Sample size and optimal designs in stratified comparative trials to establish the equivalence of treatment effects among two ethnic groups

When a new investigational medicine is intended to be applied to populations with different ethnic backgrounds, a stratified comparative phase III trial using ethnic groups as strata may be conducted to assess the influence of ethnic factors on clinical outcomes of this new medicine. In this paper, based on a binomial model with odds ratio as the measure of the treatment effect, we derive the score test and the associated sample size formula for establishing the equivalence/noninferiority of the treatment effects of a medicine among two ethnic groups. A simplified test together with its sample size formula are also given. Taking into account the sample size, cost, and power of testing, respectively, we derive the optimal design parameters, i.e., the allocation among treatment groups and ethnic groups, based on the simplified test.     

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.     

Nonparametric Sample Size Estimation for Sensitivity and Specificity with Multiple Observations per Subject

We propose a sample size calculation approach for the estimation of sensitivity and specificity of diagnostic tests with multiple observations per subjects. Many diagnostic tests such as diagnostic imaging or periodontal tests are characterized by the presence of multiple observations for each subject. The number of observations frequently varies among subjects in diagnostic imaging experiments or periodontal studies. Nonparametric statistical methods for the analysis of clustered binary data have been recently developed by various authors. In this paper, we derive a sample size formula for sensitivity and specificity of diagnostic tests using the sign test while accounting for multiple observations per subjects. Application of the sample size formula for the design of a diagnostic test is discussed. Since the sample size formula is based on large sample theory, simulation studies are conducted to evaluate the finite sample performance of the proposed method. We compare the performance of the proposed sample size formula with that of the parametric sample size formula that assigns equal weight to each observation. Simulation studies show that the proposed sample size formula generally yields empirical powers closer to the nominal level than the parametric method. Simulation studies also show that the number of subjects required increases as the variability in the number of observations per subject increases and the intracluster correlation increases.     

A note on sample size calculation based on propensity analysis in nonrandomized trials

In nonrandomized trials, patients are not randomly assigned to treatment groups with equal probability. Instead, the probability of assignment varies from patient to patient depending on patients baseline covariates. This often results in a non-comparable treatment groups due to treatment imbalance. As a result, the United States Food and Drug Administration (FDA) recommended that the method of propensity score analysis be employed to overcome this problem. In this note, a formula for sample size calculation is developed based on a proposed weighted Mantel-Haenszel test on the strata defined by the propensity score analysis. It was shown that the sample size formula derived by Nam (1998) based on the test statistic proposed by Gart (1985) is a special case of the sample size formula derived in this note.     

Notes on Testing Noninferiority in Ordinal Data Under the Parallel Groups Design

When testing the noninferiority of an experimental treatment to a standard (or control) treatment in a randomized clinical trial (RCT), we may come across the outcomes of patient response on an ordinal scale. We focus our discussion on testing noninferiority in ordinal data for an RCT under the parallel groups design. We develop simple test procedures based on the generalized odds ratio (GOR). We note that these test procedures not only can account for the information on the order of ordinal responses without assuming any specific parametric structural model, but also can be independent of any arbitrarily subjective scoring system. We further develop sample size determination based on the test procedure using the GOR. We apply Monte Carlo simulation to evaluate the performance of these test procedures and the accuracy of sample size calculation formula proposed here in a variety of situations. Finally, we employ the data taken from a trial comparing once-daily gatifloxican with three-times-daily co-amoxiclav in the treatment of community-acquired pneumonia to illustrate the use of these test procedures and sample size calculation formula.     

Sample size determination for a three-arm equivalence trial of Poisson and negative binomial responses

ABSTRACT

Assessing equivalence or similarity has drawn much attention recently as many drug products have lost or will lose their patents in the next few years, especially certain best-selling biologics. To claim equivalence between the test treatment and the reference treatment when assay sensitivity is well established from historical data, one has to demonstrate both superiority of the test treatment over placebo and equivalence between the test treatment and the reference treatment. Thus, there is urgency for practitioners to derive a practical way to calculate sample size for a three-arm equivalence trial. The primary endpoints of a clinical trial may not always be continuous, but may be discrete. In this paper, the authors derive power function and discuss sample size requirement for a three-arm equivalence trial with Poisson and negative binomial clinical endpoints. In addition, the authors examine the effect of the dispersion parameter on the power and the sample size by varying its coefficient from small to large. In extensive numerical studies, the authors demonstrate that required sample size heavily depends on the dispersion parameter. Therefore, misusing a Poisson model for negative binomial data may easily lose power up to 20%, depending on the value of the dispersion parameter.     

