Asymptotically efficient estimation in response adaptive trials

We examine the issue of asymptotic efficiency of estimation for response adaptive designs of clinical trials, from which the collected data set contains a dependency structure. We establish the asymptotic lower bound of exponential rates for consistent estimators. Under certain regularity conditions, we show that the maximum likelihood estimator achieves the asymptotic lower bound for response adaptive trials with dichotomous responses. Furthermore, it is shown that the maximum likelihood estimator of the treatment effect is asymptotically efficient in the Bahadur sense for response adaptive clinical trials.     

On design and inference for two-stage adaptive clinical trials with dependent data

We consider two-stage adaptive designs for clinical trials where data from the two stages are dependent. This occurs when additional data are obtained from patients during their second stage follow-up. While the proposed flexible approach allows modifications of trial design, sample size, or statistical analysis using the first stage data, there is no need for a complete prespecification of the adaptation rule. Methods are provided for an adaptive closed testing procedure, for calculating overall adjusted p-values, and for obtaining unbiased estimators and confidence bounds for parameters that are invariant to modifications. A motivating example is used to illustrate these methods.     

A Bayesian sequential design with adaptive randomization for 2‐sided hypothesis test

Bayesian sequential and adaptive randomization designs are gaining popularity in clinical trials thanks to their potentials to reduce the number of required participants and save resources. We propose a Bayesian sequential design with adaptive randomization rates so as to more efficiently attribute newly recruited patients to different treatment arms. In this paper, we consider 2‐arm clinical trials. Patients are allocated to the 2 arms with a randomization rate to achieve minimum variance for the test statistic. Algorithms are presented to calculate the optimal randomization rate, critical values, and power for the proposed design. Sensitivity analysis is implemented to check the influence on design by changing the prior distributions. Simulation studies are applied to compare the proposed method and traditional methods in terms of power and actual sample sizes. Simulations show that, when total sample size is fixed, the proposed design can obtain greater power and/or cost smaller actual sample size than the traditional Bayesian sequential design. Finally, we apply the proposed method to a real data set and compare the results with the Bayesian sequential design without adaptive randomization in terms of sample sizes. The proposed method can further reduce required sample size.     

Asymptotics of adaptive design with two alternating generating matrices

In the application of generalized Pólya urn (GPU) model to designs of clinical trials, in contrast to the classical homogeneous models, it is more realistic to assume nonhomogeneous generating matrices. However, in literature, due to mathematical difficulties, the generating matrices are either assumed to be homogeneous or asymptotically homogeneous (see Bai and Hu, 1999). In the present paper, we consider a new model which uses two alternating generating matrices. The theoretical results show that the asymptotics still hold in this nonhomogeneous case. Moreover, the simulation results also support the theoretical conclusions. Furthermore, this model provides a starting point for the future study of adaptive designs with non-convergent generating matrices.     

Adaptive designs for IVPT data with mixed scaled average bioequivalence

In vitro permeation tests (IVPT) offer accurate and cost-effective development pathways for locally acting drugs, such as topical dermatological products. For assessment of bioequivalence, the FDA draft guidance on generic acyclovir 5% cream introduces a new experimental design, namely the single-dose, multiple-replicate per treatment group design, as IVPT pivotal study design. We examine the statistical properties of its hypothesis testing method—namely the mixed scaled average bioequivalence (MSABE). Meanwhile, some adaptive design features in clinical trials can help researchers make a decision earlier with fewer subjects or boost power, saving resources, while controlling the impact on family-wise error rate. Therefore, we incorporate MSABE in an adaptive design combining the group sequential design and sample size re-estimation. Simulation studies are conducted to study the passing rates of the proposed methods—both within and outside the average bioequivalence limits. We further consider modifications to the adaptive designs applied for IVPT BE trials, such as Bonferroni's adjustment and conditional power function. Finally, a case study with real data demonstrates the advantages of such adaptive methods.     

Non-parametric group sequential designs in randomized clinical trials

This paper examines some non‐parametric group sequential designs applicable for randomized clinical trials, for comparing two continuous treatment effects taking the observations in matched pairs, or applicable in event‐based analysis. Two inverse binomial sampling schemes are considered, of which the second one is an adaptive data‐dependent design. These designs are compared with some fixed sample size competitors. Power and expected sample sizes are calculated for the proposed procedures.     

Nested combination tests with a time‐to‐event endpoint using a short‐term endpoint for design adaptations

Adaptive trial methodology for multiarmed trials and enrichment designs has been extensively discussed in the past. A general principle to construct test procedures that control the family‐wise Type I error rate in the strong sense is based on combination tests within a closed test. Using survival data, a problem arises when using information of patients for adaptive decision making, which are under risk at interim. With the currently available testing procedures, either no testing of hypotheses in interim analyses is possible or there are restrictions on the interim data that can be used in the adaptation decisions as, essentially, only the interim test statistics of the primary endpoint may be used. We propose a general adaptive testing procedure, covering multiarmed and enrichment designs, which does not have these restrictions. An important application are clinical trials, where short‐term surrogate endpoints are used as basis for trial adaptations, and we illustrate how such trials can be designed. We propose statistical models to assess the impact of effect sizes, the correlation structure between the short‐term and the primary endpoint, the sample size, the timing of interim analyses, and the selection rule on the operating characteristics.     

