Planning and analyzing adaptive group sequential survival trials

The use of adaptive methods has experienced increasing interest in the current literature on group sequential designs. Group sequential analysis in survival trials usually apply the error spending function approach due to the unpredictable amount of information available in an interim analysis. An alternative way is to apply adaptive methods where additionally the maximum amount of information and other designing parameters can be changed based on the information available at the interim stage. In this paper, it is shown how the inverse normal method can be used within a survival design using the log-rank test for comparing two survival functions. This method allows for many kinds of design modifications. In case of no modifications, the inverse normal method coincides with the commonly used analysis strategy. It is straightforward to specify effect estimates. Confidence intervals for the hazard ratio that can be calculated at each stage of the trial and intervals that can only be computed by the end of the trial are proposed. The latter also enables the calculation of median unbiased estimates. Overall p-values can be defined analogously. Properties of the analyses techniques are investigated and compared with alternative approaches. It is shown that the proposed analysis technique might help to rescue an underpowered study and opens the way to other types of changes in design. The proposed technique is implemented in the software ADDPLAN Adaptive Design, Plans and Analyses (http://www.addplan.com).     

Trendtests with adaptive scoring

The concept of adaptive two‐stage designs is applied to the problem of testing the equality of several normal means against an ordered (monotone) alternative. The likelihood‐ratio‐test proposed by Bartholomew is known to have favorable power properties when testing against a monotonic trend. Tests based on contrasts provide a flexible way to incorporate available information regarding the pattern of the unknown true means through appropriate specification of the scores. The basic idea of the presented concept is the combination of Bartholomew 's test (first stage) with an “adaptive score test” (second stage) which utilizes the information resulting from isotonic regression estimation at the first stage. In a Monte Carlo simulation study the adaptive scoring procedure is compared to the non‐adaptive two‐stage procedure using the Bartholomew test at both stages. We found that adaptive scoring may improve the power of the two stage design, in particular if the sample size at the first stage is considerably larger than at the second stage.     

Flexible designs by adaptive plans of generalized Pocock- and O'Brien-Fleming-type and by self-designing clinical trials

Flexible designs are provided by adaptive planning of sample sizes as well as by introducing the weighted inverse normal combining method and the generalized inverse chi-square combining method in the context of conducting trials consecutively step by step. These general combining methods allow quite different weighting of sequential study parts, also in a completely adaptive way, based on full information from unblinded data in previously performed stages. So, in reviewing some basic developments of flexible designing, we consider a generalizing approach to group sequentially performed clinical trials of Pocock-type, of O'Brien-Fleming-type, and of Self-designing-type. A clinical trial may be originally planned either to show non-inferiority or superiority. The proposed flexible designs, however, allow in each interim analysis to change the planning from showing non-inferiority to showing superiority and vice versa. Several examples of clinical trials with normal and binary outcomes are worked out in detail. We demonstrate the practicable performance of the discussed approaches, confirmed in an extensive simulation study. Our flexible designing is a useful tool, provided that a priori information about parameters involved in the trial is not available or subject to uncertainty.     

Power priors based on multiple historical studies for binary outcomes

Incorporating historical information into the design and analysis of a new clinical trial has been the subject of much recent discussion. For example, in the context of clinical trials of antibiotics for drug resistant infections, where patients with specific infections can be difficult to recruit, there is often only limited and heterogeneous information available from the historical trials. To make the best use of the combined information at hand, we consider an approach based on the multiple power prior that allows the prior weight of each historical study to be chosen adaptively by empirical Bayes. This choice of weight has advantages in that it varies commensurably with differences in the historical and current data and can choose weights near 1 if the data from the corresponding historical study are similar enough to the data from the current study. Fully Bayesian approaches are also considered. The methods are applied to data from antibiotics trials. An analysis of the operating characteristics in a binomial setting shows that the proposed empirical Bayes adaptive method works well, compared to several alternative approaches, including the meta‐analytic prior.     

Adaptive dose-finding: Proof of concept with type I error control

We consider an adaptive dose‐finding study with two stages. The doses for the second stage will be chosen based on the first stage results. Instead of considering pairwise comparisons with placebo, we apply one test to show an upward trend across doses. This is a possibility according to the ICH‐guideline for dose‐finding studies (ICH‐E4). In this article, we are interested in trend tests based on a single contrast or on the maximum of multiple contrasts. We are interested in flexibly choosing the Stage 2 doses including the possibility to add doses. If certain requirements for the interim decision rules are fulfilled, the final trend test that ignores the adaptive nature of the trial (naïve test) can control the type I error. However, for the more common case that these requirements are not fulfilled, we need to take the adaptivity into account and discuss a method for type I error control. We apply the general conditional error approach to adaptive dose‐finding and discuss special issues appearing in this application. We call the test based on this approach Adaptive Multiple Contrast Test. For an example, we illustrate the theory discussed before and compare the performance of several tests for the adaptive design in a simulation study.     

