Utility and pitfalls of some statistical methods in active controlled clinical trials

The generalized inference on the ratio of mean differences for fraction retention noninferiority hypothesis

The fraction retention non-inferiority hypothesis is often measured for the ratio of the effects of a new treatment to those of the control in medical research. However, the fraction retention non-inferiority test that the new treatment maintains the efficacy of control can be affected by the nuisance parameters. Herein, a heuristic procedure for testing the fraction retention non-inferiority hypothesis is proposed based on the generalized p-value (GPV) under normality assumption and heteroskedasticity. Through the simulation study, it is demonstrated that, the performance of the GPV-based method not only adequately controls the type I error rate at the nominal level but also is uniformly more powerful than the ratio test, Rothmann’s and Wang’s tests, the comparable extant methods. Finally, we illustrate the proposed method by employing a real example.

Avoiding ambiguity with the Type I error rate in noninferiority trials

This review article sets out to examine the Type I error rates used in noninferiority trials. Most papers regarding noninferiority trials only state Type I error rate without mentioning clearly which Type I error rate is evaluated. Therefore, the Type I error rate in one paper is often different from the Type I error rate in another paper, which can confuse readers and makes it difficult to understand papers. Which Type I error rate should be evaluated is related directly to which paradigm is employed in the analysis of noninferiority trial, and to how the historical data are treated. This article reviews the characteristics of the within-trial Type I error rate and the unconditional across-trial Type I error rate which have frequently been examined in noninferiority trials. The conditional across-trial Type I error rate is also briefly discussed. In noninferiority trials comparing a new treatment with an active control without a placebo arm, it is argued that the within-trial Type I error rate should be controlled in order to obtain approval of the new treatment from the regulatory agencies. I hope that this article can help readers understand the difference between two paradigms employed in noninferiority trials.

Covariate effect on constancy assumption in noninferiority clinical trials

Noninferiority (NI) clinical trials are getting a lot of attention of late due to their direct application in biosimilar studies. Because of the missing placebo arm, NI is an indirect approach to demonstrate efficacy of a test treatment. One of the key assumptions in the NI test is the constancy assumption, that is, that the effect of the reference treatment is the same in current NI trials as in historical superiority trials. However, if a covariate interacts with the treatment arms, then changes in distribution of this covariate will likely result in violation of constancy assumption. In this article, we propose four new NI methods and compare them with two existing methods to evaluate the change of background constancy assumption on the performance of these six methods. To achieve this goal, we study the impact of three elements-(1) strength of covariate, (2) degree of interaction between covariate and treatment, and (3) differences in distribution of the covariate between historical and current trials-on both the type I error rate and power using three different measures of association: difference, log relative risk, and log odds ratio. Based on this research, we recommend using a modified covariate-adjustment fixed margin method.

Bayesian approach to the design and analysis of non-inferiority trials for anti-infective products

In the absence of placebo-controlled trials, determining the non-inferiority (NI) margin for comparing an experimental treatment with an active comparator is based on carefully selected well-controlled historical clinical trials. With this approach, information on the effect of the active comparator from other sources including observational studies and early phase trials is usually ignored because of the need to maintain active comparator effect across trials. This may lead to conservative estimates of the margin that translate into larger sample-size requirements for the design and subsequent frequentist analysis, longer trial durations, and higher drug development costs. In this article, we provide methodological approaches to determine NI margins that can utilize all relevant historical data through a novel power adjusted Bayesian meta-analysis, with Dirichlet process priors, that puts ordered weights on the amount of information a set of data contributes. We also provide a Bayesian decision rule for the non-inferiority analysis that is based on a broader use of available prior information and a sample-size determination that is based on this Bayesian decision rule. Finally, the methodology is illustrated through several examples.

