A sequential procedure for monitoring clinical trials against historical controls

In this paper, we develop a sequential procedure to monitor clinical trials against historical controls. When there is a strong ethical concern about randomizing patients to existing treatment because biological and medical evidence suggests that the new treatment is potentially superior to the existing one, or when the enrollment is too limited for randomization of subjects into experimental and control groups, one can monitor the trial sequentially against historical controls if the historical data with required quality and sample size are available to form a valid reference for the trial. This design of trial is sometimes the only alternative to a randomized phase III trial design that is intended but not feasible in situations such as above. Monitoring this type of clinical trial leads to a statistical problem of comparing two population means in a situation in which data from one population are sequentially collected and compared with all data from the other population at each interim look. The proposed sequential procedures is based on the sequential conditional probability ratio test (SCPRT) by which the conclusion of the sequential test would be virtually the same as that arrived at by a non-sequential test based on all data at the planned end of the trial. We develop the sequential procedure by proposing a Brownian motion that emulates the test statistic, and then proposing an SCPRT that is adapted to the special properties of the trial.     

治疗-对照差临床意义判别所需样本量的测定

目的 提出用于治疗一对照差临床意义判别的样本量测定方法。方法 依据治疗一对照差与最小临床承认疗效差量的比较推导出所需样本量测定公式,以Monte Carlo方法展示其行为。结果 当最小临床承认疗效差量取值为零时,本文方法还原为渐近正态法。由所测样本量产生的观测功效与预定功效吻合。结论 对于以判别治疗一对照差临床意义为目的的临床试验,可用本文方法测定所需样本量。     

A comparison of the randomized play-the-winner rule and the triangular test for clinical trials with binary responses.

We consider a clinical trial model comparing an experimental treatment with a control treatment when the responses are binary. For fixed significance level and power, we compare the expected number of treatment failures for two designs--the randomized play-the-winner rule and the triangular test. The former is an example of an adaptive design while the latter is an example of a fully sequential design. We show how to determine the sample size for the randomized play-the-winner rule and how to choose the stopping boundaries for the triangular test so that the two designs have similar power functions. With this choice of design parameters, simulation indicates that the triangular test is generally more effective at reducing the expected number of treatment failures, particularly when there is a large difference between the two probabilities of success. The expected number of treatment failures can be further reduced if the triangular test is applied using the randomized play-the-winner rule to assign each patient to one of the two treatments.     

Comparing new and old screening tests when a reference procedure cannot be performed on all screenees. Example of automated cytometry for early detection of cervical cancer

Direct determination of the sensitivity and specificity of a screening test requires use of a reference procedure (such as biopsy with histopathologic analysis) that provides an estimate of true disease status. The authors present a method for comparing the accuracy of a new screening test to an old one in situations when it is not feasible to apply the reference procedure to all screenees. This method requires that only those persons who test positive on old or new screening tests be further evaluated with the reference procedure. Ratios of sensitivities and specificities are derived for rapid comparison of the two screening tests. It is shown that McNemar's test can be used for significance testing of the differences in sensitivities and specificities between two screening tests. The required sample size for a study that compares the two tests is determined.     

Choice of lambda-margin and dependency of non-inferiority trials

For a two-arm active control clinical trial designed to test for non-inferiority of the test treatment compared with the active control standard treatment, data of historical studies are often utilized. For example, with a cross-trial comparison approach (also called synthetic approach or lambda-margin approach), the trial is conducted to test the hypothesis that the mean difference or the ratio between the current test product and the active control is no larger than a certain portion of the mean difference or the ratio of the active control and placebo obtained in the historical data when the positive response indicates treatment effectiveness. The regulatory agency usually requires that the clinical trials of two different test treatments are independent in most regular cases. It also requires, in general, two independent trials of the same test treatment in order to provide confirmatory evidence of the efficacy of the test product. In this article, we derived the relationship between the correlation of the test statistics of two trials with the choice of lambda (the percentage to preserve), the sample sizes and variances under the normality assumption. We showed that the smaller a lambda, the higher the correlation between the two non-inferiority tests. It is further shown that when an 80 per cent or larger lambda is used, the correlation can be controlled to be less than 10 per cent if the variances of the response variables in the current trial are not much smaller than those of the historical studies.     

