Sample size determination for bioequivalence assessment using a multiplicative model

In bioequivalence studies C _max and AUCserve as the primary pharmacokinetic characteristics of rate and extent of absorption. Based on pharmacokinetic relationships and on empirical evidence, the distribution of these characteristics corresponds to a multiplicative model, which implies a logarithmic normal distribution in the case of a parametric analysis. Hence, consideration is given to exact and approximate formulas of sample sizes in the case of a multiplicative model.     

ESTIMATION FOLLOWING EXTENSION OF A STUDY ON THE BASIS OF CONDITIONAL POWER

Proschan and Hunsberger [1] Proschan, M A and Hunsberger, S A. 1995. Designed Extension of Studies Based on Conditional Power. Biometrics, 51: 1315–1324. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar] propose a method based on conditional power for designed extension of a study beyond its originally intended sample size. Their data-dependent sampling method can be viewed as a two-stage procedure in which the target total sample size is dependent upon the data observed at the first stage. We demonstrate that the maximum likelihood estimate of the parameter of interest upon completion may be biased, and that this bias is similar in direction and magnitude to that commonly associated with estimation following a group sequential test with predetermined target total sample size. Furthermore, we show how a bias adjusted estimate may be formed.     

随机对照药物临床试验样本量估计

如何正确估计样本量是随机对照药物临床试验设计阶段的主要研究内容之一。本文在对随机对照临床试验样本量估计的影响因素一一分析的基础上,通过实例介绍临床试验样本量估计的分析过程,并讨论了临床试验样本量估计中的注意事项,为随机对照临床试验正确估计样本量提供参考。     

Sample Size Estimation Based on Event Data for a Two-Stage Survival Adaptive Trial with Different Durations

In clinical development, an adaptive design combining results from two separate studies (e.g., a seamless adaptive design with a dose finding study phase and a confirmatory study phase) is commonly considered. The purpose of an adaptive design is not only to reduce lead time between the two studies, but also to evaluate the treatment effect in a more efficient way. In this paper, the focus is on the case where the study objectives are the same but the time durations of the study periods are different in the two stages. In particular, event data are collected in both stages. Statistical procedure for combining data observed from the two different stages is discussed. Furthermore, results on hypotheses testing and sample size calculation are derived for the comparison of two treatments.     

Adaptive Budgets in Clinical Trials

We consider situations where a drug developer gets access to additional financial resources when a promising result has been observed in a preplanned interim analysis during a clinical trial that should lead to the registration of the drug. First, the option that the drug developer completely puts the additional resources into increasing the second-stage sample size has been investigated. If investors invest more the larger the observed interim effect, this may not be a reasonable strategy. Then, additional sample sizes are applied when the conditional power is already very large and hardly any impact on the overall power can be expected. Nevertheless, further reducing the Type II error rate in promising situations may be of interest for a drug developer. In a second step, sample size was based on a utility function including the reward of registration (which was allowed to depend on the observed effect size at the end of the trial) and sampling costs. Utility as a function of the sample size may have more than one local maximum, one of them at the lowest per group sample size. For small effects, an optimal strategy could be to apply the smallest sample size accepted by regulators.     

A Conditional Power Approach to the Evaluation of Predictive Power

In the 1960s and 1970s, almost all clinical trials were designed with a single efficacy analysis at the end. Despite this design, many NIH-sponsored clinical trials were reviewed periodically by Policy Advisory Boards (now called Data and Safety Monitoring Boards). At these reviews, clinicians on the Board often asked: “If the current trend continues, what is the chance that we will have a positive study at the end?” We discuss how to put this question into a statistical framework and provide a simple answer. The “chance” is called conditional power (CP) or predictive power (PP). We discuss the use of CP and PP for early termination of a clinical trial. The concepts of CP and PP can also be applied to sample size determination for a new study or reestimation of sample size in an adaptive design.     