Bayesian approach to non-inferiority trials for normal means

Regulatory framework recommends that novel statistical methodology for analyzing trial results parallels the frequentist strategy, e.g. the new method must protect type-I error and arrive at a similar conclusion. Keeping these in mind, we construct a Bayesian approach for non-inferiority trials with normal response. A non-informative prior is assumed for the mean response of the experimental treatment and Jeffrey's prior for its corresponding variance when it is unknown. The posteriors of the mean response and variance of the treatment in historical trials are then assumed as priors for its corresponding parameters in the current trial, where that treatment serves as the active control. From these priors, a Bayesian decision criterion is derived to determine whether the experimental treatment is non-inferior to the active control. This criterion is evaluated and compared with the frequentist method using simulation studies. Results show that both Bayesian and frequentist approaches perform alike, but the Bayesian approach has a higher power when the variances are unknown. Both methods also arrive at the same conclusion of non-inferiority when applied on two real datasets. A major advantage of the proposed Bayesian approach lies in its ability to provide posterior probabilities for varying effect sizes of the experimental treatment over the active control.

The network meta-analytic-predictive approach to non-inferiority trials

In non-inferiority clinical trials, a test treatment is compared to an active-control rather than to placebo. Such designs are considered when placebo is unethical or not feasible. The critical question is whether the test treatment would have been superior to placebo, had placebo been used in the non-inferiority trial. This question can only be addressed indirectly, based on information from relevant historical trials with data on active-control and placebo. The network meta-analytic-predictive approach to non-inferiority trials is based on a network meta-analysis of the data from the historical trials and the non-inferiority trial, and the prediction of the putative test vs. placebo effect in the non-inferiority trial. The approach extends previous work by incorporating between-trial variability for all relevant parameters and focusing on the parameters in the non-inferiority trial rather than on population means. Two prominent examples with binary outcomes are used to illustrate the approach.

Modelling of the outcome of non-inferiority trials by integration of historical data

The approval and differentiation of new compounds in clinical development often demands non-inferiority trials, in which the test drug is compared against a reference treatment. However, non-inferiority trials impose major operational burden with serious ethical and scientific implications for the development of new medicines. Traditional approaches make limited use of historical information on placebo and neglect inter-trial variability, relying on the constancy assumption that the control-to-placebo effect size is maintained across trials. We propose a model-based approach that overcomes such limitations and may be used as a tool to explore differentiation during clinical development. Parameter distributions are introduced which reflect the heterogeneity of trials. The method is illustrated using data from impetigo trials. Based on simulation scenarios, this Bayesian technique yields a definitive, consistent increase in the statistical power over two accepted statistical methods, allowing lower sample size requirements for the assessment of non-inferiority.

An evidential approach to non-inferiority clinical trials

We present likelihood methods for defining the non-inferiority margin and measuring the strength of evidence in non-inferiority trials using the 'fixed-margin' framework. Likelihood methods are used to (1) evaluate and combine the evidence from historical trials to define the non-inferiority margin, (2) assess and report the smallest non-inferiority margin supported by the data, and (3) assess potential violations of the constancy assumption. Data from six aspirin-controlled trials for acute coronary syndrome and data from an active-controlled trial for acute coronary syndrome, Organisation to Assess Strategies for Ischemic Syndromes (OASIS-2) trial, are used for illustration. The likelihood framework offers important theoretical and practical advantages when measuring the strength of evidence in non-inferiority trials. Besides eliminating the influence of sample spaces and prior probabilities on the 'strength of evidence in the data', the likelihood approach maintains good frequentist properties. Violations of the constancy assumption can be assessed in the likelihood framework when it is appropriate to assume a unifying regression model for trial data and a constant control effect including a control rate parameter and a placebo rate parameter across historical placebo controlled trials and the non-inferiority trial. In situations where the statistical non-inferiority margin is data driven, lower likelihood support interval limits provide plausibly conservative candidate margins.

Challenges in the design and analysis of non-inferiority trials: a case study

BACKGROUND

The literature on the design, conduct, and analysis of non-inferiority trials is continuously evolving. Several design issues continue to be researched including the choice of active control, choice of non-inferiority margin, and optimal analytic approaches. To date, there has been relatively little in the literature documenting actual experiences with implementing available methodology for non-inferiority trials.

