Three-arm Non-inferiority Trial Research Articles

Simultaneous confidence intervals for an extended Koch-Röhmel design in three-arm non-inferiority trials.

Three-arm 'gold-standard' non-inferiority trials are recommended for indications where only unstable reference treatments are available and the use of a placebo group can be justified ethically. For such trials, several study designs have been suggested that use the placebo group for testing 'assay sensitivity', that is, the ability of the trial to replicate efficacy. Should the reference fail in the given trial, then non-inferiority could also be shown with an ineffective experimental treatment and hence becomes useless. In this article, we extend the so-called Koch-Röhmel design where a proof of efficacy for the experimental treatment is required in order to qualify for the non-inferiority test. While the efficacy of the experimental treatment is an indication of assay sensitivity, it does not guarantee that the reference is sufficiently efficient to let the non-inferiority claim be meaningful. It has, therefore, been suggested to adaptively test the non-inferiority only if the reference demonstrates superiority to placebo and otherwise to test -superiority of the experimental treatment over placebo, where is chosen in such a way that it provides proof of non-inferiority with regard to the reference's historical effect. In this article, we extend the previous work by complementing its adaptive test with compatible simultaneous confidence intervals. Confidence intervals are commonly used and suggested by regulatory guidelines for non-inferiority trials. We show how to adopt different approaches to simultaneous confidence intervals from the literature to the setting of three-arm non-inferiority trials and compare these methods in a simulation study. Finally, we apply these methods to a real clinical trial example.

Non-Parametric Non-Inferiority Assessment in a Three-Arm Trial with Non-Ignorable Missing Data

A three-arm non-inferiority trial including a placebo is usually utilized to assess the non-inferiority of an experimental treatment to a reference treatment. Existing methods for assessing non-inferiority mainly focus on the fully observed endpoints. However, in some clinical trials, treatment endpoints may be subject to missingness for various reasons, such as the refusal of subjects or their migration. To address this issue, this paper aims to develop a non-parametric approach to assess the non-inferiority of an experimental treatment to a reference treatment in a three-arm trial with non-ignorable missing endpoints. A logistic regression is adopted to specify a non-ignorable missingness data mechanism. A semi-parametric imputation method is proposed to estimate parameters in the considered logistic regression. Inverse probability weighting, augmented inverse probability weighting and non-parametric methods are developed to estimate treatment efficacy for known and unknown parameters in the considered logistic regression. Under some regularity conditions, we show asymptotic normality of the constructed estimators for treatment efficacy. A bootstrap resampling method is presented to estimate asymptotic variances of the estimated treatment efficacy. Three Wald-type statistics are constructed to test the non-inferiority based on the asymptotic properties of the estimated treatment efficacy. Empirical studies show that the proposed Wald-type test procedure is robust to the misspecified missingness data mechanism, and behaves better than the complete-case method in the sense that the type I error rates for the former are closer to the pre-given significance level than those for the latter.

Improving grading of recommendations assessment, development, and evaluation evidence tables part 4: a three-arm noninferiority randomized trial demonstrates improved understanding of content in summary of findings tables with a new format

ObjectivesTo evaluate alternative formats of summary of findings (SoF) tables for single comparison with multiple outcomes. Study Design and SettingWe conducted a three-arm randomized controlled noninferiority trial (RCT) in the following systematic review (SR) users: researchers, clinical practice guideline developers, health care providers, policymakers, and knowledge transfer organizations to measure understanding, accessibility, satisfaction, and preference across the current grading of recommendations assessment, development, and evaluation (GRADE) SoF, an alternative GRADE SoF, or an adapted evidence-based practice center (EPC) program SoF table. ResultsOne Hundred Seventy-Nine participants were randomized, and 129 participants completed the RCT (n = 47 current GRADE, n = 41 alternative GRADE, n = 41 adapted EPC). Understanding the certainty of evidence and treatment effect was comparable across groups. The adapted EPC SoF table was inferior for quantifying risk and RD compared to the alternatives (<35% correct vs. >85% correct). Participants reported increased satisfaction when SoF tables presented number needed to treat (NNT), anticipated absolute effect differences, and narrative syntheses for evidence that could not be meta-analyzed. Participants reported accessibility to information as significantly better in both GRADE SoF tables, when compared with the adapted EPC SoF table. Participants preferred the alternative GRADE SoF table format. ConclusionThe alternative GRADE SoF table is a promising format for SR users preferring a comprehensive presentation of SR results for single comparisons.

