Improved bounds for group testing designs

Group testing designs (GTDs), both adaptive and nonadaptive, are useful in reducing the number of tests needed to identify the defective items from a given set of at least six items. In this paper, we obtain improved bounds on the number of group tests necessary for both adaptive and nonadaptive GTDs. It is established that any nonadaptive GTD needs at least $2n$ group tests for identifying all the defective items from a group of $2^n$ items having at most 2 defective items. In the same context, an adaptive multistage GTD with a maximum of $2n$ group tests is presented here. It is further shown that under restrictions on group size, optimal nonadaptive GTDs can be constructed using Generalized Petersen Graphs. Also presented is the construction of a family of two-stage adaptive GTDs that are useful under certain conditions.     

Optimal Bayesian two-phase designs

In this paper we present a Bayesian decision theoretic approach to the two-phase design problem. The solution of such sequential decision problems is usually difficult to obtain because of their reliance on preposterior analysis. In overcoming this problem, we adopt the Mont-Carlo-based approach of Müller and Parmigiani (1995) and develop optimal Bayesian designs for two-phase screening tests. A rather attractive feature of the Monte-Carlo approach is that it facilitates the preposterior analysis by replacing it with a sequence of scatter plot smoothing/regression techniques and optimization of the corresponding fitted surfaces. The method is illustrated for depression in adolescents using data from past studies.     

Bayesian D-optimal supersaturated designs

We introduce a new class of supersaturated designs using Bayesian D-optimality. The designs generated using this approach can have arbitrary sample sizes, can have any number of blocks of any size, and can incorporate categorical factors with more than two levels. In side by side diagnostic comparisons based on the E(s²)$E(s^2)$ criterion for two-level experiments having even sample size, our designs either match or out-perform the best designs published to date. The generality of the method is illustrated with quality improvement experiment with 15 runs and 20 factors in 3 blocks.     

Bayesian networks for imputation

Summary.  Bayesian networks are particularly useful for dealing with high dimensional statistical problems. They allow a reduction in the complexity of the phenomenon under study by representing joint relationships between a set of variables through conditional relationships between subsets of these variables. Following Thibaudeau and Winkler we use Bayesian networks for imputing missing values. This method is introduced to deal with the problem of the consistency of imputed values: preservation of statistical relationships between variables ( statistical consistency ) and preservation of logical constraints in data ( logical consistency ). We perform some experiments on a subset of anonymous individual records from the 1991 UK population census.     

Bayesian D-optimal designs for exponential regression models

We consider the Bayesian D-optimal design problem for exponential growth models with one, two or three parameters. For the one-parameter model conditions on the shape of the density of the prior distribution and on the range of its support are given guaranteeing that a one-point design is also Bayesian D-optimal within the class of all designs. In the case of two parameters the best two-point designs are determined and for special prior distributions it is proved that these designs are Bayesian D-optimal. Finally, the exponential growth model with three parameters is investigated. The best three-point designs are characterized by a nonlinear equation. The global optimality of these designs cannot be proved analytically and it is demonstrated that these designs are also Bayesian D-optimal within the class of all designs if gamma-distributions are used as prior distributions.     

Some bounds on balanced block designs

Bounds on the latest root of the C-matrix and the number of blocks for a variance-balanced block design are given. These results contain the well-known results as special cases.     

Efficient designs for constrained mixture experiments

Many practical experiments on mixtures (where the components sum to one) include additional lower or upper bounds on components, or on linear combinations of them. Usually theory cannot be used to obtain a good design, and algorithmic methods are necessary. Some of the available methods are discussed. Their performance is evaluated on some examples, and the form of the optimal design is investigated.     

Efficient designs for animal carcinogenicity experiments

In a typical carcinogenicity study, animals, usually rats or mice. are divided into a control and two to three dose groups of 50 or more by randomization. A chemical is administered at a constant daily dose rate for a major portion of the lifetime of the test animals, for example, two years. In general, such an experiment is expensive and time consuming In this paper, we propose an efficient design with reduced sample size and/or shortened study duration. An equal number of animals per dose group is considered in this study. A power study of the age-adjusted trend test, for the turnor incidence rate for single-sacrifice experiments proposed by Kodell et al. (Drug Information Journal, 1997) is conducted. A Monte Carlo simulation study is performed to compare the performance of the trend test for the standard design and various reduced designs. Based on the Kodell et al. test, the 21-month study duration with sample size 50 per group is recommended as the best, reduced design over the traditional 2-year study design with the same sample size.     

Bayesian prediction bounds for the pareto lifetime model

Suppose that the length of time in years for which a business operates until failure has a Pareto distribution. Let x₁ ≤ x₂ x₃ ≤…≤z_k denote the survival lifetimes of the first k of a random sample of n businesses. Bayesian predictions are to be made on the ordered failure times of t h e remaining (n-k) businesses, using the conditional probability density function. Examples are given to illustrate our results.     

Bayesian hierarchical models for adaptive basket trial designs

Basket trials evaluate a single drug targeting a single genetic variant in multiple cancer cohorts. Empirical findings suggest that treatment efficacy across baskets may be heterogeneous. Most modern basket trial designs use Bayesian methods. These methods require the prior specification of at least one parameter that permits information sharing across baskets. In this study, we provide recommendations for selecting a prior for scale parameters for adaptive basket trials by using Bayesian hierarchical modeling. Heterogeneity among baskets attracts much attention in basket trial research, and substantial heterogeneity challenges the basic assumption of exchangeability of Bayesian hierarchical approach. Thus, we also allowed each stratum-specific parameter to be exchangeable or nonexchangeable with similar strata by using data observed in an interim analysis. Through a simulation study, we evaluated the overall performance of our design based on statistical power and type I error rates. Our research contributes to the understanding of the properties of Bayesian basket trial designs.     