PURPOSE

This article serves as a case study and highlights some of the challenges encountered in the design of a Phase III non-inferiority trial in status epilepticus that is being conducted under a Food and Drug Administration Investigational New Drug Application (IND).

METHODS

The IND application was put on clinical hold by the Food Drug and Administration due to concerns with the design. Specifically, support for the active control, non-inferiority margin, and overall interpretability of trial results were questioned, and a recommendation was made to consider a superiority design. The authors describe their interactions with the Food Drug and Administration and their application of available methods and approaches to address these concerns.

RESULTS

The investigators' response to the clinical hold provided detailed information to support the conduct of a non-inferiority trial. The study team received Food Drug and Administration approval to initiate the trial in October 2008. The trial enrollment began in June 2009 and is being conducted by roughly 800 paramedic units in over 40 Emergency Medicine Service systems across the United States.

LIMITATIONS

There is still a great deal of methodological research needed to fully understand the application and impact of the non-inferiority trial design.

CONCLUSIONS

It is evident that non-inferiority trials have an important place in clinical trial design and analysis. These trials may be the only way and only opportunity to answer certain questions; so, they must be designed and conducted with rigor. This case study is an attempt to share our experiences in implementation.

Meeting the demand for more sophisticated study designs. A proposal for a new type of clinical trial: the hybrid design

Background Treatment effect is traditionally assessed through either superiority or non-inferiority clinical trials. Investigators may find that because of safety concerns and/or wide variability across strata of the superiority margin of active controls over placebo, neither a superiority nor a non-inferiority trial design is ethical or practical in some disease populations. Prior knowledge may allow and drive study designers to consider more sophisticated designs for a clinical trial. Design In this paper, the authors propose hybrid designs which may combine a superiority design in one subgroup with a non-inferiority design in another subgroup or combine designs with different control regimens in different subgroups in one trial when a uniform design is unethical or impractical. The authors show how the hybrid design can be planned and how inferences can be made. Through two examples, the authors illustrate the scenarios where hybrid designs are useful while the conventional designs are not preferable. Conclusion The hybrid design is a useful alternative to current superiority and non-inferiority designs.

Strength of evidence of non-inferiority trials-The adjustment of the type I error rate in non-inferiority trials with the synthesis method

In non-inferiority trials that employ the synthesis method several types of dependencies among test statistics occur due to sharing of the same information from the historical trial. The conditions under which the dependencies appear may be divided into three categories. The first case is when a new drug is approved with single non-inferiority trial. The second case is when a new drug is approved if two independent non-inferiority trials show positive results. The third case is when two new different drugs are approved with the same active control. The problem of the dependencies is that they can make the type I error rate deviate from the nominal level. In order to study such deviations, we introduce the unconditional and conditional across-trial type I error rates when the non-inferiority margin is estimated from the historical trial, and investigate how the dependencies affect the type I error rates. We show that the unconditional across-trial type I error rate increases dramatically as does the correlation between two non-inferiority tests when a new drug is approved based on the positive results of two non-inferiority trials. We conclude that the conditional across-trial type I error rate involves the unknown treatment effect in the historical trial. The formulae of the conditional across-trial type I error rates provide us with a way of investigating the conditional across-trial type I error rates for various assumed values of the treatment effect in the historical trial.

A covariate-adjustment regression model approach to noninferiority margin definition

To maintain the interpretability of the effect of experimental treatment (EXP) obtained from a noninferiority trial, current statistical approaches often require the constancy assumption. This assumption typically requires that the control treatment effect in the population of the active control trial is the same as its effect presented in the population of the historical trial. To prevent constancy assumption violation, clinical trial sponsors were recommended to make sure that the design of the active control trial is as close to the design of the historical trial as possible. However, these rigorous requirements are rarely fulfilled in practice. The inevitable discrepancies between the historical trial and the active control trial have led to debates on many controversial issues. Without support from a well-developed quantitative method to determine the impact of the discrepancies on the constancy assumption violation, a correct judgment seems difficult. In this paper, we present a covariate-adjustment generalized linear regression model approach to achieve two goals: (1) to quantify the impact of population difference between the historical trial and the active control trial on the degree of constancy assumption violation and (2) to redefine the active control treatment effect in the active control trial population if the quantification suggests an unacceptable violation. Through achieving goal (1), we examine whether or not a population difference leads to an unacceptable violation. Through achieving goal (2), we redefine the noninferiority margin if the violation is unacceptable. This approach allows us to correctly determine the effect of EXP in the noninferiority trial population when constancy assumption is violated due to the population difference. We illustrate the covariate-adjustment approach through a case study.