A Comparison of Procedures for Adaptive Choice of Location Tests in Flexible Two‐Stage Designs

Although linear rank statistics for the two‐sample problem are distribution free tests, their power depends on the distribution of the data. In the planning phase of an experiment, researchers are often uncertain about the shape of this distribution and so the choice of test statistic for the analysis and the determination of the required sample size are based on vague information. Adaptive designs with interim analysis can potentially overcome both problems. And in particular, adaptive tests based on a selector statistic are a solution to the first. We investigate whether adaptive tests can be usefully implemented in flexible two‐stage designs to gain power. In a simulation study, we compare several methods for choosing a test statistic for the second stage of an adaptive design based on interim data with the procedure that applies adaptive tests in both stages. We find that the latter is a sensible approach that leads to the best results in most situations considered here. The different methods are illustrated using a clinical trial example.     

A comparison of methods for constructing confidence intervals after phase II/III clinical trials

Recently, in order to accelerate drug development, trials that use adaptive seamless designs such as phase II/III clinical trials have been proposed. Phase II/III clinical trials combine traditional phases II and III into a single trial that is conducted in two stages. Using stage 1 data, an interim analysis is performed to answer phase II objectives and after collection of stage 2 data, a final confirmatory analysis is performed to answer phase III objectives. In this paper we consider phase II/III clinical trials in which, at stage 1, several experimental treatments are compared to a control and the apparently most effective experimental treatment is selected to continue to stage 2. Although these trials are attractive because the confirmatory analysis includes phase II data from stage 1, the inference methods used for trials that compare a single experimental treatment to a control and do not have an interim analysis are no longer appropriate. Several methods for analysing phase II/III clinical trials have been developed. These methods are recent and so there is little literature on extensive comparisons of their characteristics. In this paper we review and compare the various methods available for constructing confidence intervals after phase II/III clinical trials.     

Information fraction estimation based on the number of events within the standard treatment regimen

For a Phase III randomized trial that compares survival outcomes between an experimental treatment versus a standard therapy, interim monitoring analysis is used to potentially terminate the study early based on efficacy. To preserve the nominal Type I error rate, alpha spending methods and information fractions are used to compute appropriate rejection boundaries in studies with planned interim analyses. For a one-sided trial design applied to a scenario in which the experimental therapy is superior to the standard therapy, interim monitoring should provide the opportunity to stop the trial prior to full follow-up and conclude that the experimental therapy is superior. This paper proposes a method called total control only (TCO) for estimating the information fraction based on the number of events within the standard treatment regimen. Based on theoretical derivations and simulation studies, for a maximum duration superiority design, the TCO method is not influenced by departure from the designed hazard ratio, is sensitive to detecting treatment differences, and preserves the Type I error rate compared to information fraction estimation methods that are based on total observed events. The TCO method is simple to apply, provides unbiased estimates of the information fraction, and does not rely on statistical assumptions that are impossible to verify at the design stage. For these reasons, the TCO method is a good approach when designing a maximum duration superiority trial with planned interim monitoring analyses.     

A Bootstrap Procedure for Adaptive Selection of the Test Statistic in Flexible Two‐Stage Designs

Adaptive two‐stage designs allow a data‐driven change of design characteristics during the ongoing trial. One of the available options is an adaptive choice of the test statistic for the second stage of the trial based on the results of the interim analysis. Since there is often only a vague knowledge of the distribution shape of the primary endpoint in the planning phase of a study, a change of the test statistic may then be considered if the data indicate that the assumptions underlying the initial choice of the test are not correct. Collings and Hamilton proposed a bootstrap method for the estimation of the power of the two‐sample Wilcoxon test for shift alternatives. We use this approach for the selection of the test statistic. By means of a simulation study, we show that the gain in terms of power may be considerable when the initial assumption about the underlying distribution was wrong, whereas the loss is relatively small when in the first instance the optimal test statistic was chosen. The results also hold true for comparison with a one‐stage design. Application of the method is illustrated by a clinical trial example.     