A boundary‐optimized rejection region test for the two‐sample binomial problem

Testing the equality of 2 proportions for a control group versus a treatment group is a well‐researched statistical problem. In some settings, there may be strong historical data that allow one to reliably expect that the control proportion is one, or nearly so. While one‐sample tests or comparisons to historical controls could be used, neither can rigorously control the type I error rate in the event the true control rate changes. In this work, we propose an unconditional exact test that exploits the historical information while controlling the type I error rate. We sequentially construct a rejection region by first maximizing the rejection region in the space where all controls have an event, subject to the constraint that our type I error rate does not exceed α for any true event rate; then with any remaining α we maximize the additional rejection region in the space where one control avoids the event, and so on. When the true control event rate is one, our test is the most powerful nonrandomized test for all points in the alternative space. When the true control event rate is nearly one, we demonstrate that our test has equal or higher mean power, averaging over the alternative space, than a variety of well‐known tests. For the comparison of 4 controls and 4 treated subjects, our proposed test has higher power than all comparator tests. We demonstrate the properties of our proposed test by simulation and use our method to design a malaria vaccine trial.     

红球藻软胶囊抗氧化功能评价研究

目的观察红球藻软胶囊的抗氧化功能。方法 117名符合条件的受试者随机分为对照组(60人)和试验组(57人),试验组每人每日口服红球藻软胶囊1次,每次1粒,连续服用30天。观察受试者一般状况,检测安全性指标和功效性指标,采用自身前后对照和组间对照两种研究方法进行对比研究。结果试验期间受试者一般状况良好,体检各项安全性指标亦未见异常,表明受试样品对人体无不良影响。试验后试食组血超氧化物歧化酶(SOD)活性显著高于试验前、且显著高于对照组。结论红球藻软胶囊有一定的抗氧化功能。     

Sample size calculation for the one‐sample log‐rank test

An improved method of sample size calculation for the one‐sample log‐rank test is provided. The one‐sample log‐rank test may be the method of choice if the survival curve of a single treatment group is to be compared with that of a historic control. Such settings arise, for example, in clinical phase‐II trials if the response to a new treatment is measured by a survival endpoint. Present sample size formulas for the one‐sample log‐rank test are based on the number of events to be observed, that is, in order to achieve approximately a desired power for allocated significance level and effect the trial is stopped as soon as a certain critical number of events are reached. We propose a new stopping criterion to be followed. Both approaches are shown to be asymptotically equivalent. For small sample size, though, a simulation study indicates that the new criterion might be preferred when planning a corresponding trial. In our simulations, the trial is usually underpowered, and the aspired significance level is not exploited if the traditional stopping criterion based on the number of events is used, whereas a trial based on the new stopping criterion maintains power with the type‐I error rate still controlled. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimum sample size determination in stratified case-control studies with cost considerations.

We investigate sample size determination for Cochran's test for stratified case-control studies when samples of cases and controls are allocated to maximize the asymptotic efficiency of Cochran's test subject to fixed total cost with cost per control varying by strata. We consider two situations typical of strata-matched case-control studies: when one samples both cases and controls and when cases are given and one samples controls. In each situation we develop and study an asymptotic method for finding the sample size required for a specific power under the optimum allocation proposed by Nam and Fears. Also, for the second situation, we investigate an asymptotic method for determining the common ratio, k, in one-to-k strata-matched case-control studies without cost consideration for a given power. When cases are given, neither the optimum nor the standard control sample sizes appear in a closed form; we present numerical methods for calculating these sample sizes and illustrate them with examples. We find the reduction in total cost obtained under the optimum allocation compared to standard allocation more pronounced as the differences in stratum-specific costs of sampling controls increase.     