Exact tests using two correlated binomial variables in contemporary cancer clinical trials

New therapy strategies for the treatment of cancer are rapidly emerging because of recent technology advances in genetics and molecular biology. Although newer targeted therapies can improve survival without measurable changes in tumor size, clinical trial conduct has remained nearly unchanged. When potentially efficacious therapies are tested, current clinical trial design and analysis methods may not be suitable for detecting therapeutic effects. We propose an exact method with respect to testing cytostatic cancer treatment using correlated bivariate binomial random variables to simultaneously assess two primary outcomes. The method is easy to implement. It does not increase the sample size over that of the univariate exact test and in most cases reduces the sample size required. Sample size calculations are provided for selected designs.

Assessing non-inferiority: a combination approach

Non-inferiority designs are growing in importance as a strategy for comparing new drugs with established therapies. Because it is not possible to show that a new drug and the established therapy have identical efficacy profiles, non-inferiority trials are designed to demonstrate that the new drug is not inferior to an established drug (the 'control') relative to a prespecified 'non-inferiority margin'. No objective principle guides the choice of the non-inferiority margin, and controversies about the margin have, in some cases, had important consequences for drug development. We argue that some of these controversies have arisen because non-inferiority trials must achieve two objectives. They must demonstrate not only that the new drug is not inferior to the control drug by the non-inferiority margin, but also that the new drug is superior to placebo. When the second objective is not considered explicitly, it can distort the choice of the non-inferiority margin. Some methods designed to address both objectives through the choice of the non-inferiority margin lead to overly stringent non-inferiority criteria. We describe an approach to non-inferiority analysis that combines two tests, a traditional test for non-inferiority and a test for superiority based on a synthetic estimate of the effect of the new treatment relative to placebo. The synthetic estimate may be 'discounted' to address concerns about assay inconstancy. We discuss power and sample size considerations for the proposed procedure.

Comparison of idraparinux with vitamin K antagonists for prevention of thromboembolism in patients with atrial fibrillation: a randomised, open-label, non-inferiority trial

BACKGROUND

Vitamin K antagonists, the current standard treatment for prophylaxis against stroke and systemic embolism in patients with atrial fibrillation, require regular monitoring and dose adjustment; an unmonitored, fixed-dose anticoagulant regimen would be preferable. The aim of this randomised, open-label non-inferiority trial was to compare the efficacy and safety of idraparinux with vitamin K antagonists.

METHODS

Patients with atrial fibrillation at risk for thromboembolism were randomly assigned to receive either subcutaneous idraparinux (2.5 mg weekly) or adjusted-dose vitamin K antagonists (target of an international normalised ratio of 2-3). Assessment of outcome was done blinded to treatment. The primary efficacy outcome was the cumulative incidence of all stroke and systemic embolism. The principal safety outcome was clinically relevant bleeding. Analyses were done by intention to treat; the non-inferiority hazard ratio was set at 1.5. This trial is registered with ClinicalTrials.gov, number NCT00070655.

FINDINGS

The trial was stopped after randomisation of 4576 patients (2283 to receive idraparinux, 2293 to receive vitamin K antagonists) and a mean follow-up period of 10.7 (SD 5.4) months because of excess clinically relevant bleeding with idraparinux (346 cases vs 226 cases; 19.7 vs 11.3 per 100 patient-years; p<0.0001). There were 21 instances of intracranial bleeding with idraparinux and nine with vitamin K antagonists (1.1 vs 0.4 per 100 patient-years; p=0.014); elderly patients and those with renal impairment were at greater risk of such complications. There were 18 cases of thromboembolism with idraparinux and 27 cases with vitamin K antagonists (0.9 vs 1.3 per 100 patient-years; hazard ratio 0.71, 95% CI 0.39-1.30; p=0.007), satisfying the non-inferiority criterion. There were 62 deaths with idraparinux and 61 with vitamin K anatagonists (3.2 vs 2.9 per 100 patient-years; p=0.49).

