On clinical trials with a high placebo response rate.

The basic problem that causes the frequent failure of a standard randomized parallel placebo-controlled clinical trial with a high placebo response rate is the underestimation of the treatment effect by the observed relative treatment difference. A two-period sequential parallel enrichment design has been proposed where the first period is a standard parallel design and at the end of the first period, the placebo non-responders are identified and re-randomized in the second period. Based on such a design, available methods have primarily focused on testing either the first period treatment null hypothesis or the global null hypothesis defined as the joint period 1 and period 2 treatment effect null hypothesis by a test statistic which is either derived from a combined statistic or defined directly as a weighted z-score where the weights are functions of some population and design parameters satisfying certain power optimality criterion. However, in some cases, it is not clear what their combined statistics are estimating and in others, the combined statistics are estimating the apparent treatment effect; but generally, there is no discussion of the need to provide a proper assessment of the treatment effect for the intended study population. It should be clear that an appropriate assessment of the treatment effect for the intended study population is critical for the benefit/risk analysis as well as the proper dosage recommendation. Any benefit/risk analysis and dosage recommendation that are based on an apparent treatment effect from a standard parallel design such as the first period of a sequential parallel enrichment design tend to underestimate the benefit/risk ratio which in turn may lead to overdosing recommendation. It is the purpose of this paper to introduce the concept of an adjusted treatment effect which is derived by adjusting the apparent treatment effect from the first period of a sequential parallel enrichment design with information from the second period subject to a consistency condition. The adjustment properly compensates for the high placebo response rate. It is proposed that this adjusted treatment effect should be used to assess the treatment effect for the intended study population and should be the basis for the benefit/risk analysis and the dosage recommendation.

Understanding the FDA guidance on adaptive designs: historical, legal, and statistical perspectives.

The recent Food and Drug Administration (FDA) guidance for industry on adaptive designs is perhaps one of the important undertakings by CDER/CBER Office of Biostatistics. Undoubtedly, adaptive designs may affect almost all phases of clinical development and impact nearly all aspects of clinical trial planning, execution and statistical inference. Thus, it is a significant accomplishment for the Office of Biostatistics to develop this well-thought-out and all-encompassing guidance document. In this paper, we discuss some critical topical issues of adaptive designs with supporting methodological work from either existing literature, additional technical notes, or accompanying papers. In particular, we provide numerous sources of design, conduct, analysis, and interpretation bias that arise from statistical procedures. We illustrate, as a result, and caution that substantial research is necessary for many adaptive designs to meet required scientific standards prior to their applications in clinical trials.

A method for testing a prespecified subgroup in clinical trials.

In clinical trials, investigators are often interested in the effect of a given study treatment on a subgroup of patients with certain clinical or biological attributes in addition to its effect on the overall study population. Such a subgroup analysis would become even more important to the study sponsor if an efficacy claim can be made for the subgroup when the test for the overall study population fails at a prespecified alpha level. In practice, such a claim is often dependent on prespecification of the subgroup and certain implicit or explicit requirements placed on the study results due to ethical or regulatory concerns. By carefully considering these requirements, we propose a general statistical methodology for testing both the overall and subgroup hypotheses, which has optimal power and strongly controls the familywise Type I error rate.

A ratio test in active control non-inferiority trials with a time-to-event endpoint.

There are essentially two kinds of non-inferiority hypotheses in an active control trial: fixed margin and ratio hypotheses. In a fixed margin hypothesis, the margin is a prespecified constant and the hypothesis is defined in terms of a single parameter that represents the effect of the active treatment relative to the control. The statistical inference for a fixed margin hypothesis is straightforward. The outstanding issue for a fixed margin non-inferiority hypothesis is how to select the margin, a task that may not be as simple as it appears. The selection of a fixed non-inferiority margin has been discussed in a few articles (Chi et al., 2003; Hung et al., 2003; Ng, 1993). In a ratio hypothesis, the control effect is also considered as an unknown parameter, and the noninferiority hypothesis is then formulated as a ratio in terms of these two parameters, the treatment effect and the control effect. This type of non-inferiority hypothesis has also been called the fraction retention hypothesis because the ratio hypothesis can be interpreted as a retention of certain fraction of the control effect. Rothmann et al. (2003) formulated a ratio non-inferiority hypothesis in terms of log hazards in the time-to-event setting. To circumvent the complexity of having to deal with a ratio test statistic, the ratio hypothesis was linearized to an equivalent hypothesis under the assumption that the control effect is positive. An associated test statistic for this linearized hypothesis was developed. However, there are three important issues that are not addressed by this method. First, the retention fraction being defined in terms of log hazard is difficult to interpret. Second, in order to linearize the ratio hypothesis, Rothmann's method has to assume that the true control effect is positive. Third, the test statistic is not powerful and thus requires a huge sample size, which renders the method impractical. In this paper, a ratio hypothesis is defined directly in terms of the hazard. A natural ratio test statistic can be defined and is shown to have the desired asymptotic normality. The demand on sample size is much reduced. In most commonly encountered situations, the sample size required is less than half of those needed by either the fixed margin approach or Rothmann's method.