Sample size determination in stratified trials to establish the equivalence of two treatments

When designing a trial to establish that a new treatment is as effective as a standard one, the conventional test procedure and sample size based on a null hypothesis of no difference between two treatments is inappropriate. Several authors have investigated test statistics and corresponding sample sizes based on the null hypothesis that the standard treatment is more effective than the new by at least some specific value for a single 2 × 2 table. This paper considers a trial that involves several 2 × 2 tables and presents an approximate formula for the sample size required to obtain a given power of a one-tailed score test for a null hypothesis of a specific common non-zero difference between two treatments across strata. I show that the sample size for a trial based on an unstratified test is always larger than that based on a stratified test when the design is balanced.     

Challenge of multiple co-primary endpoints: a new approach

There are many disorders where regulatory agencies have required a new treatment to demonstrate efficacy on multiple co-primary endpoints, all significant at the one-sided 2.5 per cent level, before accepting the treatment's effect for the disorder. This requirement, rooted in the intersection-union (IU) test, has led many researchers to increase the study sample size to make up for the reduction in the statistical power at the study level. Unfortunately, the increase in sample size could be substantial when the endpoints are minimally correlated and the treatment effects on the multiple endpoints are comparable. In this paper, we demonstrate that the frequentist concept of controlling the maximum false positive rate, even when applied to a restricted null space, has only limited success in keeping the sample size increase at a reasonable level. We therefore propose an approach that is based on the notion of controlling an average type I error rate. By employing an upper bound for the average type I error rate, the new approach provides an adjustment to the significance level that depends only on the correlation among the endpoints. For the most common case of two or three co-primary endpoints, the adjusted significance level is at most 5 per cent (one-sided) when the endpoints are moderately correlated. We show how sample size could be calculated under the proposed approach and contrast the needed sample size with that required under the IU test. We provide additional comments and discuss why the new approach is consistent with the principle requiring evidence of significance in the drug development and approval process.     

A studentized permutation test for three‐arm trials in the ‘gold standard’ design

The ‘gold standard’ design for three‐arm trials refers to trials with an active control and a placebo control in addition to the experimental treatment group. This trial design is recommended when being ethically justifiable and it allows the simultaneous comparison of experimental treatment, active control, and placebo. Parametric testing methods have been studied plentifully over the past years. However, these methods often tend to be liberal or conservative when distributional assumptions are not met particularly with small sample sizes. In this article, we introduce a studentized permutation test for testing non‐inferiority and superiority of the experimental treatment compared with the active control in three‐arm trials in the ‘gold standard’ design. The performance of the studentized permutation test for finite sample sizes is assessed in a Monte Carlo simulation study under various parameter constellations. Emphasis is put on whether the studentized permutation test meets the target significance level. For comparison purposes, commonly used Wald‐type tests, which do not make any distributional assumptions, are included in the simulation study. The simulation study shows that the presented studentized permutation test for assessing non‐inferiority in three‐arm trials in the ‘gold standard’ design outperforms its competitors, for instance the test based on a quasi‐Poisson model, for count data. The methods discussed in this paper are implemented in the R package ThreeArmedTrials which is available on the comprehensive R archive network (CRAN). Copyright © 2016 John Wiley & Sons, Ltd.     

Meta-analysis of 2-treatment clinical trials including both continuous and dichotomous results.

To expedite the timely creation of medical practice guidelines, a meta-analytic method was developed to combine both dichotomous survival data and continuous physiologic data from multiple studies of differing experimental design, which compare the same innovative clinical intervention to standard care. An aggregate ratio, R*, of the observed treatment effect to a clinically optimal treatment effect for studies in a series is computed and compared to the 95% confidence limit for R* under the null hypothesis. Input data for continuous variables include sample means, standard errors, and sample sizes. Input data for dichotomous variables include group proportions and sizes. The analysis can be done using a simple, 1-page spreadsheet. It allows one to judge biological significance, to test for statistical significance, to compare subgroups of studies, to test for outliers, and to compute the power of the meta-analysis. These features are demonstrated for studies of interposed abdominal compression-cardiopulmonary resuscitation.     