INTERPRETATION

In patients with atrial fibrillation at risk for thromboembolism, long-term treatment with idraparinux was no worse than vitamin K antagonists in terms of efficacy, but caused significantly more bleeding.

Controlling the type 1 error rate in non-inferiority trials

Two different approaches have been proposed for establishing the efficacy of an experimental therapy through a non-inferiority trial: The fixed-margin approach involves first defining a non-inferiority margin and then demonstrating that the experimental therapy is not worse than the control by more than this amount, and the synthesis approach involves combining the data from the non-inferiority trial with the data from historical trials evaluating the effect of the control. In this paper, we introduce a unified approach that has both these approaches as special cases and show how the parameters of this approach can be selected to control the unconditional type 1 error rate in the presence of departures from the assumptions of assay sensitivity and constancy. It is shown that the fixed-margin approach can be extremely inefficient and that it is always possible to achieve equivalent control of the unconditional type 1 error rate, with higher power, by using an appropriately chosen synthesis method.

Preservation of effect and the regulatory approval of new treatments on the basis of non-inferiority trials

The criteria for approval of an experimental treatment on the basis of active-controlled non-inferiority trials often include demonstration of 'preservation of effect' relative to the active control. While this appears on its surface to be a reasonable criterion, on closer inspection it can be shown to lead to serious logical inconsistencies. In particular, an experimental treatment may have clinical trial results that are superior to those for the standard treatment and yet fail to meet this criterion for approval. In this paper we propose a set of principles that will help avoid these logical inconsistencies, and we argue that the qualities of an experimental treatment that are required for approval should be consistent regardless of the presence or absence of existing treatments and the type of study design used to evaluate the treatment.

The role of intention to treat in analysis of noninferiority studies

In analysing clinical trials designed to show superiority of one treatment compared to another, it is standard to use an intention to treat analytic approach. In active-controlled noninferiority studies, this is not standard, due to concerns that such an analysis will inflate the chance of falsely rejecting the null hypothesis, accepting therapeutic noninferiority when it is not justified. The reasons for using intention to treat (ITT) approaches in superiority studies include a desire to capture all information on study subjects, a need to prevent bias, and assurance that comparative groups are, on average, equivalent in prognostic factors. In this commentary, we argue that these same justifications carry over to noninferiority studies, and that for those and other reasons it should be the preferred analytic approach. We review regulatory guidelines, and propose a number of approaches to minimizing the potential disadvantages of the ITT approach in the noninferiority setting.

Simultaneous test for superiority and noninferiority hypotheses in active-controlled clinical trials

Two stage switching between testing for superiority (SUP) and noninferiority (NI) has been an important statistical issue in the design and analysis of the active-controlled clinical trials. Tsong and Zhang (2005) has shown that the Type I error rates do not change when switching between SUP and NI with the traditional generalized historical control (GHC) approach, however, they may change when switching with the cross-trial comparison (X-trial) approach. Tsong and Zhang (2005) further proposed a simultaneous test for both hypotheses to avoid the problem. The procedure was based on Fieller's confidence interval proposed by Hauschke et al. (1999). Since with the X-trial approach, using the simultaneous test, superiority is tested using all four treatment arms (current test and active control arms, active control and placebo arms in historical trials), the Type I error rate and power are expected to be somewhat different from the conventional superiority test (using the current test and active control arms only). Through a simulation study, we demonstrate that the Type I error rate and power between simultaneous test and the conventional superiority test are compatible. We also examine the impact of the assumption of equal variances of the current trial and the historical trial.

