Adaptive Designs to Maximize Power in Clinical Trials with Multiple Treatments

Abstract

We consider a clinical trial with three competing treatments and study designs that allocate subjects sequentially in order to maximize the power of relevant tests. Two different criteria are considered: the first is to find the best treatment and the second is to order all three. The power converges to one in an exponential rate and we find the optimal allocation that maximizes this rate by large deviation theory. For the first criterion the optimal allocation has the plausible property that it assigns a small fraction of subjects to the inferior treatment. The optimal allocation depends heavily on the unknown parameters and, therefore, in order to implement it, a sequential adaptive scheme is considered. At each stage of the trial the parameters are estimated and the next subject is allocated according to the estimated optimal allocation. We study the asymptotic properties of this design by large deviations theory and the small sample behavior by simulations. Our results demonstrate that, unlike the two-treatments case, adaptive design can provide significant improvement in power.     

Computation of optimal group sequential designs

We propose a method of simulation to compute optimal group sequential tests that minimize the average sample size and meet significance level and power requirements. Optimal designs can be used in clinical trials directly, and provide a standard for assessing the e?ciency of other designs as well. The proposed method is conceptually simple and straightforward.     

Non-pinched, minimum energy distillation designs

Non-pinched, minimum energy solutions are important class of distillation designs that offer the potential advantage of a better trade-off between capital investment and operating costs. In this paper, two important tasks associated with non-pinched distillation designs are studied. Thus the novel contributions of this work to the literature are

(1) A comprehensive methodology for finding non-pinched minimum energy designs.

(2) Understanding of the reasons for the existence of non-pinched distillation designs.

It is shown that the recent shortest stripping line distance approach of Lucia et al. [Lucia, A., Amale, A. and Taylor, R., 2007, Distillation pinch points and more. Comput Chem Eng, available on-line] is capable of systematically and reliably finding non-pinched, minimum energy distillation designs. In addition, we provide an understanding of the reasons behind the existence of non-pinched designs, which include trajectories that follow unstable branches of a pinch point curve in azeotropic systems, the inherent looping structure of trajectories in hydrocarbon separations, and the presence of ancillary constraints in multi-unit processes like extraction/distillation. Several distillation examples are studied and many numerical results and geometric illustrations are presented that show the shortest stripping line distance methodology is indeed a powerful and systematic tool for computing non-pinched, minimum energy designs and that support the underlying reason we provide for the existence of non-pinched designs.     

Group sequential crossover trial designs with strong control of the familywise error rate

Crossover designs are an extremely useful tool to investigators, and group sequential methods have proven highly proficient at improving the efficiency of parallel group trials. Yet, group sequential methods and crossover designs have rarely been paired together. One possible explanation for this could be the absence of a formal proof of how to strongly control the familywise error rate in the case when multiple comparisons will be made. Here, we provide this proof, valid for any number of initial experimental treatments and any number of stages, when results are analyzed using a linear mixed model. We then establish formulae for the expected sample size and expected number of observations of such a trial, given any choice of stopping boundaries. Finally, utilizing the four-treatment, four-period TOMADO trial as an example, we demonstrate that group sequential methods in this setting could have reduced the trials expected number of observations under the global null hypothesis by over 33%.     

旋塞阀失效后的修复

本文介绍了建峰化肥厂尿素装置中旋塞阀的应用情况、结构形式、失效及失效后的修复方法、修复步骤与修复要点。这种修复技术具有经济实用、省时方便的优点。     

Thermal behavior of gradient charring materials with improved iterative method

The lightweight material of the thermal protection system for a reentry vehicle has become a trend in order to maximize the payload. To explore the effect of gradient density on the thermal behavior of charring materials, a pyrolysis layer model considering of variable density is developed and discretized with the central difference method. An iterative method is improved to look for the locations of the moving interfaces and boundary in each time step. Taken different gradient phenolic impregnated carbon ablator under a return trajectory heat flux for the Orion vehicle as example, their thermal behavior and effective heat capacities are simulated using the code written. Numerical results indicate that the gradient designs can improve the thermal protection performance of charring materials effectively. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47076.     

On the distribution of a concomitant statistic in a sequential trial

In this paper the distribution of a concomitant statistic in a Gaussian sequential setting is characterized. It is shown that the distribution of such a statistic, conditional on the value of the stopping time, can be represented as a convolution of a normal random variable with a stochastic integral of the monitoring process of the trial. For continuous sequential designs the characteristic function of this stochastic integral is shown to satisfy an integral equation. The tools developed here are relevant for secondary inference problems in sequential clinical trials.     