Sample size considerations for studies comparing survival curves using historical controls

Formulas are derived for determination of the number of patients needed in a prospective comparison of survival curves, when the control group patients have already been followed for some period. Although an explicit formula for the required sample size is not available, the computing is straightforward, and tables of examples are presented. Situations are described when one might need to allocate some new patients to the control group, rather than exclusively to the experimental group.     

Bayesian sample size for diagnostic test studies in the absence of a gold standard: Comparing identifiable with non‐identifiable models

Diagnostic tests rarely provide perfect results. The misclassification induced by imperfect sensitivities and specificities of diagnostic tests must be accounted for when planning prevalence studies or investigations into properties of new tests. The previous work has shown that applying a single imperfect test to estimate prevalence can often result in very large sample size requirements, and that sometimes even an infinite sample size is insufficient for precise estimation because the problem is non‐identifiable. Adding a second test can sometimes reduce the sample size substantially, but infinite sample sizes can still occur as the problem remains non‐identifiable. We investigate the further improvement possible when three diagnostic tests are to be applied. We first develop methods required for studies when three conditionally independent tests are available, using different Bayesian criteria. We then apply these criteria to prototypic scenarios, showing that large sample size reductions can occur compared to when only one or two tests are used. As the problem is now identifiable, infinite sample sizes cannot occur except in pathological situations. Finally, we relax the conditional independence assumption, demonstrating in this once again non‐identifiable situation that sample sizes may substantially grow and possibly be infinite. We apply our methods to the planning of two infectious disease studies, the first designed to estimate the prevalence of Strongyloides infection, and the second relating to estimating the sensitivity of a new test for tuberculosis transmission. The much smaller sample sizes that are typically required when three as compared to one or two tests are used should encourage researchers to plan their studies using more than two diagnostic tests whenever possible. User‐friendly software is available for both design and analysis stages greatly facilitating the use of these methods. Copyright © 2010 John Wiley & Sons, Ltd.     

Sample size requirements for stratified prospective studies with null hypothesis of non-unity relative risk using the score test

The standard test of the null hypothesis of unity of the relative risk seeks to determine if two treatments differ. It does not apply when the requirement is either to establish the equivalence of two treatments or to determine whether the relative risk is less than a specified value other than one. This paper presents the asymptotic power function of the score test for the null hypothesis of a specified value of a common relative risk for stratified prospective studies and proposes an approximate formula for the sample size required for a specific power of the test. One can obtain a sample size formula for stratified studies with the standard null hypothesis of unity relative risk as a special case of this formula.     

Sizing clinical trials when comparing bivariate time‐to‐event outcomes

Clinical trials with multiple primary time‐to‐event outcomes are common. Use of multiple endpoints creates challenges in the evaluation of power and the calculation of sample size during trial design particularly for time‐to‐event outcomes. We present methods for calculating the power and sample size for randomized superiority clinical trials with two correlated time‐to‐event outcomes. We do this for independent and dependent censoring for three censoring scenarios: (i) the two events are non‐fatal; (ii) one event is fatal (semi‐competing risk); and (iii) both are fatal (competing risk). We derive the bivariate log‐rank test in all three censoring scenarios and investigate the behavior of power and the required sample sizes. Separate evaluations are conducted for two inferential goals, evaluation of whether the test intervention is superior to the control on: (1) all of the endpoints (multiple co‐primary) or (2) at least one endpoint (multiple primary). Copyright © 2017 John Wiley & Sons, Ltd.     