Power and Sample Size Calculation for Microarray Studies

Microarray is a technology to screen a large number of genes to discover those differentially expressed between clinical subtypes or different conditions of human diseases. Gene discovery using microarray data requires adjustment for the large-scale multiplicity of candidate genes. The family-wise error rate (FWER) has been widely chosen as a global type I error rate adjusting for the multiplicity. Typically in microarray data, the expression levels of different genes are correlated because of coexpressing genes and the common experimental conditions shared by the genes on each array. To accurately control the FWER, the statistical testing procedure should appropriately reflect the dependency among the genes. Permutation methods have been used for accurate control of the FWER in analyzing microarray data. It is important to calculate the required sample size at the design stage of a new (confirmatory) microarray study. Because of the high dimensionality and complexity of the correlation structure in microarray data, however, there have been no sample size calculation methods accurately reflecting the true correlation structure of real microarray data. We propose sample size and power calculation methods that are useful when pilot data are available to design a confirmatory experiment. If no pilot data are available, we recommend a two-stage sample size recalculation based on our proposed method using the first stage data as pilot data. The calculated sample sizes are shown to accurately maintain the power through simulations. A real data example is taken to illustrate the proposed method.     

Statistical Analysis for Two-Stage Seamless Design with Different Study Endpoints

In the pharmaceutical industry, it is desirable to apply an adaptive seamless trial design to combine two separate clinical studies that are normally conducted for achieving separate objectives such as a Phase II study for dose finding and a Phase III confirmatory study for efficacy. As a result, an adaptive seamless Phase II{/}III trial design consisting of two phases, namely a learning phase and a confirmatory phase, is commonly considered in pharmaceutical development. In some cases, however, the study endpoints for the two separate studies may be different due to long treatment duration. In this case, test statistics for the final analysis based on the combined data are necessary developed. In this paper, a test statistic utilizing data collected from both phases is proposed assuming that there is a well established relationship between the two different study endpoints. Formula for sample size calculation based on the proposed test statistic is derived. Sample size allocation at the two phases is also discussed.     

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。     

Sample size determination for the two one-sided tests procedure in bioequivalence

Approximate formulae of sample sizes for Schuirmann's two one-sided tests procedure are derived for bioequivalence studies with the 2×2 crossover design. These formulae are simple enough to be carried out with a pocket calculator.     

THE ATTRACTIVENESS OF THE CONCEPT OF A PROSPECTIVELY DESIGNED TWO-STAGE CLINICAL TRIAL

ABSTRACT

The clinical development process can be viewed as a succession of trials, possibly overlapping in calendar time. The design of each trial may be influenced by results from previous studies and other currently proceeding trials, as well as by external information. Results from all of these trials must be considered together in order to assess the efficacy and safety of the proposed new treatment. Meta-analysis techniques provide a formal way of combining the information. We examine how such methods can be used in combining results from: (1) a collection of separate studies, (2) a sequence of studies in an organized development program, and (3) stages within a single study using a (possibly adaptive) group sequential design. We present two examples. The first example concerns the combining of results from a Phase IIb trial using several dose levels or treatment arms with those of the Phase III trial comparing the treatment selected in Phase IIb against a control. This enables a “seamless transition” from Phase IIb to Phase III. The second example examines the use of combination tests to analyze data from an adaptive group sequential trial.     

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.     

On Power and Sample Size Calculation in Ethnic Sensitivity Studies

In ethnic sensitivity studies, it is of interest to know whether the same dose has the same effect over populations in different regions. Glasbrenner and Rosenkranz (2006 Glasbrenner , M. and Rosenkranz , G. ( 2006 ). A note on ethnic sensitivity studies . Journal of Biopharmaceutical Statistics 16 : 15 – 23 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) proposed a criterion for ethnic sensitivity studies in the context of different dose-exposure models. Their method is liberal in the sense that their sample size will not achieve the target power. We will show that the power function can be easily calculated by numeric integration, and the sample size can be determined by bisection.     

Probability monitoring procedures for sample size determination

ABSTRACT

In clinical research, power analysis is often performed for sample size calculation. The purpose is to achieve a desired power of correctly detecting a clinically meaningful difference at a pre-specified level of significance if such a difference truly exists. However, in some situations such as (i) clinical trials with extremely low incidence rates and (ii) for rare disease drug development clinical trials, power analysis for sample size calculation may not be feasible because (i) it may require a huge sample size for detecting a relatively small difference and (ii) eligible patients may not be available for a small target patient population. In these cases, other procedures for sample size determination with certain statistical assurance are needed. In this article, an innovative method based on a probability monitoring procedure is proposed for sample size determination. The concept is to select an appropriate sample size for controlling the probability of crossing safety and/or efficacy boundaries. For rare disease clinical development, an adaptive probability monitoring procedure may be applied if a multiple-stage adaptive trial design is used.     