A COMPILATION OF THE D-OPTIMAL DESIGNS IN CHEMICAL KINETICS

This paper links the chemical kinetic models that obey the framework of nonlinear statistical models with optimal design theory. We provide the appropriate optimal designs for them, so that the involved parameters can be estimated as well as possible. Therefore, the D-optimality criterion is adopted, under the optimal design approach, for a number of models used in chemical kinetic applications. In the tables, the collected results are presented for 15 models.     

GROUP SEQUENTIAL TESTS WITH OUTCOME-DEPENDENT TREATMENT ASSIGNMENT

We consider group sequential comparisons of two treatments in which subjects' treatment assignments may be based on previously observed responses. We present theory for the joint distribution of the sequence of test statistics in such a study and show that this has a standard form when treatment assignment is based only on the current estimate of the treatment difference. This theory supports the inclusion of adaptive sampling rules in standard group designs, maintaining the usual Type I and II error probabilities; results extend to the case where a linear model is fitted at each analysis to adjust for covariates. Simulation results show the expected number of subjects receiving the inferior treatment can be reduced by up to 10 or 15% with increases in total sample size of around 1 to 3%. More aggressive strategies can reduce the number on the inferior treatment by up to 30 or 40%, on average, but at the price of substantial increases in total sample size.     

On a Type of Probability Stopping Rule for Toxicity Study

Abstract

In early phase cancer clinical trials where toxicity events follow independent and identical Bernoulli distributions indexed by patients, the Bayesian stopping rule has been used for continuous monitoring of toxicity along with an affordable maximum sample size (N). This article studies some properties of an heuristic procedure where the trial will stop at the first time that the posterior probability that the toxicity rate (p) is greater than a threshold (η) is greater than certain probability threshold (τ). Specifically, we study the pattern formed by stopping times and regions, recursive stopping probability computation, and toxicity rate estimation. Some relevant theoretical results are given. The presented results are potentially useful for guiding toxicity clinical trial designs.     

A class of adaptive designs

For sequential entrance of patients in a clinical trial several adaptive designs are given by different authors from intuitive considerations. The object of such designs is to allocate the entering patients among two or more competing treatments. Here we provide a unified approach to derive a broad class of such designs through a recursion relation of the allocation probabilities of the successive entering patients. A special class of adaptive designs including the standard randomized play the winner rule is obtained from the relation. Here both the instantaneous and delayed response cases are covered     

Sequential estimation in the group testing problem

Estimation using pooled sampling has long been an area of interest in the group testing literature. Such research has focused primarily on the assumed use of fixed sampling plans (i), although some recent papers have suggested alternative sequential designs that sample until a predetermined number of positive tests (ii). One major consideration, including in the new work on sequential plans, is the construction of debiased estimators that either reduce or keep the mean square error from inflating. However, whether under the above or other sampling designs unbiased estimation is in fact possible has yet to be established in the literature. In this article, we introduce a design that samples until a fixed number of negatives (iii), and show that an unbiased estimator exists under this model, whereas unbiased estimation is not possible for either of the preceding designs (i) and (ii). We present new estimators under the different sampling plans that are either unbiased or that have reduced bias relative to those already in use as well as generally improve on the mean square error. Numerical studies are done in order to compare designs in terms of bias and mean square error under practical situations with small and medium sample sizes.     

Sequential estimation with data-dependent allocation and time trends

This note concerns the estimation of treatment difference following a sequential test in which two treatments are to be compared and treatment allocation is data-dependent. Woodroofe(1989) considered this problem when the responses are independent and identically distributed. In this paper, it is shown that woodroof'es asymptotic results also work well for the modified sequential test of coad (1991), which allows for possible linear time trends in the data.     

Optimal Decision Rules for Biomarker-Based Subgroup Selection for a Targeted Therapy in Oncology

Throughout recent years, there has been a rapidly increasing interest regarding the evaluation of so-called targeted therapies. These therapies are assumed to show a greater benefit in a pre-specified subgroup of patients—commonly identified by a predictive biomarker—as compared to the total patient population of interest. This situation has led to the necessity to develop biostatistical methods allowing an efficient evaluation of such treatments. Among others, adaptive enrichment designs have been proposed as a solution. These designs allow the selection of the most promising patient population based on an efficacy analysis at interim and restricting recruitment to these patients afterwards. As has recently been shown, the performance of the applied interim decision rule in such a design plays a crucial role in ensuring a successful trial. In this work, we investigate the situation when the primary outcome of the trial is a binary variable. Optimal decision rules are derived which incorporate the uncertainty about the treatment effects. These optimal decision rules are evaluated with respect to their performance in an adaptive enrichment design in terms of correct selection probability and power, and are compared to proposed ad hoc decision rules. Our methods are illustrated by means of a clinical trial example.     