Noninferiority Testing Beyond Simple Two-Sample Comparison

In order to fulfill the requirement of a new drug application, a sponsor often need to conduct multiple clinical trials. Often these trials are of designs more complicated than a randomized two-sample single-factor study. For example, these trials could be designed with multiple centers, multiple factors, covariates, group sequential and/or adaptive scheme, etc. When an active standard treatment used as the control treatment in a two-arm clinical trial, the efficacy of the test treatment is often established by performing a noninferiority test through comparison of the test treatment and the active standard treatment. Typically, the noninferiority trials are designed with either a generalized historical control approach (i.e., noninferiority margin approach or delta-margin approach) or a cross-trial comparison approach (i.e., synthesis approach or lambda-margin approach). Many of the statistical properties of the approaches discussed in the literature were focused on testing in a simple two sample comparison form. We studied the limitations of the two approaches for the consideration of switching between superiority and noninferiority testing, feasibility to be applied with group sequential design, constancy assumption requirements, test dependency in multiple trials, analysis of homogeneity of efficacy among centers in a multi-center trial, data transformation and changing analysis method from the historical studies. Our evaluation shows that the cross-trial comparison approach is more restricted to simple two sample comparison with normal approximation test because of its poor properties with more complicated design and analysis. On the other hand, the generalized historical control comparison approach may have more flexible properties when the variability of the margin delta is indeed negligibly small.

Issues with Statistical Risks for Testing Methods in Noninferiority Trial Without a Placebo ARM

Noninferiority trials without a placebo arm often require an indirect statistical inference for assessing the effect of a test treatment relative to the placebo effect or relative to the effect of the selected active control treatment. The indirect inference involves the direct comparison of the test treatment with the active control from the noninferiority trial and the assessment, via some type of meta-analyses, of the effect of the active control relative to a placebo from historical studies. The traditional within-noninferiority-trial Type I error rate cannot ascertain the statistical risks associated with the indirect inference, though this error rate is of the primary consideration under the frequentist statistical framework. Another kind of Type I error rate, known as across-trial Type I error rate, needs to be considered in order that the statistical risks associated with the indirect inference can be controlled at a small level. Consideration of the two kinds of Type I error rates is also important for defining a noninferiority margin. For the indirect statistical inference, the practical utility of any method that controls only the across-trial Type I error rate at a fixed small level is limited.

Multiple Testing of Noninferiority Hypotheses in Active Controlled Trials

For noninferiority testing with the maximum allowable noninferiority margin being prespecified, one can perform valid statistical testing at the same alpha level for multiple noninferiority hypotheses with margins being smaller than this maximum margin. This is easily comprehensible because only one confidence level is used to assess which margins within the interval bounded by the maximum margin can be ruled out. If different confidence intervals are used, e.g., the interval generated from the intent-to-treat population is used for testing superiority and the interval generated from the per-protocol population is used for testing noninferiority, the problem of multiplicity will surface and the adjustment of alpha for each testing may be needed. All these predicate on the condition that at least a certain element of the maximum allowable noninferiority margin, whether it is the entire margin or the fraction of the active control effect to be retained, must be fixed in advance. None of these elements can be allowed to be influenced directly or indirectly by any analysis of the noninferiority trial data. Otherwise, the noninferiority analysis may be invalid.

A Bootstrap-Based Test for Establishing Noninferiority in Clinical Trials

A randomized, active-control clinical trial setting with the objective of testing noninferiority for a continuous response variable is considered. Noninferiority margin is based on the concept of preserving a certain fraction of the active control effect. Noninferiority is established if the ratio of the lower (upper) limit of the two-sided 95% confidence interval for the treatment difference to the estimated mean of the active control is greater (less) than a certain fraction. The nominal significance level is not maintained by the above confidence interval-based noninferiority test. We use bootstrapping to derive an accurate lower (upper) limit of the same confidence interval, which approximates the nominal significance level better and improves the power.