Test non-inferiority and sample size determination based on the odds ratio under a cluster randomized trial with noncompliance

Because the odds ratio (OR) possesses certain desirable statistical properties, the OR has been recommended elsewhere to measure the relative treatment effect in establishing non-inferiority. For cost efficiency, we may often employ a cluster randomized trial (CRT), in which randomized units are clusters of patients. Furthermore, it is not uncommon to encounter data in which there are patients not complying with their assigned treatment. Under the Dirichlet multinomial model, we have developed a test statistic for assessing non-inferiority based on the OR between two treatments under a CRT with noncompliance. We have further derived a sample size formula accounting for both noncompliance and the intraclass correlation for a desired power 1 - β of detecting non-inferiority with respect to the OR at a nominal α level. Using Monte Carlo simulation, we have evaluated the performance of the proposed test statistic and sample size formula. Finally, we use the CRT studying the effect of vitamin A supplementation on mortality among preschool children to illustrate the use of the sample size formula given here.     

Sample Size Computation for Two-Sample Noninferiority Log-Rank Test

When an experimental therapy is less extensive, less toxic, or less expensive than a standard therapy, we may want to prove that the former is not worse than the latter through a noninferiority trial. In this article, we discuss a modification of the log-rank test for noninferiority trials with survival endpoint and propose a sample size formula that can be used in designing such trials. Performance of our sample size formula is investigated through simulations. Our formula is applied to design a real clinical trial.     

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.     

Test Non-Inferiority and Sample Size Determination Based on the Odds Ratio Under a Cluster Randomized Trial with Noncompliance

Because the odds ratio (OR) possesses certain desirable statistical properties, the OR has been recommended elsewhere to measure the relative treatment effect in establishing non-inferiority. For cost efficiency, we may often employ a cluster randomized trial (CRT), in which randomized units are clusters of patients. Furthermore, it is not uncommon to encounter data in which there are patients not complying with their assigned treatment. Under the Dirichlet multinomial model, we have developed a test statistic for assessing non-inferiority based on the OR between two treatments under a CRT with noncompliance. We have further derived a sample size formula accounting for both noncompliance and the intraclass correlation for a desired power 1 ? β of detecting non-inferiority with respect to the OR at a nominal α level. Using Monte Carlo simulation, we have evaluated the performance of the proposed test statistic and sample size formula. Finally, we use the CRT studying the effect of vitamin A supplementation on mortality among preschool children to illustrate the use of the sample size formula given here.     

Single-Arm Phase II Survival Trial Design Under the Proportional Hazards Model

For designing single-arm phase II trials with time-to-event endpoints, a sample size formula is derived for the modified one-sample log-rank test under the proportional hazards model. The derived formula enables new methods for designing trials that allow a flexible choice of the underlying survival distribution. Simulation results showed that the proposed formula provides an accurate estimation of sample size. The sample size calculation has been implemented in an R function for the purpose of trial design. Supplementary materials for this article are available online.     

Sample Size Calculation for the van Elteren Test Adjusting for Ties

In this article we study sample size calculation methods for the asymptotic van Elteren test. Because the existing methods are only applicable to continuous data without ties, in this article we develop a new method that can be used on ordinal data. The new method has a closed form formula and is very easy to calculate. The new sample size formula performs very well because our simulations show that the corresponding actual powers are close to the nominal powers.     

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.     

Sample size calculation for the van Elteren test adjusting for ties

In this article we study sample size calculation methods for the asymptotic van Elteren test. Because the existing methods are only applicable to continuous data without ties, in this article we develop a new method that can be used on ordinal data. The new method has a closed form formula and is very easy to calculate. The new sample size formula performs very well because our simulations show that the corresponding actual powers are close to the nominal powers.     

Sample size determination for testing equality in a cluster randomized trial with noncompliance

For administrative convenience or cost efficiency, we may often employ a cluster randomized trial (CRT), in which randomized units are clusters of patients rather than individual patients. Furthermore, because of ethical reasons or patient's decision, it is not uncommon to encounter data in which there are patients not complying with their assigned treatments. Thus, the development of a sample size calculation procedure for a CRT with noncompliance is important and useful in practice. Under the exclusion restriction model, we have developed an asymptotic test procedure using a tanh(-1)(x) transformation for testing equality between two treatments among compliers for a CRT with noncompliance. We have further derived a sample size formula accounting for both noncompliance and the intraclass correlation for a desired power 1 - β at a nominal α level. We have employed Monte Carlo simulation to evaluate the finite-sample performance of the proposed test procedure with respect to type I error and the accuracy of the derived sample size calculation formula with respect to power in a variety of situations. Finally, we use the data taken from a CRT studying vitamin A supplementation to reduce mortality among preschool children to illustrate the use of sample size calculation proposed here.     

