Bayesian doubly adaptive randomization in clinical trials

Bayesian adaptive randomization has attracted increasingly attention in the literature and has been implemented in many phase II clinical trials. Doubly adaptive biased coin design (DBCD) is a superior choice in response-adaptive designs owing to its promising properties. In this paper, we propose a randomized design by combining Bayesian adaptive randomization with doubly adaptive biased coin design. By selecting a fixed tuning parameter, the proposed randomization procedure can target an explicit allocation proportion, and assign more patients to the better treatment simultaneously. Moreover, the proposed randomization is efficient to detect treatment differences. We illustrate the proposed design by its applications to both discrete and continuous responses, and evaluate its operating features through simulation studies.     

单次重复试验的三水平析因设计的分析

由于试验材料、费用和时间等条件的限制,仅有单次重复试验的三水平析因设计经常要应用在农业、工业和医学临床试验等领域。例如,在医学临床试验中,为找到影响治疗关节炎效果的重要因子和最佳治疗方案需要考虑2个三水平的因子:A(药物治疗)和B(运动治疗),由于只能找到9位病情相似的病人进行试验,故只能实施仅有单次重复试验的三水平析因设计3~2。不幸的是,交互作用A×B也可能存在,这样就没有剩余自由度用于估计误差的方差,从而通常的方差分析方法不再能用于数据分析。针对上述问题,本文提出了三个基于均方误差的检验统计量用于分析单次重复试验的三水平析因设计。通过实例表明用这些方法不仅能检验所考虑因子的主效应,而且还能同时检验交互效应。相应检验所用的一些常用临界值提供在附录中。并且,还通过大量的模拟研究对所提出的三个检验方法进行了比较。结果显示,T_~((3))检验在三个检验方法中具有最大的功效。     

Analysis of means approach in advanced designs

Analysis of means (ANOM), similar to Shewhart control chart that exhibits individual mean effects on a graphical display, is an attractive alternative mean testing procedure for the analysis of variance (ANOVA). The procedure is primarily used to analyze experimental data from designs with only fixed effects. Recently introduced, the ANOM procedure based on the q‐distribution (ANOMQ procedure) generalizes the ANOM approach to random effects models. This article reveals that the application of ANOM and ANOMQ procedures in advanced designs such as hierarchically nested and split‐plot designs with fixed, random, and mixed effects enhances the data visualization aspect in graphical testing. Data from two real‐world experiments are used to illustrate the proposed procedure; furthermore, these experiments exhibit the ANOM procedures' visualization ability compared with ANOVA from the point of view of the practitioner.     

多档次试验结果下的一种罐子模型

针对多档次试验结果的情况, 本文构造了一种罐子模型, 并在此模型中建立了极限理论. 理论和例子表明, 这种临床试验设计, 既符合人道精神, 又保持较好的统计效率\bd 因此该文有应用参考价值.     

Generalized optimal designs and contingency plans in linear systems

To select an optimal linear design means to select the best subset from a set of possible products or opportunities for commitment and to construct the corresponding optimal contingency plans for coping with the changes of decision parameters. Based on Lee, Shi and Yu, this paper discusses a method for generating generalized good designs from known potentially good designs. We describe how to use the multi-criteria and multi-constraint-level (MC²) simplex method to identify the generalized optimal designs and their related optimal contingency plans. A procedure for effectively and systematically solving the problem of selecting linear designs is proposed.     

Construction of efficient experimental designs under multiple resource constraints

The aim of this paper is twofold. First, we introduce ‘resource constraints’ as a general concept that covers many practical restrictions on experimental design. Second, to compute optimal or near‐optimal exact designs of experiments under multiple resource constraints, we propose a tabu search heuristic related to the Detmax procedure. To illustrate the scope and performance of the proposed method, we chose the criterion of D‐optimality and computed efficient designs for (i) a block model with limits on the numbers of blocks and on the replications of treatments, (ii) a quadratic regression model with simultaneous marginal and cost constraints, and (iii) a non‐linear regression model with simultaneous direct and cost constraints. As we show, the proposed method generates similar or better results compared with algorithms specialized for computing optimal designs under less general constraints. Copyright © 2015 John Wiley & Sons, Ltd.     

Asymptotic results on a class of adaptive multi-treatment designs

The play-the-winner (PW) rule is an important method in clinical trials where patients can be assigned to one of the two treatments. In the PW rule, the probability of the next patient to be assigned to a particular treatment only depends on the response of the current patient. In this paper, we consider a general kind of PW rule for multi-treatment adaptive designs, in which the probability that a treatment is assigned to the next patient depends upon both the response of the previous patient and an estimated parameter, e.g., the observed success rate. Using this kind of adaptive designs, more information of previous stages are used to update the model at each stage, and more patients may be assigned to better treatments. The strong consistency and the asymptotic normality are established for the allocation proportions.     