抗肿瘤药物贝叶斯Ⅰ期临床试验设计方法比较研究

Ⅰ期临床试验的主要目的是探索药物毒性最大耐受剂量MTD,而MTD估计的准确与否将影响之后的Ⅱ期和Ⅲ期临床试验研究的结果.抗肿瘤药物Ⅰ期试验的特点是直接对病人进行试验,且样本量较小,这对构造估计精确度高并具有安全性保障要求的统计设计方法提出了挑战.回顾三种常用的Ⅰ期试验设计方法有:3+3设计、CRM设计和mTPI设计.3+3设计是应用较为广泛的传统方法,后两者是当前常用的贝叶斯自适应试验设计方法.通过大量模拟研究对三种方法从最优分配、安全性和估计MTD精确性三方面给以全面考察,并结合中国实际得出mTPI设计是比较适合推荐的Ⅰ期临床试验设计方法的结论.     

Discrete adaptive design in attribute life testing

Properties of a discrete adaptive design in attribute life testing situation are studied. It is shown that the design is strongly consistent and asymptotically normal. Some examples are discussed to show that the design could be used in a wide range of ields, Finally, we give some simulation results to compare the discrete adaptive desigin with some continuous optimal designs.     

Practical approaches for design and analysis of clinical trials of infertility treatments: crossover designs and the Mantel–Haenszel method are recommended

Crossover designs have some advantages over standard clinical trial designs and they are often used in trials evaluating the efficacy of treatments for infertility. However, clinical trials of infertility treatments violate a fundamental condition of crossover designs, because women who become pregnant in the first treatment period are not treated in the second period. In previous research, to deal with this problem, some new designs, such as re‐randomization designs, and analysis methods including the logistic mixture model and the beta‐binomial mixture model were proposed. Although the performance of these designs and methods has previously been evaluated in large‐scale clinical trials with sample sizes of more than 1000 per group, the actual sample sizes of infertility treatment trials are usually around 100 per group. The most appropriate design and analysis for these moderate‐scale clinical trials are currently unclear. In this study, we conducted simulation studies to determine the appropriate design and analysis method of moderate‐scale clinical trials for irreversible endpoints by evaluating the statistical power and bias in the treatment effect estimates. The Mantel–Haenszel method had similar power and bias to the logistic mixture model. The crossover designs had the highest power and the smallest bias. We recommend using a combination of the crossover design and the Mantel–Haenszel method for two‐period, two‐treatment clinical trials with irreversible endpoints. Copyright © 2015 John Wiley & Sons, Ltd.     

AIDE: Adaptive intrapatient dose escalation designs to accelerate Phase I clinical trials

Designing Phase I clinical trials is challenging when accrual is slow or sample size is limited. The corresponding key question is: how to efficiently and reliably identify the maximum tolerated dose (MTD) using a sample size as small as possible? We propose model-assisted and model-based designs with adaptive intrapatient dose escalation (AIDE) to address this challenge. AIDE is adaptive in that the decision of conducting intrapatient dose escalation depends on both the patient's individual safety data, as well as other enrolled patient's safety data. When both data indicate reasonable safety, a patient may perform intrapatient dose escalation, generating toxicity data at more than one dose. This strategy not only provides patients the opportunity to receive higher potentially more effective doses, but also enables efficient statistical learning of the dose-toxicity profile of the treatment, which dramatically reduces the required sample size. Simulation studies show that the proposed designs are safe, robust, and efficient to identify the MTD with a sample size that is substantially smaller than conventional interpatient dose escalation designs. Practical considerations are provided and R code for implementing AIDE is available upon request.     

Adaptative Designs for Multi-Arm Clinical Trials: The Play-the-Winner Rule Revisited

Adaptative designs for clinical trials that are based on a generalization of the “play-the-winner” rule are considered as an alternative to previously developed models. Theoretical and numerical results show that these designs perform better for the usual criteria. Bayesian methods are proposed for the statistical analysis of these designs.     