A simple formula for sample size calculation in equivalence studies

Bioequivalence and clinical equivalence can be claimed based on the two one-sided test approach or the confidence interval approach. Consequently the power function of the equivalence test can be derived from either noncentral t-distribution or central t-distribution. The sample size is then determined from the power function either by numerical method or closed formulas. In this paper, we propose a simple formula for sample size calculation based on central t-distribution. The proposed formula has better properties than those currently available and it can be easily applied in all equivalence studies.     

计量资料非劣效临床试验样本量及把握度的计算与SAS程序实现

目的：利用SAS简易快速对计量资料非劣效临床试验进行样本量及把握度的计算方法：比较公式及SAS编程两种计算方法,同时给出反推把握度的SAS宏程序。结果：公式和SAS程序两种计算方法的结果一致,利用SAS程序可以直接给出结果,无需要再进行查表获得相关参数,更简单、快捷。结论：利用本文提供的程序可以更好的帮助研究者理解与运用此程序进行样本量和把握度的估算,为此类新药临床试验服务。     

中心效应及中心间样本不均衡对临床疗效评价的影响

目的:本文分析和探讨在多中心临床试验中,中心效应、中心与处理的交互作用以及各中心样本量不均衡对治疗效果评价的影响。方法:以二分类资料两组比较为例,采用计算机模拟试验,分别探讨各中心10种不同样本分配比例、3种中心效应时,对临床疗效的检验效能及Ⅰ类错误的影响。结果:在不存在中心效应,或有中心效应但中心与处理间无交互作用情况下,不同样本量的分配比例对检验效能的影响不大,Ⅰ类错误可控。当中心与处理间存在交互作用时,即使中心间样本量均衡,检验效能也有所下降,Ⅰ类错误亦增加,随着各中心样本均衡性变差,检验效能随之略有降低,I类错误亦随之少许增加。结论:在多中心临床试验中,若中心与处理间存在交互作用,会对疗效评价有影响,而中心间样本均衡性对结果影响较小。在临床试验设计时应给予高度重视。     

Ethnicity and ethnic identity as predictors of drug norms and drug use among preadolescents in the US Southwest

This article reports the results of research exploring how ethnicity and ethnic identity may "protect" adolescents against drug use and help them form antidrug use norms. This study was conducted in 1998 and is based on a sample of 4364 mostly Mexican American seventh graders residing in a large southwestern city of diverse acculturation statuses. It aims at testing existing findings by conducting the research within the unique geographic and ethnic context of the Southwest region of the United States. This research examines how strength of ethnic identity plays a distinctive role in drug use behavior among the various ethnic groups represented in the sample: Mexican Americans, other Latinos, American Indians, African Americans, non-Hispanic Whites, and those of mixed ethnic backgrounds. Positive ethnic identity (i.e., strong ethnic affiliation, attachment, and pride) was associated with less substance use and stronger antidrug norms in the sample overall. Unexpectedly, the apparently protective effects of positive ethnic identity were generally stronger for non-Hispanic White respondents (a numerical minority group in this sample) than for members of ethnic minority groups. Implications for prevention programs tailored for Mexican/Mexican American students are discussed.     

Ethnicity and Ethnic Identity as Predictors of Drug Norms and Drug Use Among Preadolescents in the US Southwest

This article reports the results of research exploring how ethnicity and ethnic identity may “protect” adolescents against drug use and help them form antidrug use norms. This study was conducted in 1998 and is based on a sample of 4364 mostly Mexican American seventh graders residing in a large southwestern city of diverse acculturation statuses. It aims at testing existing findings by conducting the research within the unique geographic and ethnic context of the Southwest region of the United States. This research examines how strength of ethnic identity plays a distinctive role in drug use behavior among the various ethnic groups represented in the sample: Mexican Americans, other Latinos, American Indians, African Americans, non-Hispanic Whites, and those of mixed ethnic backgrounds. Positive ethnic identity (i.e., strong ethnic affiliation, attachment, and pride) was associated with less substance use and stronger antidrug norms in the sample overall. Unexpectedly, the apparently protective effects of positive ethnic identity were generally stronger for non-Hispanic White respondents (a numerical minority group in this sample) than for members of ethnic minority groups. Implications for prevention programs tailored for Mexican/Mexican American students are discussed.