Some issues with composite endpoints in clinical trials.

This article discusses some important issues that may arise in the current usage of composite endpoints as primary endpoints for demonstrating the efficacy of new drugs in clinical trials. The discussion focuses on time-to-event composite endpoints. Issues discussed include validity of a composite endpoint, the often lack of follow-up of patients beyond first event, the analysis of a composite endpoint, its sub-composite and individual component endpoints and their interpretation. Actual published examples in the literature are used to illustrate some of these problems. It is recommended that a clinical trial using a composite endpoint as the primary endpoint should be designed to include patient follow-up beyond the first event if possible. For data collected from such trials, basic formats for tabular presentation of trial data and for results of analysis of the composite endpoint, its sub-composite and individual component endpoints are proposed for transparency and ease of interpretation.

Hypotheses and type I error in active-control noninferiority trials.

A fundamental assumption in the design and analysis of an active-control noninferiority trial is that the active control is truly effective. If this assumption does not hold, i.e., the active control is not effective, a harmful drug may be approved based on the result of a noninferiority trial. The assessment of the assumption is usually based on statistically significant results of historical randomized clinical trials on the active control, in which the conclusion may be falsely positive. This false positive rate, however, is not taken into consideration in current noninferiority trial test procedures. In this paper, various possible hypotheses for noninferiority trials are presented. The noninferiority hypotheses correctly associated with the objective of noninferiority trials are suggested. However, since there are no data collected for placebo in a noninferiority trial, this hypothesis cannot be directly tested by using data from noninferiority studies alone. The claim of noninferiority is based on the significant test for the control effect in historical trials and the significant test for noninferiority in a current noninferiority trial with a given fraction retention or margin. The false positive rate associated with such noninferiority test procedure is defined in this paper. The simulation result demonstrates the magnitude of the false positive rate inflation associated with the noninferiority test procedure.

Evaluation of health-related quality-of-life measures in oncology drug product applications: issues and concerns.

Health-related quality-of-life outcomes as reported by patients are valuable data and ideally should be critical to evaluating clinical benefit. The unblinded or open-label designs commonly adapted in oncology trials have the potential to introduce selection bias, reporting bias, and analyses bias. In this paper, issues surrounding use of patient reported outcomes to evaluate oncology drug products, including definition of hypothesis, study design, analysis, and interpretation of patient reported outcome data, are reported.

Design and analysis of non-inferiority mortality trials in oncology.

The recent revision of the Declaration of Helsinki and the existence of many new therapies that affect survival or serious morbidity, and that therefore cannot be denied patients, have generated increased interest in active-control trials, particularly those intended to show equivalence or non-inferiority to the active-control. A non-inferiority hypothesis has historically been formulated in terms of a fixed margin. This margin was historically designed to exclude a 'clinically meaningful difference', but has become recognized that the margin must also be no larger than the assured effect of the control in the new study. Depending on how this 'assured effect' is determined or estimated, the selected margin may be very small, leading to very large sample sizes, especially when there is an added requirement that a loss of some specified fraction of the assured effect must be ruled out. In cases where it is appropriate, this paper proposes non-inferiority analyses that do not involve a fixed margin, but can be described as a two confidence interval procedure that compares the 95 per cent two-sided CI for the difference between the treatment and the control to a confidence interval for the control effect (based on a meta-analysis of historical data comparing the control to placebo) that is chosen to preserve a study-wide type I error rate of about 0.025 (similar to the usual standard for a superiority trial) for testing for retention of a prespecified fraction of the control effect. The approach assumes that the estimate of the historical active-control effect size is applicable in the current study. If there is reason to believe that this effect size is diminished (for example, improved concomitant therapies) the estimate of this historical effect could be reduced appropriately. The statistical methodology for testing this non-inferiority hypothesis is developed for a hazard ratio (rather than an absolute difference between treatments, because a hazard ratio seems likely to be less population dependent than the absolute difference). In the case of oncology, the hazard ratio is the usual way of comparing treatments with respect to time to event (time to progression or survival) endpoints. The proportional hazards assumption is regarded as reasonable (approximately holding). The testing procedures proposed are conditionally equivalent to two confidence interval procedures that relax the conservatism of two 95 per cent confidence interval testing procedures and preserve the type I error rate at a one-sided 0.025 level. An application of this methodology to Xeloda, a recently approved drug for the treatment of metastatic colorectal cancers, is illustrated. Other methodologies are also described and assessed - including a point estimate procedure, a Bayesian procedure and two delta-method confidence interval procedures. Published in 2003 by John Wiley & Sons, Ltd.