Adaptive Bayesian compound designs for dose finding studies

We consider the problem of how to efficiently and safely design dose finding studies. Both current and novel utility functions are explored using Bayesian adaptive design methodology for the estimation of a maximum tolerated dose (MTD). In particular, we explore widely adopted approaches such as the continual reassessment method and minimizing the variance of the estimate of an MTD. New utility functions are constructed in the Bayesian framework and are evaluated against current approaches. To reduce computing time, importance sampling is implemented to re-weight posterior samples thus avoiding the need to draw samples using Markov chain Monte Carlo techniques. Further, as such studies are generally first-in-man, the safety of patients is paramount. We therefore explore methods for the incorporation of safety considerations into utility functions to ensure that only safe and well-predicted doses are administered. The amalgamation of Bayesian methodology, adaptive design and compound utility functions is termed adaptive Bayesian compound design (ABCD). The performance of this amalgamation of methodology is investigated via the simulation of dose finding studies. The paper concludes with a discussion of results and extensions that could be included into our approach.     

Efficient initial designs for binary response data

In this paper we introduce a binary search algorithm that efficiently finds initial maximum likelihood estimates for sequential experiments where a binary response is modeled by a continuous factor. The problem is motivated by switching measurements on superconducting Josephson junctions. In this quantum mechanical experiment, the current is the factor controlled by the experimenter and a binary response indicating the presence or the absence of a voltage response is measured. The prior knowledge on the model parameters is typically poor, which may cause the common approaches of initial estimation to fail. The binary search algorithm is designed to work reliably even when the prior information is very poor. The properties of the algorithm are studied in simulations and an advantage over the initial estimation with equally spaced factor levels is demonstrated. We also study the cost-efficiency of the binary search algorithm and find the approximately optimal number of measurements per stage when there is a cost related to the number of stages in the experiment.     

Efficient experimental designs for sigmoidal growth models

For the Weibull- and Richards-regression model robust designs are determined by maximizing a minimum of D  - or _D1$D_1$-efficiencies, taken over a certain range of the non-linear parameters. It is demonstrated that the derived designs yield a satisfactory solution of the optimal design problem for this type of model in the sense that these designs are efficient and robust with respect to misspecification of the unknown parameters. Moreover, the designs can also be used for testing the postulated form of the regression model against a simplified sub-model.     

On bounds for the efficiency of block designs for comparing test treatments with a control

In this paper we study the class of augmented balanced incomplete block designs, which are used for comparing a control treatment with a set of test treatments. Under the A- criterion we establish a condition that enables us to determine the most efficient augmented design and we suggest some methods to compute a lower bound for the efficiency of these designs. For 3≤k≤10, v≥k, we list the parameters of the most efficient designs with a lower bound for their efficiency or, if known, mention their optimality.     

Bayesian optimal phase II designs with dual-criterion decision making

The conventional phase II trial design paradigm is to make the go/no-go decision based on the hypothesis testing framework. Statistical significance itself alone, however, may not be sufficient to establish that the drug is clinically effective enough to warrant confirmatory phase III trials. We propose the Bayesian optimal phase II trial design with dual-criterion decision making (BOP2-DC), which incorporates both statistical significance and clinical relevance into decision making. Based on the posterior probability that the treatment effect reaches the lower reference value (statistical significance) and the clinically meaningful value (clinical significance), BOP2-DC allows for go/consider/no-go decisions, rather than a binary go/no-go decision. BOP2-DC is highly flexible and accommodates various types of endpoints, including binary, continuous, time-to-event, multiple, and coprimary endpoints, in single-arm and randomized trials. The decision rule of BOP2-DC is optimized to maximize the probability of a go decision when the treatment is effective or minimize the expected sample size when the treatment is futile. Simulation studies show that the BOP2-DC design yields desirable operating characteristics. The software to implement BOP2-DC is freely available at www.trialdesign.org .     

Bayesian single-arm phase II trial designs with time-to-event endpoints

For the cancer clinical trials with immunotherapy and molecularly targeted therapy, time-to-event endpoint is often a desired endpoint. In this paper, we present an event-driven approach for Bayesian one-stage and two-stage single-arm phase II trial designs. Two versions of Bayesian one-stage designs were proposed with executable algorithms and meanwhile, we also develop theoretical relationships between the frequentist and Bayesian designs. These findings help investigators who want to design a trial using Bayesian approach have an explicit understanding of how the frequentist properties can be achieved. Moreover, the proposed Bayesian designs using the exact posterior distributions accommodate the single-arm phase II trials with small sample sizes. We also proposed an optimal two-stage approach, which can be regarded as an extension of Simon's two-stage design with the time-to-event endpoint. Comprehensive simulations were conducted to explore the frequentist properties of the proposed Bayesian designs and an R package BayesDesign can be assessed via R CRAN for convenient use of the proposed methods.     

A Bayesian criterion for selecting super saturated screening designs

Super-saturated designs in which the number of factors under investigation exceeds the number of experimental runs have been suggested for screening experiments initiated to identify important factors for future study. Most of the designs suggested in the literature are based on natural but ad hoc criteria. The “average s²” criteria introduced by Booth and Cox (Technometrics 4 (1962) 489) is a popular choice. Here, a decision theoretic approach is pursued leading to an optimality criterion based on misclassification probabilities in a Bayesian model. In certain cases, designs optimal under the average s² criterion are also optimal for the new criterion. Necessary conditions for this to occur are presented. In addition, the new criterion often provides a strict preference between designs tied under the average s² criterion, which is advantageous in numerical search as it reduces the number of local minima.