Conditional distance correlation screening for sparse ultrahigh-dimensional models

This paper is concerned with feature screening for ultrahigh-dimensional covariates under general varying-coefficient models. With the sparsity principle and based on the conditional distance correlation, we develop a new marginal feature screening procedure called CDC-SIS to select significant covariates and show that it possesses the sure screening property and ranking consistency property under some regularity conditions. The proposed procedure enjoys two appealing merits. First, the model we considered is more flexible than traditional varying-coefficients regression models, so the method can be used in a wider range of applications. Second, CDC-SIS can be used directly to deal with grouped predictor variables and multivariate responses. We assess the finite sample properties of the proposed procedure by Monte Carlo studies, and illustrate our method by an empirical analysis of a real data set. Compared with other similar works, our procedure yields better performance.     

Monitoring Phase II Comparative Clinical Trials with Two Endpoints and Penalty for Adverse Events

Adverse events in Phase II comparative clinical trials have received limited attention in the literature. Bersimis et al. (Stat Med 34:197–214, 2014) in proposed a class of comparative sequential designs with bivariate endpoints, where as a special case, the termination of the clinical trial due to the occurrence of a severe adverse event is treated. In this paper, using the Markov chain embedding technique, we extend this class of designs proposing two new designs, which treat cases where the development of an adverse event does not immediately stop the clinical trial, but penalizes appropriately the treatment that caused it. In both designs the penalty can be chosen either by assessing the severity of the adverse event or by optimizing the power. The numerical results show an excellent performance, achieving small expected sample sizes in conjunction with large values for power, satisfying in this way the ethical requirement for small sample sizes and fast decisions in clinical practice. The formulation of the procedure as a stochastic process is elegantly accomplished while it offers the necessary mathematical framework for further generalizing the designs covering more cases such as group sequential designs, etc.     

An effective algorithm for generation of factorial designs with generalized minimum aberration

Fractional factorial designs are popular and widely used for industrial experiments. Generalized minimum aberration is an important criterion recently proposed for both regular and non-regular designs. This paper provides a formal optimization treatment on optimal designs with generalized minimum aberration. New lower bounds and optimality results are developed for resolution-III designs. Based on these results, an effective computer search algorithm is provided for sub-design selection, and new optimal designs are reported.     

临床试验中的几种最优自适应设计

在临床试验中,当病人序贯地来到时,我们总想自适应地为病人在两种可供选择的治疗方案中选择较优的一种治疗方案,由于受实验者是病人,所以这就显得特别重要.本文中,基于统计有效性,我们讨论临床试验中几种依赖于未知参数的最优配置规则,并提出相应的自适应设计模型,同时获得一些渐近性质.而这些渐近性质又表明文中提出的自适应设计模型能达到临床试验中的渐近最优配置规则.     

Optimal adaptive generalized Pólya urn design for multi-arm clinical trials

A class of optimal adaptive multi-arm clinical trial designs is proposed based on an extended generalized Pólya urn (GPU) model. The design is applicable to both the qualitative and quantitative responses and achieves, asymptotically, some pre-specified optimality criterion. Such criterion is specified by a functional of the response distributions and is implemented through the relationship between the design matrix and its first eigenvector. The asymptotic properties of the design are studied using the existing methods on GPU. Some examples for commonly used clinical designs are given as illustration.     

Comparing exponential location parameters with several controls under heteroscedasticity

Suppose that random samples are taken from \(k\) treatment groups and \(l\) control groups, where the observations in each group have a two-parameter exponential distribution. We consider the problem of constructing simultaneous confidence intervals for the differences between location parameters of the treatment groups and the control groups when the scale parameters may be unequal. Using the parametric bootstrap approach, we develop a new multiple comparisons procedure when the scale parameters and sample sizes are possibly unequal. We then present a simulation study in which we compare the performance of our proposed procedure with two other procedures. The results of our simulations indicate that our proposed procedure performs better than other procedures. The usefulness of our proposed procedure is illustrated with an example.     