A hierarchical testing procedure for three arm non-inferiority trials

Non-inferiority trials are becoming very popular for comparative effectiveness research. Non-inferiority trials establish that the effect of an experimental treatment is not worse than that of a reference treatment by more than a specified margin. A three-arm non-inferiority trial that includes the placebo, experimental treatment, and a reference treatment is considered. It has been criticized that the conventional approach for three-arm non-inferiority trials loses power for the non-inferiority hypothesis test unless the power of the assay sensitivity test is close to one. In order to overcome this situation, a novel hierarchical testing procedure with two stages for three-arm non-inferiority trials is developed. The family-wise error rate (FWER) is investigated analytically and numerically of the proposed test procedure. Numerical studies indicate that the suggested method controls FWER and has more power than the traditional approach particularly when the power of that assay sensitivity test is not close to one. Through these empirical studies, it is shown that the proposed method can be successfully applied in practice.

Bayesian sample size determination in a three-arm non-inferiority trial with binary endpoints

ABSTRACT A three-arm non-inferiority trial including a test treatment, a reference treatment, and a placebo is recommended to assess the assay sensitivity and internal validity of a trial when applicable. Existing methods for designing and analyzing three-arm trials with binary endpoints are mainly developed from a frequentist viewpoint. However, these methods largely depend on large sample theories. To alleviate this problem, we propose two fully Bayesian approaches, the posterior variance approach and Bayes factor approach, to determine sample size required in a three-arm non-inferiority trial with binary endpoints. Simulation studies are conducted to investigate the performance of the proposed Bayesian methods. An example is illustrated by the proposed methodologies. Bayes factor method always leads to smaller sample sizes than the posterior variance method, utilizing the historical data can reduce the required sample size, simultaneous test requires more sample size to achieve the desired power than the non-inferiority test, the selection of the hyperparameters has a relatively large effect on the required sample size. When only controlling the posterior variance, the posterior variance criterion is a simple and effective option for obtaining a rough outcome. When conducting a previous clinical trial, it is recommended to use the Bayes factor criterion in practical applications.

Sample Size Calculation for “Gold-Standard” Noninferiority Trials With Fixed Margins and Negative Binomial Endpoints

For clinical trials in patients with asthma, chronic obstructive pulmonary disease, and relapsing-remitting multiple sclerosis, regulatory guidelines state that a noninferiority clinical trial is an option. Aiming at establishing assay sensitivity, a three-arm noninferiority trial, including an experimental treatment, a reference treatment, and a placebo, the so-called gold-standard noninferiority trial, is recommended. In addition, in the clinical trials for the above diseases, the number of events per unit time is often used as a primary or key secondary endpoint. There are two issues to be addressed in determining the sample size for gold-standard noninferiority trials: the hypotheses to be tested for assay sensitivity, and overdispersion of the number of events. To address these two issues, we propose a sample size calculation method for gold-standard noninferiority trials with two fixed margins and negative binomial endpoints. In a simulation, we show that the proposed hypothesis-testing method achieves the target power, while controlling the Type I error rate at a nominal level, and that the sample size calculation method has adequate power accuracy. Moreover, we illustrate an application of our proposed method for a clinical trial of mild asthma.

Simultaneous tests of non inferiority and superiority in three-arm clinical studies with heterogeneous variance

Non inferiority (NI) trials with the possibility of multiple experimental treatments have been increasingly used to find substitutes for standard therapies (e.g., to reduce side effects). NI trials seek to determine whether an experimental treatment can provide a suitable replacement for the standard treatment by examining the clinical significance of the loss of efficacy that is associated with the new treatment. In this article, we focus on three-arm NI trials, which include a placebo to provide direct verification of the assay sensitivity. Furthermore, it is reasonable to conduct superiority tests for experimental treatments that have been confirmed to be non inferior to the standard treatment. Several methodologies have recently been developed to provide stage-wise test procedures for this purpose. However, the applicability of these methods is limited owing to their requirement of homogeneity of variance. In this article, we seek to generalize the existing methods to more practical settings that allow the treatment variance to be heterogeneous. We also discuss sample size determination when the test power is given. Clinical examples are used to illustrate our proposed procedures.