Time‐to‐event continual reassessment method incorporating treatment cycle information with application to an oncology phase I trial

Delayed dose limiting toxicities (i.e. beyond first cycle of treatment) is a challenge for phase I trials. The time‐to‐event continual reassessment method (TITE‐CRM) is a Bayesian dose‐finding design to address the issue of long observation time and early patient drop‐out. It uses a weighted binomial likelihood with weights assigned to observations by the unknown time‐to‐toxicity distribution, and is open to accrual continually. To avoid dosing at overly toxic levels while retaining accuracy and efficiency for DLT evaluation that involves multiple cycles, we propose an adaptive weight function by incorporating cyclical data of the experimental treatment with parameters updated continually. This provides a reasonable estimate for the time‐to‐toxicity distribution by accounting for inter‐cycle variability and maintains the statistical properties of consistency and coherence. A case study of a First‐in‐Human trial in cancer for an experimental biologic is presented using the proposed design. Design calibrations for the clinical and statistical parameters are conducted to ensure good operating characteristics. Simulation results show that the proposed TITE‐CRM design with adaptive weight function yields significantly shorter trial duration, does not expose patients to additional risk, is competitive against the existing weighting methods, and possesses some desirable properties.     

Conditional Point Estimation in Adaptive Group Sequential Test Designs

It is well known that point estimates in group sequential designs are biased. This also applies to adaptive designs that enable, e.g., data driven reassessments of group sample sizes. For triangular designs, Whitehead (1986) (Biometrika 73 , 573–581) proposed a bias adjusted estimate. But this estimate is not feasible in adaptive designs although it is in group sequential designs. Furthermore, there is a waste of information because it does not use the information at which stage the trial was stopped. We present a modification which does use this information and which is applicable to adaptive designs. The modified estimate achieves an improvement in group sequential designs and shows similar results in adaptive designs.     

Inference on Multiple Endpoints in Clinical Trials with Adaptive Interim Analyses

Planned interim analyses which permit early stopping or sample size adaption of a trial are desirable for ethical and scientific reasons. Multiple test procedures allow inference about several hypotheses within a single clinical trial. In this paper, a method which combines multiple testing with adaptive interim analyses whilst controlling the experimentwise error rate is proposed. The general closed testing principle, the situation of a priori ordered hypotheses, and application of the Bonferroni-Holm method are considered. The practical application of the method is demonstrated by an example.     

Hierarchical commensurate and power prior models for adaptive incorporation of historical information in clinical trials

Bayesian clinical trial designs offer the possibility of a substantially reduced sample size, increased statistical power, and reductions in cost and ethical hazard. However when prior and current information conflict, Bayesian methods can lead to higher than expected type I error, as well as the possibility of a costlier and lengthier trial. This motivates an investigation of the feasibility of hierarchical Bayesian methods for incorporating historical data that are adaptively robust to prior information that reveals itself to be inconsistent with the accumulating experimental data. In this article, we present several models that allow for the commensurability of the information in the historical and current data to determine how much historical information is used. A primary tool is elaborating the traditional power prior approach based upon a measure of commensurability for Gaussian data. We compare the frequentist performance of several methods using simulations, and close with an example of a colon cancer trial that illustrates a linear models extension of our adaptive borrowing approach. Our proposed methods produce more precise estimates of the model parameters, in particular, conferring statistical significance to the observed reduction in tumor size for the experimental regimen as compared to the control regimen.     

Adaptive designs with arbitrary dependence structure

Adaptive designs were originally developed for independent and uniformly distributed p‐values. There are trial settings where independence is not satisfied or where it may not be possible to check whether it is satisfied. In these cases, the test statistics and p‐values of each stage may be dependent. Since the probability of a type I error for a fixed adaptive design depends on the true dependence structure between the p‐values of the stages, control of the type I error rate might be endangered if the dependence structure is not taken into account adequately. In this paper, we address the problem of controlling the type I error rate in two‐stage adaptive designs if any dependence structure between the test statistics of the stages is admitted (worst case scenario). For this purpose, we pursue a copula approach to adaptive designs. For two‐stage adaptive designs without futility stop, we derive the probability of a type I error in the worst case, that is for the most adverse dependence structure between the p‐values of the stages. Explicit analytical considerations are performed for the class of inverse normal designs. A comparison with the significance level for independent and uniformly distributed p‐values is performed. For inverse normal designs without futility stop and equally weighted stages, it turns out that correcting for the worst case is too conservative as compared to a simple Bonferroni design.     