Adaptive graph‐based multiple testing procedures

Multiple testing procedures defined by directed, weighted graphs have recently been proposed as an intuitive visual tool for constructing multiple testing strategies that reflect the often complex contextual relations between hypotheses in clinical trials. Many well‐known sequentially rejective tests, such as (parallel) gatekeeping tests or hierarchical testing procedures are special cases of the graph based tests. We generalize these graph‐based multiple testing procedures to adaptive trial designs with an interim analysis. These designs permit mid‐trial design modifications based on unblinded interim data as well as external information, while providing strong family wise error rate control. To maintain the familywise error rate, it is not required to prespecify the adaption rule in detail. Because the adaptive test does not require knowledge of the multivariate distribution of test statistics, it is applicable in a wide range of scenarios including trials with multiple treatment comparisons, endpoints or subgroups, or combinations thereof. Examples of adaptations are dropping of treatment arms, selection of subpopulations, and sample size reassessment. If, in the interim analysis, it is decided to continue the trial as planned, the adaptive test reduces to the originally planned multiple testing procedure. Only if adaptations are actually implemented, an adjusted test needs to be applied. The procedure is illustrated with a case study and its operating characteristics are investigated by simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

Empirical likelihood for generalized linear models with fixed and adaptive designs

Empirical likelihood inference for generalized linear models with fixed and adaptive designs is considered. It is shown that the empirical log-likelihood ratio at the true parameters converges to the standard chi-square distribution. Furthermore, we obtain the maximum empirical likelihood estimate of the unknown parameter and the resulting estimator is shown to be asymptotically normal. Some simulations are conducted to illustrate the proposed method.     

Optimal and lead-in adaptive allocation for binary outcomes: A comparison of Bayesian methods

We compare posterior and predictive estimators and probabilities in response-adaptive randomization designs for two- and three-group clinical trials with binary outcomes. Adaptation based upon posterior estimates are discussed, as are two predictive probability algorithms: one using the traditional definition, the other using a skeptical distribution. Optimal and natural lead-in designs are covered. Simulation studies show that efficacy comparisons lead to more adaptation than center comparisons, though at some power loss, skeptically predictive efficacy comparisons and natural lead-in approaches lead to less adaptation but offer reduced allocation variability. Though nuanced, these results help clarify the power-adaptation trade-off in adaptive randomization.     

Threshold‐free estimation of functional antibody titers of a group B streptococcus opsonophagocytic killing assay

Opsonophagocytic killing assays (OPKA) are routinely used for the quantification of bactericidal antibodies in blood serum samples. Quantification of the OPKA readout, the titer, provides the basis for the statistical analysis of vaccine clinical trials having functional immune response endpoints. Traditional OPKA titers are defined as the maximum serum dilution yielding a predefined bacterial killing threshold value, and they are estimated by fitting a dose‐response model to the dilution‐killing curve. This paper illustrates a novel definition of titer, the threshold‐free titer, which preserves biological interpretability while not depending on any killing threshold or on a postulated shape of the dose‐response curve. These titers are shown to be more precise than the traditional threshold‐based titers when using simulated and experimental group B streptococcus OPKA experimental data. Also, titer linearity is shown to be not measurable when using threshold‐based titers, whereas it becomes measurable using threshold‐free titers. The biological interpretability and operational characteristics demonstrated here indicate that threshold‐free titers are an appropriate tool for the routine analysis of OPKA data. Copyright © 2015 John Wiley & Sons, Ltd.     

Balanced incomplete Latin square designs

Latin squares have been widely used to design an experiment where the blocking factors and treatment factors have the same number of levels. For some experiments, the size of blocks may be less than the number of treatments. Since not all the treatments can be compared within each block, a new class of designs called balanced incomplete Latin squares (BILS) is proposed. A general method for constructing BILS is proposed by an intelligent selection of certain cells from a complete Latin square via orthogonal Latin squares. The optimality of the proposed BILS designs is investigated. It is shown that the proposed transversal BILS designs are asymptotically optimal for all the row, column and treatment effects. The relative efficiencies of a delete-one-transversal BILS design with respect to the optimal designs for both cases are also derived; it is shown to be close to 100%, as the order becomes large.     

An efficient sequential design of clinical trials

We propose an efficient group sequential monitoring rule for clinical trials. At each interim analysis both efficacy and futility are evaluated through a specified loss structure together with the predicted power. The proposed design is robust to a wide range of priors, and achieves the specified power with a saving of sample size compared to existing adaptive designs. A method is also proposed to obtain a reduced-bias estimator of treatment difference for the proposed design. The new approaches hold great potential for efficiently selecting a more effective treatment in comparative trials. Operating characteristics are evaluated and compared with other group sequential designs in empirical studies. An example is provided to illustrate the application of the method.     

On the efficiency of adaptive designs for flexible interim decisions in clinical trials

It is shown that the optimal group sequential designs considered in Tsiatis and Mehta [2003. On the inefficiency of the adaptive design for monitoring clinical trials. Biometrika 90, 367–378] are special cases of the more general flexible designs which allow for a valid inference after adapting a predetermined way to spend the rejection and acceptance probabilities. An unforeseen safety issue in a clinical trial, for example, could make a change of the preplanned number of interim analyses and their sample sizes appropriate. We derive flexible designs which have equivalent rejection and acceptance regions if no adaptation is performed, but at the same time allow for an adaptation of the spending functions, and have a conditional optimality property.