Pooling designs for outcomes under a Gaussian random effects model

Due to the rising cost of laboratory assays, it has become increasingly common in epidemiological studies to pool biospecimens. This is particularly true in longitudinal studies, where the cost of performing multiple assays over time can be prohibitive. In this article, we consider the problem of estimating the parameters of a Gaussian random effects model when the repeated outcome is subject to pooling. We consider different pooling designs for the efficient maximum likelihood estimation of variance components, with particular attention to estimating the intraclass correlation coefficient. We evaluate the efficiencies of different pooling design strategies using analytic and simulation study results. We examine the robustness of the designs to skewed distributions and consider unbalanced designs. The design methodology is illustrated with a longitudinal study of premenopausal women focusing on assessing the reproducibility of F2-isoprostane, a biomarker of oxidative stress, over the menstrual cycle.     

Analysis of a model for random competition

A random competition model is reformulated as an urn model and its behavior is analysed.     

A model-independent approach to the theory of experimental designs and a special discussion of bib. i general definition and designs with one or two block factors

Experimental designs are definded by introducing an assignment matrix Z. It is shown by block designs and double block designs that using Z or an operator on Z otherwise defined, well known designs can be got as special cases. Till now we didn' find an experimental design which could not be defined by our matrix Z. The definitions of properties of experimental designs can be given independently of the model of the statistical analysis. This is shown for the property of balance of block designs.     

应用试验设计提高蝮蛇抗栓酶产量的研究

试验设计是研究使试验过程科学化、合理化的一门学科。本文介绍了应用试验设计方法寻找生产蝮蛇抗栓酶的最佳工艺,从而有效地提高了产品产量,并取得明显经济效益     

First capture success in two dimensions: The search for prey by a random walk predator in a comprehensive space of random walks

Random walk models are an important tool used for understanding how complex organisms redistribute themselves through space and time in search of targets such as food, shelter, or mates. These walks are easily studied with agent-based models, which can be used to ask which search strategy is best according to some efficiency metric. Current studies however, generally do not consider the full range of potential random walks, success metrics, and constraints on the walker, and implementation details vary widely. It is therefore difficult to compare results across studies. In this paper, we investigate predator search behaviour in a comprehensive space of key movement variables that allows the predator to select from a continuum of random walks ranging from Brownian walks (BWs) to correlated random walks (CorRWs) which include directional persistence, to composite random walks (ComRWs) which feature intensive and extensive search modes (ISMs and ESMs), and finally to more complex correlated composite random walks (CCRWs). We specifically focus on the search behaviour of a predator between the initiation of a search for a prey item and the first successful acquisition of a prey target: we call this interval the “search-to-capture” event. We measure the predator's success against three metrics of energetic cost: (1) the time elapsed, (2) the distance travelled, and (3) an equally weighted combination of time and distance. In addition, we explore the effect of three different constraints on the predator: (1) hunting success in the extensive search mode, (2) detection radius when in the extensive search mode, and (3) prey density. Our work confirms the broadly held notion that CCRW movement patterns should always outperform BWs, but find instructive cases where other walks are superior. We also show that, within the CCRW category, there is a wide range of possible walks and rank these according to measures of energetic cost. Our work also offers insights into the evolutionary pressures surrounding the “search-to-capture” event, and suggests that CCRW predators with low hunting success in one movement mode experience higher evolutionary pressures and are thus more likely to adopt a nearly optimal random walk. Our work highlights the need for comprehensive studies that examine several aspects of random walks simultaneously.     

Optimal spending functions for asymmetric group sequential designs

We present optimized group sequential designs where testing of a single parameter theta is of interest. We require specification of a loss function and of a prior distribution for theta. For the examples presented, we pre-specify Type I and II error rates and minimize the expected sample size over the prior distribution for theta. Minimizing the square of sample size rather than the sample size is found to produce designs with slightly less aggressive interim stopping rules and smaller maximum sample sizes with essentially identical expected sample size. We compare optimal designs using Hwang-Shih-DeCani and Kim-DeMets spending functions to fully optimized designs not restricted by a spending function family. In the examples selected, we also examine when there might be substantial benefit gained by adding an interim analysis. Finally, we provide specific optimal asymmetric spending function designs that should be generally useful and simply applied when a design with minimal expected sample size is desired.     

Two-stage designs for gene-disease association studies

The goal of this article is to describe a two-stage design that maximizes the power to detect gene-disease associations when the principal design constraint is the total cost, represented by the total number of gene evaluations rather than the total number of individuals. In the first stage, all genes of interest are evaluated on a subset of individuals. The most promising genes are then evaluated on additional subjects in the second stage. This will eliminate wastage of resources on genes unlikely to be associated with disease based on the results of the first stage. We consider the case where the genes are correlated and the case where the genes are independent. Using simulation results, it is shown that, as a general guideline when the genes are independent or when the correlation is small, utilizing 75% of the resources in stage 1 to screen all the markers and evaluating the most promising 10% of the markers with the remaining resources provides near-optimal power for a broad range of parametric configurations. This translates to screening all the markers on approximately one quarter of the required sample size in stage 1.     

Optimum experimental designs for multinomial logistic models

Multinomial responses frequently occur in dose level experiments. For example, in a study of the influence of gamma radiation on the emergence of house flies (Musca domestica L., 1758), three disjoint outcomes occurred: death before the pupae opened, death during emergence, and life after emergence. Although the flies are easy to breed, this sort of bioassay is, in general, very expensive since it requires the use of a gamma radiation source. Experiments therefore need to be designed to involve the minimum number of different doses. Here the theory of optimum experimental design is applied to provide efficient experiments to estimate the parameters of those multinomial logistic models that are a special case of the multivariate logistic models of Glonek and McCullagh (1995, Journal of the Royal Statistical Society, Series B 57, 533-546). The purpose is to reduce the overall experimental cost. The general equivalence theorem (Fedorov, 1972, Theory of Optimal Experiments) is adapted to this class of models, providing an effective method of generating and checking the optimality of designs. One example on flies demonstrates the method, which can be easily implemented.     

Directed walk designs for dose-response problems with competing failure modes

We examine adaptive allocation designs for the problem of determining the optimal therapeutic dose for subjects in early-phase clinical trials. A subject can fail due to lack of efficacy or due to a toxic reaction. Successful subjects will have both a positive response and no toxic side effects. Thus, we seek to maximize the product of the nontoxicity and efficacy dose-response curves. We are interested in sampling rules that perform well along several criteria, including the ethical criterion that, as often as possible, experimental subjects be treated at or close to the maximum in question. Statistically, we wish to identify the optimum dose with high probability at the close of the experiment. Here, we propose designs that combine new allocation policies, directed walks, with new smoothed shape-constrained curve-fitting techniques. These are compared with a variety of other curve-fitting techniques and with up-and-down and equal allocation rules.