Adaptive group sequential designs for clinical trials: combining the advantages of adaptive and of classical group sequential approaches

A general method is presented integrating the concept of adaptive interim analyses into classical group sequential testing. This allows the researcher to represent every group sequential plan as an adaptive trial design and to make design changes during the course of the trial after every interim analysis in the same way as with adaptive designs. The concept of adaptive trial designing is thereby generalized to a large variety of possible sequential plans.     

Adaptive two-stage designs for single-arm phase IIA cancer clinical trials

The main purpose of a phase IIA trial of a new anticancer therapy is to determine whether the therapy has sufficient promise against a specific type of tumor to warrant its further development. The therapy will be rejected for further investigation if the true response rate is less than some uninteresting level and the test of hypothesis is powered at a specific target response rate. Two-stage designs are commonly used for this situation. However, in many situations investigators often express concern about uncertainty in targeting the alternative hypothesis to study power at the planning stage. In this article, motivated by a real example, we propose a strategy for adaptive two-stage designs that will use the information at the first stage of the study to either reject the therapy or continue testing with either an optimistic or a skeptic target response rate, while the type I error rate is controlled. We also introduce new optimal criteria to reduce the expected total sample size.     

Ethical Considerations for Outcome‐adaptive Trial Designs: A Clinical Researcher's Perspective

In a typical comparative clinical trial the randomization scheme is fixed at the beginning of the study, and maintained throughout the course of the trial. A number of researchers have championed a randomized trial design referred to as ‘outcome‐adaptive randomization.’ In this type of trial, the likelihood of a patient being enrolled to a particular arm of the study increases or decreases as preliminary information becomes available suggesting that treatment may be superior or inferior. While the design merits of outcome‐adaptive trials have been debated, little attention has been paid to significant ethical concerns that arise in the conduct of such studies. These include loss of equipoise, lack of processes for adequate informed consent, and inequalities inherent in the research design which could lead to perceptions of injustice that may have negative implications for patients and the research enterprise. This article examines the ethical difficulties inherent in outcome‐adaptive trials.     

A comparison of methods for adaptive treatment selection

Traditionally drug development is generally divided into three phases which have different aims and objectives. Recently so-called adaptive seamless designs that allow combination of the objectives of different development phases into a single trial have gained much interest. Adaptive trials combining treatment selection typical for Phase II and confirmation of efficacy as in Phase III are referred to as adaptive seamless Phase II/III designs and are considered in this paper. We compared four methods for adaptive treatment selection, namely the classical Dunnett test, an adaptive version of the Dunnett test based on the conditional error approach, the combination test approach, and an approach within the classical group-sequential framework. The latter two approaches have only recently been published. In a simulation study we found that no one method dominates the others in terms of power apart from the adaptive Dunnett test that dominates the classical Dunnett by construction. Furthermore, scenarios under which one approach outperforms others are described.     

Utility‐Based Optimization of Combination Therapy Using Ordinal Toxicity and Efficacy in Phase I/II Trials

Summary An outcome‐adaptive Bayesian design is proposed for choosing the optimal dose pair of a chemotherapeutic agent and a biological agent used in combination in a phase I/II clinical trial. Patient outcome is characterized as a vector of two ordinal variables accounting for toxicity and treatment efficacy. A generalization of the Aranda‐Ordaz model (1981, Biometrika 68 , 357–363) is used for the marginal outcome probabilities as functions of a dose pair, and a Gaussian copula is assumed to obtain joint distributions. Numerical utilities of all elementary patient outcomes, allowing the possibility that efficacy is inevaluable due to severe toxicity, are obtained using an elicitation method aimed to establish consensus among the physicians planning the trial. For each successive patient cohort, a dose pair is chosen to maximize the posterior mean utility. The method is illustrated by a trial in bladder cancer, including simulation studies of the method's sensitivity to prior parameters, the numerical utilities, correlation between the outcomes, sample size, cohort size, and starting dose pair.     

Unbiased estimation of selected treatment means in two-stage trials

Straightforward estimation of a treatment's effect in an adaptive clinical trial can be severely hindered when it has been chosen from a larger group of potential candidates. This is because selection mechanisms that condition on the rank order of treatment statistics introduce bias. Nevertheless, designs of this sort are seen as a practical and efficient way to fast track the most promising compounds in drug development. In this paper we extend the method of Cohen and Sackrowitz (1989) who proposed a two-stage unbiased estimate for the best performing treatment at interim. This enables their estimate to work for unequal stage one and two sample sizes, and also when the quantity of interest is the best, second best, or j -th best treatment out of k. The implications of this new flexibility are explored via simulation.