Identification of the minimum non-inferior dose in a three-arm non-inferiority trial

Non-inferiority (NI) trials have gained recognition as an effective tool with which to search for substitutes for a standard treatment that is associated with certain undesirable features, such as adverse side-effects, an exorbitant cost, or an extremely complicated therapeutic regimen. Statistical methods have been developed for NI studies with multiple experimental treatments. However, experimental treatments sometimes represent a new treatment with various dose levels, and in such circumstances, identification of the minimum non-inferior dose is a reasonable objective of the trial. Thus, we examine several potential testing procedures with respect to this testing objective. A simulation study is conducted to evaluate their performance, and determination of the sample size is discussed. Two clinical examples are provided to illustrate the proposed method.

Bayesian Approach for Assessing Non-Inferiority in Three-Arm Trials for Risk Ratio and Odds Ratio

In this article, we consider three-arm noninferiority (NI) trial that includes an experimental, a reference, and a placebo arm. While the risk difference (RD) is the most common and well-explored functional form for testing efficacy (or effectiveness), for binary outcomes, recent FDA guideline suggested other measures, such as relative risk (RR) and odds ratio (OR) on the basis of which NI can be claimed. However, developing test based on these different functions of binary outcomes are challenging since the construction and interpretation of NI margin for such functions are not trivial extensions of RD-based approach. Recently, we have proposed Frequentist approach for testing NI for these functionals. In this article, we further develop Bayesian approaches for testing NI based on effect retention approach for RR and OR. Bayesian paradigm provides a natural path to integrate historical trials’ information, as well as it allows using patients’/clinicians’ opinions as prior information via sequential learning. In addition we discuss, in detail, the sample size/power calculation which could be readily used while designing such trials in practice.

NONPARAMETRIC TESTING FOR MULTIPLE SURVIVAL FUNCTIONS WITH NON-INFERIORITY MARGINS.

New nonparametric tests for the ordering of multiple survival functions are developed with the possibility of right censorship taken into account. The motivation comes from non-inferiority trials with multiple treatments. The proposed tests are based on nonparametric likelihood ratio statistics, which are known to provide more powerful tests than Wald-type procedures, but in this setting have only been studied for pairs of survival functions or in the absence of censoring. We introduce a novel type of pool adjacent violator algorithm that leads to a complete solution of the problem. The limit distributions can be expressed as weighted sums of squares involving projections of certain Gaussian processes onto the given ordered alternative. A simulation study shows that the new procedures have superior power to a competing combined-pairwise Cox model approach. We illustrate the proposed methods using data from a three-arm non-inferiority trial.

Non-inferiority testing for risk ratio, odds ratio and number needed to treat in three-arm trial

Three-arm non-inferiority (NI) trial including the experimental treatment, an active reference treatment, and a placebo where the outcome of interest is binary are considered. While the risk difference (RD) is the most common and well explored functional form for testing efficacy (or effectiveness), however, recent FDA guideline suggested measures such as relative risk (RR), odds ratio (OR), number needed to treat (NNT) among others, on the basis of which NI can be claimed for binary outcome. Albeit, developing test based on these different functions of binary outcome are challenging. This is because the construction and interpretation of NI margin for such functions are non-trivial extensions of RD based approach. A Frequentist test based on traditional fraction margin approach for RR, OR and NNT are proposed first. Furthermore a conditional testing approach is developed by incorporating assay sensitivity (AS) condition directly into NI testing. A detailed discussion of sample size/power calculation are also put forward which could be readily used while designing such trials in practice. A clinical trial data is reanalyzed to demonstrate the presented approach.