Non-inferiority trial design for recurrent events

We describe methods for designing non-inferiority trials with recurrent event responses arising from mixed-Poisson models. Sample size formulae are derived for trials in which treatment effects are expressed as relative rates and as absolute differences in cumulative mean functions at a particular time. Simulation studies are conducted to provide empirical validation of the frequency properties of the design and testing procedures under the null and alternative hypotheses using both mixed-Poisson models and robust marginal methods. The robustness of the design to mis-specification of the random effect distribution is also studied empirically. Sample size requirements based on the proposed method are contrasted with those from a design based on the time to the first event for a motivating study of patients with bone metastases at risk of skeletal complications. When the between-patient heterogeneity in the event rate is small, there may be a considerable reduction in sample size with recurrent event outcomes.

Testing superiority and non-inferiority hypotheses in active controlled clinical trials

Switching between testing for superiority and non-inferiority has been an important statistical issue in the design and analysis of active controlled clinical trial. In practice, it is often conducted with a two-stage testing procedure. It has been assumed that there is no type I error rate adjustment required when either switching to test for non-inferiority once the data fail to support the superiority claim or switching to test for superiority once the null hypothesis of non-inferiority is rejected with a pre-specified non-inferiority margin in a generalized historical control approach. However, when using a cross-trial comparison approach for non-inferiority testing, controlling the type I error rate sometimes becomes an issue with the conventional two-stage procedure. We propose to adopt a single-stage simultaneous testing concept as proposed by Ng (2003) to test both non-inferiority and superiority hypotheses simultaneously. The proposed procedure is based on Fieller's confidence interval procedure as proposed by Hauschke et al. (1999).

A regulatory perspective on choice of margin and statistical inference issue in non-inferiority trials

Without a placebo arm, any non-inferiority inference involving assessment of the placebo effect under the active control trial setting is difficult. The statistical risk for falsely concluding non-inferiority cannot be evaluated unless the constancy assumption approximately holds that the effect of the active control under the historical trial setting where the control effect can be assessed carries to the noninferiority trial setting. The constancy assumption cannot be checked because of missing the placebo arm in the non-inferiority trial. Depending on how serious the violation of the assumption is thought to be, one may need to seek an alternative design strategy that includes a cushion for a very conservative non-inferiority analysis or shows superiority of the experimental treatment over the control. Determination of the non-inferiority margin depends on what objective the non-inferiority analysis is intended to achieve. The margin can be a fixed margin or a margin functionally defined. Between-trial differences always exist and need to be properly considered.

Active-controlled, non-inferiority trials in oncology: arbitrary limits, infeasible sample sizes and uninformative data analysis. Is there another way?

In oncology, it may not always be possible to evaluate the efficacy of new medicines in placebo-controlled trials. Furthermore, while some newer, biologically targeted anti-cancer treatments may be expected to deliver therapeutic benefit in terms of better tolerability or improved symptom control, they may not always be expected to provide increased efficacy relative to existing therapies. This naturally leads to the use of active-control, non-inferiority trials to evaluate such treatments. In recent evaluations of anti-cancer treatments, the non-inferiority margin has often been defined in terms of demonstrating that at least 50% of the active control effect has been retained by the new drug using methods such as those described by Rothmann et al., Statistics in Medicine 2003; 22:239-264 and Wang and Hung Controlled Clinical Trials 2003; 24:147-155. However, this approach can lead to prohibitively large clinical trials and results in a tendency to dichotomize trial outcome as either 'success' or 'failure' and thus oversimplifies interpretation. With relatively modest modification, these methods can be used to define a stepwise approach to design and analysis. In the first design step, the trial is sized to show indirectly that the new drug would have beaten placebo; in the second analysis step, the probability that the new drug is superior to placebo is assessed and, if sufficiently high in the third and final step, the relative efficacy of the new drug to control is assessed on a continuum of effect retention via an 'effect retention likelihood plot'. This stepwise approach is likely to provide a more complete assessment of relative efficacy so that the value of new treatments can be better judged.

