹ glucose. A combination of fermentation of this novel substrate (LCS) to butanol together with product recovery by gas stripping may economically benefit this fermentation. Mention of trade names of commercial products in this article/publication is solely for the purpose of providing scientific information and does not imply recommendation or endorsement by the United States Department of Agriculture.     

Bioequivalence of generic aerosol bronchodilators: what are the issues?

I have attempted to address some critical issues relating to the introduction of generic aerosol bronchodilators in Canada. I approached Genpharm to obtain information on the data submitted to the HPB, including the number of subjects involved, but the company refused to divulge this information because it was concerned about the use of such information by its competitors. In addition to the in-vitro testing conducted by the HPB, should a single pharmacodynamic study be sufficient to demonstrate the safety and efficacy of a drug that serves such a critical role in the prevention of serious illness and possibly death? If so, what will constitute the minimum requirements for the design of such a study? In general, what should be the minimum standards required for safety, efficacy and bioequivalence of aerosol bronchodilators? The next phase rests with the provincial governments. What criteria will they use to determine whether a generic aerosol bronchodilator will be considered bioequivalent? It is essential that the criteria for bioequivalence be developed by experts, and ideally those criteria should be agreed upon and accepted by federal and provincial regulatory bodies before a product is given the status of bioequivalence. Unless such a step is taken it will be difficult to have confidence that products can be considered interchangeable. The issue of interchangeability of aerosol bronchodilators demands immediate attention. Regulatory agencies are caught between those groups with vested interests on both sides. Since patients will either benefit or suffer as a consequence of regulatory decisions, action must be taken to ensure that the best decisions are made. Scientists, clinicians and government officials should convene as soon as possible to formulate a satisfactory approach to this problem of interchangeability. The medical and pharmaceutical professions need reliable information, and patients should not be denied less expensive generic drugs if it can be determined that they are comparable to the innovator''s product.     

Data adaptive interim modification of sample sizes for candidate-gene association studies

OBJECTIVES: The use of conventional Transmission/Disequilibrium tests in the analysis of candidate-gene association studies requires the precise and complete pre-specification of the total number of trios to be sampled to obtain sufficient power at a certain significance level (type I error risk). In most of these studies, very little information about the genetic effect size will be available beforehand and thus it will be difficult to calculate a reasonable sample size. One would therefore wish to reassess the sample size during the course of a study. METHOD: We propose an adaptive group sequential procedure which allows for both early stopping of the study with rejection of the null hypothesis (H0) and for recalculation of the sample size based on interim effect size estimates when H0 cannot be rejected. The applicability of the method which was developed by Müller and Sch?fer [Biometrics 2001;57:886-891] in a clinical context is demonstrated by a numerical example. Monte Carlo simulations are performed comparing the adaptive procedure with a fixed sample and a conventional group sequential design. RESULTS: The main advantage of the adaptive procedure is its flexibility to allow for design changes in order to achieve a stabilized power characteristic while controlling the overall type I error and using the information already collected. CONCLUSIONS: Given these advantages, the procedure is a promising alternative to traditional designs.     

Fixed or random? On the reliability of mixed‐effects models for a small number of levels in grouping variables

Biological data are often intrinsically hierarchical (e.g., species from different genera, plants within different mountain regions), which made mixed‐effects models a common analysis tool in ecology and evolution because they can account for the non‐independence. Many questions around their practical applications are solved but one is still debated: Should we treat a grouping variable with a low number of levels as a random or fixed effect? In such situations, the variance estimate of the random effect can be imprecise, but it is unknown if this affects statistical power and type I error rates of the fixed effects of interest. Here, we analyzed the consequences of treating a grouping variable with 2–8 levels as fixed or random effect in correctly specified and alternative models (under‐ or overparametrized models). We calculated type I error rates and statistical power for all‐model specifications and quantified the influences of study design on these quantities. We found no influence of model choice on type I error rate and power on the population‐level effect (slope) for random intercept‐only models. However, with varying intercepts and slopes in the data‐generating process, using a random slope and intercept model, and switching to a fixed‐effects model, in case of a singular fit, avoids overconfidence in the results. Additionally, the number and difference between levels strongly influences power and type I error. We conclude that inferring the correct random‐effect structure is of great importance to obtain correct type I error rates. We encourage to start with a mixed‐effects model independent of the number of levels in the grouping variable and switch to a fixed‐effects model only in case of a singular fit. With these recommendations, we allow for more informative choices about study design and data analysis and make ecological inference with mixed‐effects models more robust for small number of levels.     

Sensitivity of the erythrocyte micronucleus assay: dependence on number of cells scored and inter-animal variability

Until recently, the in vivo erythrocyte micronucleus assay has been scored using microscopy. Because the frequency of micronucleated cells is typically low, cell counts are subject to substantial binomial counting error. Counting error, along with inter-animal variability, limit the sensitivity of this assay. Recently, flow cytometric methods have been developed for scoring micronucleated erythrocytes and these methods enable many more cells to be evaluated than is possible with microscopic scoring. Using typical spontaneous micronucleus frequencies reported in mice, rats, and dogs we calculate the counting error associated with the frequency of micronucleated reticulocytes as a function of the number of reticulocytes scored. We compare this counting error with the inter-animal variability determined by flow cytometric scoring of sufficient numbers of cells to assure that the counting error is less than the inter-animal variability, and calculate the minimum increases in micronucleus frequency that can be detected as a function of the number of cells scored. The data show that current regulatory guidelines allow low power of the test when spontaneous frequencies are low (e.g., < or =0.1%). Tables and formulas are presented that provide the necessary numbers of cells that must be scored to meet the recommendation of the International Working Group on Genotoxicity Testing that sufficient cells be scored to reduce counting error to less than the inter-animal variability, thereby maintaining a more uniform power of detection of increased micronucleus frequencies across laboratories and species.     