Sample size determination for fold-increase endpoints defined by paired interval-censored data

Medical studies often define binary end-points by comparing the ratio of a pair of measurements at baseline and end-of-study to a clinically meaningful cut-off. For example, vaccine trials may define a response as at least a four-fold increase in antibody titers from baseline to end-of-study. Accordingly, sample size is determined based on comparisons of proportions. Since the pair of measurements is quantitative, modeling the bivariate cumulative distribution function to estimate the proportion gives more precise results than using dichotomization of data. This is known as the distributional approach to the analysis of proportions. However, this can be complicated by interval-censoring. For example, due to the nature of some laboratory measurement methods, antibody titers are interval-censored. We derive a sample size formula based on the distributional approach for paired interval-censored data. We compare the sample size requirement in detecting an intervention effect using the distributional approach to a conventional approach of dichotomization. Some practical guidance on applying the sample size formula is given.     

Sample size determination with familywise control of both type I and type II errors in clinical trials

The concept of controlling familywise type I and type II errors at the same time is essentially an integrated process to deal with multiplicity issues in clinical trials. The process will select a multiple testing procedure (MTP) which controls the familywise type I error and calculate the per hypothesis sample size such that the “studywise power” is maintained at desired level. The power of a study can be defined in several ways and it depends on the objective. In this article, we provide general guidance on how to make the selection of MTPs and calculate sample size simultaneously. We introduce the concept of strong and weak control of the familywise type II error and generalized familywise type II error. We also proposed the novel Bonferroni+ and optimal Bonferroni+ procedures to allocate per hypothesis type II error. We demonstrated the value of the proposed work as it cannot be replaced by simple simulations. A real clinical trial is discussed throughout the article as an example.     

A Bayesian Approach on Sample Size Calculation for Comparing Means

ABSTRACT

In clinical research, parameters required for sample size calculation are usually unknown. A typical approach is to use estimates from some pilot studies as the true parameters in the calculation. This approach, however, does not take into consideration sampling error. Thus, the resulting sample size could be misleading if the sampling error is substantial. As an alternative, we suggest a Bayesian approach with noninformative prior to reflect the uncertainty of the parameters induced by the sampling error. Based on the informative prior and data from pilot samples, the Bayesian estimators based on appropriate loss functions can be obtained. Then, the traditional sample size calculation procedure can be carried out using the Bayesian estimates instead of the frequentist estimates. The results indicate that the sample size obtained using the Bayesian approach differs from the traditional sample size obtained by a constant inflation factor, which is purely determined by the size of the pilot study. An example is given for illustration purposes.     

Sample size determination for bioequivalence assessment using a multiplicative model.

In bioequivalence studies Cmax and AUC serve as the primary pharmacokinetic characteristics of rate and extent of absorption. Based on pharmacokinetic relationships and on empirical evidence, the distribution of these characteristics corresponds to a multiplicative model, which implies a logarithmic normal distribution in the case of a parametric analysis. Hence, consideration is given to exact and approximate formulas of sample sizes in the case of a multiplicative model.     

Sample Size Re-Estimation without Breaking the Blind in Clinical Trial

From a regulatory perspective, it is important that the sample size recalculation is performed such that all persons involved in the study remain blinded. The proposed method is an extension of the work by Shih and Zhao (1997) to continuous endpoints. The treatment means are constructed by the convex combinations of the stratum means and then estimated by using the linear model of the stratum responses. In this article, the properties of the proposed estimators are studied. Simulation experiments are conducted to evaluate the difference between two estimators. The unblind estimators for the population mean and the population variance perform better than those of the blind estimators in terms of bias and mean square errors in the most of cases. Given a particular sample size, the accuracies of the blind means and the blind variances depend on the treatment proportions in each stratum. An example of interim analysis is given in this article to illustrate the use of sample size determination. The proposed sample size calculations are recommended in the interim analyses to meet Committee for Proprietary Medical Products requirement, retaining the blinding.     

Sample Size Determination Based on Rank Tests in Clinical Trials

Abstract

The problem of sample size determination based on three commonly used nonparametric rank based tests, namely, one-sample Wilcoxon's rank sum test, two-sample's Wilcoxon's rank sum test, and the rank-based test for independence is studied. Explicit formulas for variabilities of the test statistics under the alternative hypotheses are derived. Consequently, close forms of power functions of these test statistics are obtained for sample size determination utilizing the concept of higher order polynominal equations. Simulation studies were performed to evaluate the finite samples performance of the derived sample size formulas. The results indicates that the derived methods work well with moderate sample size.