On non-inferiority margin and statistical tests in active control trials

The problem of selecting a non-inferiority margin and the corresponding statistical test for non-inferiority in active control trials is considered. For selection of non-inferiority margin, the guideline by the International Conference on Harmonization (ICH) recommends that the non-inferiority margin should be chosen in such a way that if the non-inferiority of the test therapy to the active control agent is claimed, the test therapy is not only non-inferior to the active control agent, but also superior to the placebo. Furthermore, variability should be taken into account. Along this line, a method for selecting non-inferiority margins with some statistical justification is proposed. Statistical tests for non-inferiority designed in the situation where the non-inferiority margin is an unknown parameter are derived. An example concerning a cancer trail for testing non-inferiority with the primary study endpoint of the time to disease progression is presented to illustrate the proposed method.

Enoxaparin in the Treatment of Deep Vein Thrombosis With or Without Pulmonary Embolism

STUDY OBJECTIVES

Low-molecular-weight heparins have been compared with unfractionated heparin (UFH) for treatment of deep vein thrombosis (DVT). However, a comparison of their efficacy in the presence or absence of pulmonary embolism (PE) has not been studied. We estimated the efficacy and safety of enoxaparin vs UFH in patients with proximal DVT with/without symptomatic PE using a meta-analysis of individual data from randomized controlled trials.

DESIGN AND SETTING

Randomized controlled trials were identified from MEDLINE, EMBASE, abstracts from international meetings on venous thromboembolism (VTE), previous meta-analyses, and trial data provided by the sponsor.

PARTICIPANTS

For inclusion, randomized controlled trials had to be properly randomized; include patients with objectively diagnosed DVT; compare enoxaparin twice daily with UFH; use objective methods to assess recurrent symptomatic VTE, major bleeding, and death at 3 months; and include blind evaluation of clinical events.

MEASUREMENTS

A meta-analysis was performed using the logarithm of the relative risk (RR) method. Enoxaparin in DVT treatment with/without symptomatic PE was considered noninferior to UFH for preventing VTE at 3 months if the upper limit of the 95% confidence interval (CI) of the RR (enoxaparin/UFH) was lower than a prespecified noninferiority margin (1.61). No increase in major bleeding or mortality should be observed.

RESULTS

The meta-analysis included individual data from three randomized controlled trials (749 patients and 754 patients in the enoxaparin and UFH groups, respectively). The observed RR (enoxaparin/UFH) of VTE was 0.81 (95% CI, 0.52 to 1.26) for the intention-to-treat population (RR, 0.70; 95% CI, 0.43 to 1.13; for per-protocol analysis). Results did not differ for patients with clinical PE (235 patients; RR, 0.84) and without clinical PE (1,268 patients; RR, 0.71), with a nonsignificant heterogeneity test between groups (p = 0.76). A trend in favor of enoxaparin was observed for reduced mortality and major bleeding.

CONCLUSIONS

The efficacy and safety of enoxaparin vs UFH for DVT treatment is not modified by the presence of symptomatic PE.

Bridging bioequivalence studies

In some new regions, an innovative drug of the original region was not marketed. However, after the patent of the innovative drug is expired, a generic copy of the innovative drug from the original region was introduced and approved for marketing in the new region. Another generic copy manufactured by the local sponsor of the new region is seeking for approval in the new region. Despite unavailability of the innovative drug, the regulatory authority of the new region still wants to approve the local generic copy based on assessment of bioequivalence between the local generic drug and the innovative drug. Following the bridging concept suggested by the ICH E5 guidance, we propose a method to evaluate average bioequivalence between the generic copy of the new region and the innovative drug of the original region using the generic copy of the original region as the bridging reference formulation. Sample size required by the bioequivalence study in the new region is also provided. Numerical examples illustrate the proposed method.

Equivalence and noninferiority trials - are they viable alternatives for registration of new drugs? (III)

The scientific community's reliance on active-controlled trials is steadily increasing, as widespread agreement emerges concerning the role of these trials as viable alternatives to placebo trials. These trials present substantial challenges with regard to design and interpretation as their complexity increases, and the potential need for larger sample sizes impacts the cost and time variables of the drug development process. The potential efficacy and safety benefits derived from these trials may never be demonstrated by other methods. Active-controlled trials can develop valuable data to inform both prescribers and patients about the dose- and time-dependent actions of any new drug and can contribute to the management and communication of risks associated with the relevant therapeutic products.