Response-adaptive treatment allocation for non-inferiority trials with heterogeneous variances

In clinical studies, patients usually accrue sequentially. The response-adaptive design has been shown to be a valuable treatment allocation apparatus that skews the treatment allocation probabilities to achieve certain objectives such as reducing the number of patients who receive inferior treatments. The doubly adaptive biased coin design was successfully derived for the three-arm non-inferiority (NI) trial. For an NI study, an experimental treatment can be considered a possible substitute for the standard treatment if the loss of clinically tolerable efficacy is compensated by benefits such as the alleviation of side effects. Previous applications of the doubly adaptive biased coin design in NI trials were developed only for homogeneous treatment variances. However, it is worth to examine the more complicated, but nevertheless popular, scenarios in which the treatment variances are heterogeneous. The proposed treatment allocation scheme is superior when the treatment variances differ and remains very competitive when they are homogeneous. A clinical example is given for demonstrative purposes.

A more efficient three-arm non-inferiority test based on pooled estimators of the homogeneous variance.

Hida and Tango established a statistical testing framework for the three-arm non-inferiority trial including a placebo with a pre-specified non-inferiority margin to overcome the shortcomings of traditional two-arm non-inferiority trials (such as having to choose the non-inferiority margin). In this paper, we propose a new method that improves their approach with respect to two aspects. We construct our testing statistics based on the best unbiased pooled estimators of the homogeneous variance; and we use the principle of intersection-union tests to determine the rejection rule. We theoretically prove that our test is better than that of Hida and Tango for large sample sizes. Furthermore, when that sample size was small or moderate, our simulation studies showed that our approach performed better than Hida and Tango's. Although both controlled the type I error rate, their test was more conservative and the statistical power of our test was higher.

Non-inferiority test based on transformations for non-normal distributions

Non-inferiority trials are becoming very popular for comparative effectiveness research. These trials are required to show that the effect of an experimental treatment is not worse than that of a reference treatment by more than a specified margin. Hence non-inferiority trials are of great importance, when superiority cannot be claimed. A three-arm non-inferiority trial consists of a placebo, a reference treatment, and an experimental treatment is considered. However unlike the traditional choices, it is assumed that the distributions of the end points corresponding to these treatments are unknown and suggested test procedures for a three-arm non-inferiority trial based on monotone transformations in conjunction with a normal approximation. The resulting test procedures are flexible and robust. Theoretical properties of the proposed methods are also investigated. The performance of the suggested test procedures is compared to their counterparts using simulations. In terms of type I error and power, the proposed methods perform better than their counterparts in most cases. The usefulness of the proposed methods is further illustrated through an example.

Some practical considerations in three-arm non-inferiority trial design.

Non-inferiority trials aim to demonstrate whether an experimental therapy is not unacceptably worse than an active reference therapy already in use. When applicable, a three-arm non-inferiority trial, including an experiment therapy, an active reference therapy, and a placebo, is often recommended to assess assay sensitivity and internal validity of a trial. In this paper, we share some practical considerations based on our experience from a phase III three-arm non-inferiority trial. First, we discuss the determination of the total sample size and its optimal allocation based on the overall power of the non-inferiority testing procedure and provide ready-to-use R code for implementation. Second, we consider the non-inferiority goal of 'capturing all possibilities' and show that it naturally corresponds to a simple two-step testing procedure. Finally, using this two-step non-inferiority testing procedure as an example, we compare extensively commonly used frequentist p -value methods with the Bayesian posterior probability approach. Copyright © 2016 John Wiley & Sons, Ltd.

Testing of non-inferiority and superiority for three-arm clinical studies with multiple experimental treatments.

The purpose of a non-inferiority trial is to assert the efficacy of an experimental treatment compared with a reference treatment by showing that the experimental treatment retains a substantial proportion of the efficacy of the reference treatment. Statistical methods have been developed to test multiple experimental treatments in three-arm non-inferiority trials. In this paper, we report the development of procedures that simultaneously test the non-inferiority and the superiority of experimental treatments after the assay sensitivity has been established. The advantage of the proposed test procedures is the additional ability to identify superior treatments while retaining an non-inferiority testing power comparable to that of existing testing procedures. Single-step and stepwise procedures are derived and then compared with each other to determine their relative testing power and testing error in a simulation study. Finally, the suggested procedures are illustrated with two clinical examples.