世界名牌化妆品的设计与策划(待续)

详细地论述了世界名牌化妆品的设计与策划。比较全面地提出了世界名牌化妆品的各种动态和信息，为研究和创造中国的世界名牌化妆品，振兴和发展中国化妆品工业提供了有益的参考。     

Determination of the relative importance of process factors on particle size distribution in suspension polymerization using a Bayesian experimental design technique

The use of a Bayesian experimental design technique to determine the relative importance of factors that control particle size distribution (PSD) in suspension copolymerization of styrene and divinylbenzene is reported. Six factors and two responses are considered in this study. The experimental trials are of the two‐level factorial type designed with a Bayesian method. The experiments were carried out in a 5‐L pilot plant reactor. The matrix of variances of the parameter means (the prior knowledge) was estimated with the use of a preliminary compartment‐mixing (CM) model for PSD in suspension polymerization and our subjective judgement (process understanding). The responses, mean particle size and coefficient of variation, were calculated from distributions obtained with a Coulter particle counter. The results of this study provided the criteria needed to guide the future improvement of our CM‐PSD model in a balanced and effective way. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102:5577–5586, 2006     

以水平评估为契机,加强毕业设计(论文)管理

高校本科教学工作水平评估指标对毕业设计(论文)环节提出了明确的要求.本文结合水平评估的要求,细化评估观测点并形成了支撑材料体系,分析毕业设计(论文)的影响因素并提出了对策.     

Bias reduction via resampling for estimation following sequential tests

It is well known that maximum likelihood (ML) estimation results in biased estimates when estimating parameters following a sequential test. Existing bias correction methods rely on explicit calculations of the bias that are often difficult to derive. We suggest a simple alternative to the existing methods. The new approach relies on approximating the bias of the estimate using a bootstrap method. It requires bootstrapping the sequential testing process by resampling observations from a distribution based on the ML estimate. Each bootstrap process will give a new ML estimate, and the corresponding bootstrap mean can be used to calibrate the estimate. An advantage of the new method over the existing methods is that the same procedure can be used under different stopping rules and different study designs. Simulation results suggest that this method performs competitively with existing methods.     

Sequential procedures for comparing several medical treatments

The use of sequential methods in clinical trials allows inferior treatments to be eliminated early. From an ethical point of view, the advantages are substantial. However, early stopping induces estimation bias and a deterioration in precision because of reduced sample sizes. This paper considers the problem of determining which of k ≥ 2 treatments with Bernoulli responses has the highest probability of success. Two sequential procedures are investigated and compared with a fixed—sample procedure. Various properties are derived and illustrated for the cases k =2,3 and 5. It is shown that the sequential procedures can achieve a pattern of error probabilities equivalent to the fixed—sample procedure for a much lower level of expected successes lost. Approximations for the bias and standard deviation of estimators of treatment differences are obtained by using results about the distribution of stopping times for a normal process.     

Covariate-adjusted response-adaptive designs for longitudinal treatment responses: PEMF trial revisited

Response-adaptive designs have become popular for allocation of the entering patients among two or more competing treatments in a phase III clinical trial. Although there are a lot of designs for binary treatment responses, the number of designs involving covariates is very small. Sometimes the patients give repeated responses. The only available response-adaptive allocation design for repeated binary responses is the urn design by Biswas and Dewanji [Biswas A and Dewanji AA. Randomized longitudinal play-the-winner design for repeated binary data. ANZJS 2004; 46: 675-684; Biswas A and Dewanji A. Inference for a RPW-type clinical trial with repeated monitoring for the treatment of rheumatoid arthritis. Biometr J 2004; 46: 769-779.], although it does not take care of the covariates of the patients in the allocation design. In this article, a covariate-adjusted response-adaptive randomisation procedure is developed using the log-odds ratio within the Bayesian framework for longitudinal binary responses. The small sample performance of the proposed allocation procedure is assessed through a simulation study. The proposed procedure is illustrated using some real data set.