Sequential designs for phase III clinical trials incorporating treatment selection

Most statistical methodology for phase III clinical trials focuses on the comparison of a single experimental treatment with a control. An increasing desire to reduce the time before regulatory approval of a new drug is sought has led to development of two-stage or sequential designs for trials that combine the definitive analysis associated with phase III with the treatment selection element of a phase II study. In this paper we consider a trial in which the most promising of a number of experimental treatments is selected at the first interim analysis. This considerably reduces the computational load associated with the construction of stopping boundaries compared to the approach proposed by Follman, Proschan and Geller (Biometrics 1994; 50: 325-336). The computational requirement does not exceed that for the sequential comparison of a single experimental treatment with a control. Existing methods are extended in two ways. First, the use of the efficient score as a test statistic makes the analysis of binary, normal or failure-time data, as well as adjustment for covariates or stratification straightforward. Second, the question of trial power is also considered, enabling the determination of sample size required to give specified power.     

自身免疫性肝病相关抗体检测及其临床意义研究

目的：分析研究自身免疫性肝病相关抗体检测以及临床效果。方法分析我院随机抽取的2011年8月-2013年08月期间600例自身免疫性肝病相关抗体检测的患者,随机分成两组,分别为实验组与对照组,每组平均300例患者。对照组进行常规检测,其中实验组进行间接免疫荧光法以及ELISA检测法。观察两组检测法的检测情况并进行分析。结果两组患者在进行自身抗体检测后,实验组抗体检测效果明显优于对照组,其中,实验组自身抗体检测有效率为93.0%,检测无效率为7.0%,AILD 检测中有ANA 46例、ANCA 64例、SMA 34例、抗 MPO 抗体82例以及 AMA 76例;对照组中自身抗体检测有效率为78.0%,检测无效率为22.0%,AILD 检测中有ANA34例、ANCA52例、SMA29例、抗 MPO 抗体76例以及 AMA70例。结论注重对自身免疫性肝病相关抗体进行检测,有利于对肝病进行检出、诊断、鉴别诊断以及临床分析等,有利于提高自身免疫性肝病的鉴别诊断以及指导治疗效果,具有重要的临床意义。     

Controlling the type I error rate in two‐stage sequential adaptive designs when testing for average bioequivalence

In a 2×2 crossover trial for establishing average bioequivalence (ABE) of a generic agent and a currently marketed drug, the recommended approach to hypothesis testing is the two one‐sided test (TOST) procedure, which depends, among other things, on the estimated within‐subject variability. The power of this procedure, and therefore the sample size required to achieve a minimum power, depends on having a good estimate of this variability. When there is uncertainty, it is advisable to plan the design in two stages, with an interim sample size reestimation after the first stage, using an interim estimate of the within‐subject variability. One method and 3 variations of doing this were proposed by Potvin et al. Using simulation, the operating characteristics, including the empirical type I error rate, of the 4 variations (called Methods A, B, C, and D) were assessed by Potvin et al and Methods B and C were recommended. However, none of these 4 variations formally controls the type I error rate of falsely claiming ABE, even though the amount of inflation produced by Method C was considered acceptable. A major disadvantage of assessing type I error rate inflation using simulation is that unless all possible scenarios for the intended design and analysis are investigated, it is impossible to be sure that the type I error rate is controlled. Here, we propose an alternative, principled method of sample size reestimation that is guaranteed to control the type I error rate at any given significance level. This method uses a new version of the inverse‐normal combination of p‐values test, in conjunction with standard group sequential techniques, that is more robust to large deviations in initial assumptions regarding the variability of the pharmacokinetic endpoints. The sample size reestimation step is based on significance levels and power requirements that are conditional on the first‐stage results. This necessitates a discussion and exploitation of the peculiar properties of the power curve of the TOST testing procedure. We illustrate our approach with an example based on a real ABE study and compare the operating characteristics of our proposed method with those of Method B of Povin et al.