Group-sequential three-arm noninferiority clinical trial designs

ABSTRACTWe discuss group-sequential three-arm noninferiority clinical trial designs that include active and placebo controls for evaluating both assay sensitivity and noninferiority. We extend two existing approaches, the fixed margin and fraction approaches, into a group-sequential setting with two decision-making frameworks. We investigate the operating characteristics including power, Type I error rate, maximum, and expected sample sizes, as design factors vary. In addition, we discuss sample size recalculation and its impact on the power and Type I error rate via a simulation study.

Study duration for three-arm non-inferiority survival trials designed for accrual by cohorts.

Study planning is particularly complex for survival trials because it usually involves an accrual period and a continued observation period after accrual closure. The three-arm clinical trial design, which includes a test treatment, an active reference, and a placebo control, is the gold standard design for the assessment of non-inferiority. The existing statistical methods of calculating minimal sample size for non-inferiority trials with three-arm design and survival-type endpoints cannot take into consideration the accrual rate of patients to the trial, the length of accrual period, the length of continued observation period after accrual closure, and unbalanced allocation of the total sample size. The purpose of this paper is to develop a statistical method, which allows for all these sources of variability for planning non-inferiority trials with the gold standard design for censored, exponentially distributed time-to-event data. The proposed method is based on the assumption of exponentially distributed failure times and a non-inferiority test formulated in terms of the retention of effect hypotheses. It can be used to calculate the duration of accrual required to assure a desired power for non-inferiority trials with active and placebo control. We illustrate the use of the method by considering a randomized, active- and placebo-controlled trial in depression associated with Parkinson's disease. We then explore the validity of the proposed method by simulation studies. An R-language program for the implementation of the proposed algorithm is provided as supplementary material.

Correcting for non-compliance in randomized non-inferiority trials with active and placebo control using structural models.

The three-arm clinical trial design, which includes a test treatment, an active reference, and placebo control, is the gold standard for the assessment of non-inferiority. In the presence of non-compliance, one common concern is that an intent-to-treat (ITT) analysis (which is the standard approach to non-inferiority trials), tends to increase the chances of erroneously concluding non-inferiority, suggesting that the per-protocol (PP) analysis may be preferable for non-inferiority trials despite its inherent bias. The objective of this paper was to develop statistical methodology for dealing with non-compliance in three-arm non-inferiority trials for censored, time-to-event data. Changes in treatment were here considered the only form of non-compliance. An approach using a three-arm rank preserving structural failure time model and G-estimation analysis is here presented. Using simulations, the impact of non-compliance on non-inferiority trials was investigated in detail using ITT, PP analyses, and the present proposed method. Results indicate that the proposed method shows good characteristics, and that neither ITT nor PP analyses can always guarantee the validity of the non-inferiority conclusion. A Statistical Analysis System program for the implementation of the proposed test procedure is available from the authors upon request.

Testing non-inferiority of a new treatment in three-arm clinical trials with binary endpoints

BackgroundA two-arm non-inferiority trial without a placebo is usually adopted to demonstrate that an experimental treatment is not worse than a reference treatment by a small pre-specified non-inferiority margin due to ethical concerns. Selection of the non-inferiority margin and establishment of assay sensitivity are two major issues in the design, analysis and interpretation for two-arm non-inferiority trials. Alternatively, a three-arm non-inferiority clinical trial including a placebo is usually conducted to assess the assay sensitivity and internal validity of a trial. Recently, some large-sample approaches have been developed to assess the non-inferiority of a new treatment based on the three-arm trial design. However, these methods behave badly with small sample sizes in the three arms. This manuscript aims to develop some reliable small-sample methods to test three-arm non-inferiority.MethodsSaddlepoint approximation, exact and approximate unconditional, and bootstrap-resampling methods are developed to calculate p-values of the Wald-type, score and likelihood ratio tests. Simulation studies are conducted to evaluate their performance in terms of type I error rate and power.ResultsOur empirical results show that the saddlepoint approximation method generally behaves better than the asymptotic method based on the Wald-type test statistic. For small sample sizes, approximate unconditional and bootstrap-resampling methods based on the score test statistic perform better in the sense that their corresponding type I error rates are generally closer to the prespecified nominal level than those of other test procedures.ConclusionsBoth approximate unconditional and bootstrap-resampling test procedures based on the score test statistic are generally recommended for three-arm non-inferiority trials with binary outcomes.