Bayesian analysis of definitive screening designs when the response is nonnormal

Definitive screening designs (DSDs) are a class of experimental designs that allow the estimation of linear, quadratic, and interaction effects with little experimental effort if there is effect sparsity. The number of experimental runs is twice the number of factors of interest plus one. Many industrial experiments involve nonnormal responses. Generalized linear models (GLMs) are a useful alternative for analyzing these kind of data. The analysis of GLMs is based on asymptotic theory, something very debatable, for example, in the case of the DSD with only 13 experimental runs. So far, analysis of DSDs considers a normal response. In this work, we show a five‐step strategy that makes use of tools coming from the Bayesian approach to analyze this kind of experiment when the response is nonnormal. We consider the case of binomial, gamma, and Poisson responses without having to resort to asymptotic approximations. We use posterior odds that effects are active and posterior probability intervals for the effects and use them to evaluate the significance of the effects. We also combine the results of the Bayesian procedure with the lasso estimation procedure to enhance the scope of the method. Copyright © 2016 John Wiley & Sons, Ltd.     

Copula‐based robust optimal block designs

Blocking is often used to reduce known variability in designed experiments by collecting together homogeneous experimental units. A common modeling assumption for such experiments is that responses from units within a block are dependent. Accounting for such dependencies in both the design of the experiment and the modeling of the resulting data when the response is not normally distributed can be challenging, particularly in terms of the computation required to find an optimal design. The application of copulas and marginal modeling provides a computationally efficient approach for estimating population‐average treatment effects. Motivated by an experiment from materials testing, we develop and demonstrate designs with blocks of size two using copula models. Such designs are also important in applications ranging from microarray experiments to experiments on human eyes or limbs with naturally occurring blocks of size two. We present a methodology for design selection, make comparisons to existing approaches in the literature, and assess the robustness of the designs to modeling assumptions.     

Selective finite element refinement in torsional problems based on the membrane analogy

This work presents a selective finite element refinement strategy based on the h-refinement type, in the context of a posteriori error estimates considerations (error computed after the application of the proposed refining scheme), based on a graphical procedure to determine progressively better estimates for the maximum shearing stress in prismatic torsional members. It is structured in an integrated FORTRAN code and DELPHI based environment to refine an initial arbitrary finite element mesh. The proposed procedure is founded on the membrane analogy that exists between membrane deflections and the torsion problem in the sense that the location of the membrane largest gradient drives the refining procedure. It is shown that multiple level application of the proposed method to two members with different cross sectional geometries with known analytic solutions leads to progressively more accurate estimates (< 1.0% error in most cases) for the maximum shearing stresses calculations. Finally, the proposed method is applied to the torsional analysis of an L section member, showing that for this practical case the procedure results in a very accurate calculation as well.     

An efficient method for constructing uniform designs with large size

Many construction methods for (nearly) uniform designs have been proposed under the centered $L_2$ -discrepancy, and most of them are only suitable for constructing designs with small size. This paper proposes a new method, called mixture method (MM), to construct nearly symmetrical/asymmetrical uniform designs with large number of runs and/or large number of factors. The new method has the “better than given” property, i.e., the resulting design is better than existing designs in the sense of the pre-decided criterion. Moreover, the computational speed of MM is faster than most existing methods.     

A genetic algorithm for designing microarray experiments

Heuristic techniques of optimization can be useful in designing complex experiments, such as microarray experiments. They have advantages over the traditional methods of optimization, particularly in situations where the search space is discrete. In this paper, a search procedure based on a genetic algorithm is proposed to find optimal (efficient) designs for both one- and multi-factor experiments. A genetic algorithm is a heuristic optimization method that exploits the biological evolution to obtain a solution of the problem. As an example, optimal designs for \(3\times 2\) factorial microarray experiments are presented for different numbers of arrays and for various sets of research questions. Comparisons between different operators of the genetic algorithm are performed by simulation studies.     

A note on the separation of subtour elimination constraints in elementary shortest path problems

This note proposes an alternative procedure for identifying violated subtour elimination constraints (SECs) in branch-and-cut algorithms for elementary shortest path problems. The procedure is also applicable to other routing problems, such as variants of travelling salesman or shortest Hamiltonian path problems, on directed graphs. The proposed procedure is based on computing the strong components of the support graph. The procedure possesses a better worst-case time complexity than the standard way of separating SECs, which uses maximum flow algorithms, and is easier to implement.     

不平衡两因素套设计模型中方差分量比的区间估计

给出了次样本容量相等时,不平衡两因素套设计模型中方差分量之比的广义区间估计.为了研究所得区间估计的优良性,并与Burdick,Birch and Graybill给出的修正大样本(MLS)方法进行对比,进行了模拟研究和分析.结果表明所得方法优于MLS方法,特别是在极端不平衡情形.