Ligand Binding to Anion-binding Exosites Regulates Conformational Properties of Thrombin

Thrombin participates in coagulation, anticoagulation, and initiation of platelet activation. To fulfill its diverse roles and maintain hemostasis, this serine protease is regulated via the extended active site region and anion-binding exosites (ABEs) I and II. For the current project, amide proton hydrogen-deuterium exchange coupled with MALDI-TOF mass spectrometry was used to characterize ligand binding to individual exosites and to investigate the presence of exosite-active site and exosite-exosite interactions. PAR3(44–56) and PAR1(49–62) were observed to bind to thrombin ABE I and then to exhibit long range effects over to ABE II. By contrast, Hirudin(54–65) focused more on ABE I and did not transmit influences over to ABE II. Although these three ligands were each directed to ABE I, they did not promote the same conformational consequences. d-Phe-Pro-Arg-chloromethyl ketone inhibition at the thrombin active site led to further local and long range consequences to thrombin-ABE I ligand complexes with the autolysis loop often most affected. When Hirudin(54–65) was bound to ABE I, it was still possible to bind GpIbα(269–286) or fibrinogen γ′(410–427) to ABE II. Each ligand exerted its predominant influences on thrombin and also allowed interexosite communication. The results obtained support the proposal that thrombin is a highly dynamic protein. The transmission of ligand-specific local and long range conformational events is proposed to help regulate this multifunctional enzyme.     

A Transmission/Disequilibrium Test That Allows for Genotyping Errors in the Analysis of Single-Nucleotide Polymorphism Data

The present study assesses the effects of genotyping errors on the type I error rate of a particular transmission/disequilibrium test (TDT(std)), which assumes that data are errorless, and introduces a new transmission/disequilibrium test (TDT(ae)) that allows for random genotyping errors. We evaluate the type I error rate and power of the TDT(ae) under a variety of simulations and perform a power comparison between the TDT(std) and the TDT(ae), for errorless data. Both the TDT(std) and the TDT(ae) statistics are computed as two times a log-likelihood difference, and both are asymptotically distributed as chi(2) with 1 df. Genotype data for trios are simulated under a null hypothesis and under an alternative (power) hypothesis. For each simulation, errors are introduced randomly via a computer algorithm with different probabilities (called "allelic error rates"). The TDT(std) statistic is computed on all trios that show Mendelian consistency, whereas the TDT(ae) statistic is computed on all trios. The results indicate that TDT(std) shows a significant increase in type I error when applied to data in which inconsistent trios are removed. This type I error increases both with an increase in sample size and with an increase in the allelic error rates. TDT(ae) always maintains correct type I error rates for the simulations considered. Factors affecting the power of the TDT(ae) are discussed. Finally, the power of TDT(std) is at least that of TDT(ae) for simulations with errorless data. Because data are rarely error free, we recommend that researchers use methods, such as the TDT(ae), that allow for errors in genotype data.     

Interim analysis incorporating short‐ and long‐term binary endpoints

Designs incorporating more than one endpoint have become popular in drug development. One of such designs allows for incorporation of short‐term information in an interim analysis if the long‐term primary endpoint has not been yet observed for some of the patients. At first we consider a two‐stage design with binary endpoints allowing for futility stopping only based on conditional power under both fixed and observed effects. Design characteristics of three estimators: using primary long‐term endpoint only, short‐term endpoint only, and combining data from both are compared. For each approach, equivalent cut‐off point values for fixed and observed effect conditional power calculations can be derived resulting in the same overall power. While in trials stopping for futility the type I error rate cannot get inflated (it usually decreases), there is loss of power. In this study, we consider different scenarios, including different thresholds for conditional power, different amount of information available at the interim, different correlations and probabilities of success. We further extend the methods to adaptive designs with unblinded sample size reassessments based on conditional power with inverse normal method as the combination function. Two different futility stopping rules are considered: one based on the conditional power, and one from P‐values based on Z‐statistics of the estimators. Average sample size, probability to stop for futility and overall power of the trial are compared and the influence of the choice of weights is investigated.     

Sensitivity of the erythrocyte micronucleus assay: Dependence on number of cells scored and inter-animal variability

Until recently, the in vivo erythrocyte micronucleus assay has been scored using microscopy. Because the frequency of micronucleated cells is typically low, cell counts are subject to substantial binomial counting error. Counting error, along with inter-animal variability, limit the sensitivity of this assay. Recently, flow cytometric methods have been developed for scoring micronucleated erythrocytes and these methods enable many more cells to be evaluated than is possible with microscopic scoring. Using typical spontaneous micronucleus frequencies reported in mice, rats, and dogs we calculate the counting error associated with the frequency of micronucleated reticulocytes as a function of the number of reticulocytes scored. We compare this counting error with the inter-animal variability determined by flow cytometric scoring of sufficient numbers of cells to assure that the counting error is less than the inter-animal variability, and calculate the minimum increases in micronucleus frequency that can be detected as a function of the number of cells scored. The data show that current regulatory guidelines allow low power of the test when spontaneous frequencies are low (e.g., ≤0.1%). Tables and formulas are presented that provide the necessary numbers of cells that must be scored to meet the recommendation of the International Working Group on Genotoxicity Testing that sufficient cells be scored to reduce counting error to less than the inter-animal variability, thereby maintaining a more uniform power of detection of increased micronucleus frequencies across laboratories and species.