Neil A. Butler 《统计学通讯:理论与方法》2013,42(2):337-347

ABSTRACT

When spatial variation is present in experiments, it is clearly sensible to use designs with favorable properties under both generalized and ordinary least squares. This will make the statistical analysis more robust to misspecification of the spatial model than would be the case if designs were based solely on generalized least squares. In this article, treatment information is introduced as a way of studying the ordinary least squares properties of designs. The treatment information is separated into orthogonal frequency or polynomial components which are assumed to be independent under the spatial model. The well-known trend-resistant designs are those with no treatment information at the very low order frequency or polynomial components which tend to have the higher variances under the spatial model. Ideally, designs would be chosen with all the treatment information distributed at the higher-order components. However, the results in this article show that there are limits on how much trend resistance can be achieved as there are many constraints on the treatment information. In addition, appropriately chosen Williams squares designs are shown to have favorable properties under both ordinary and generalized least squares. At all times, the ordinary least squares properties of the designs are balanced against the generalized least squares objectives of optimizing neighbor balance.  相似文献   

    

Peter Zörnig 《统计学通讯:理论与方法》2014,43(9):1887-1906

We study the distributions of the random variables S_n and V_r related to a sequence of dependent Bernoulli variables, where S_n denotes the number of successes in n trials and V_r the number of trials necessary to obtain r successes. The purpose of this article is twofold: (1) Generalizing some results on the “nature” of the binomial and negative binomial distributions we show that S_n and V_r can follow any prescribed discrete distribution. The corresponding joint distributions of the Bernoulli variables are characterized as the solutions of systems of linear equations. (2) We consider a specific type of dependence of the Bernoulli variables, where the probability of a success depends only on the number of previous successes. We develop some theory based on new closed-form representations for the probability mass functions of S_n and V_r which enable direct computations of the probabilities.  相似文献   

On the Reliability of (n,f, k) and 〈n,f, k〉 Systems     

K. K. Kamalja  R. L. Shinde 《统计学通讯:理论与方法》2014,43(8):1649-1665

  相似文献   

    

Gary Witt 《统计学通讯:理论与方法》2014,43(20):4265-4280

This article describes a generalization of the binomial distribution. The closed form probability function for the probability of k successes out of n correlated, exchangeable Bernoulli trials depends on the number of trials and its two parameters: the common success probability and the common correlation. The distribution is derived under the assumption that the common correlation between all pairs of Bernoulli trials remains unchanged conditional on successes in all completed trials. The distribution was developed to model bond defaults but may be suited to biostatistical applications involving clusters of binary data encountered in repeated measurements or toxicity studies of families of organisms. Maximum likelihood estimates for the parameters of the distribution are found for a set of binary data from a developmental toxicity study on litters of mice.  相似文献   

    

Daniel Golkowski  Tim Friede  Meinhard Kieser 《Pharmaceutical statistics》2014,13(3):157-162

In drug development, bioequivalence studies are used to indirectly demonstrate clinical equivalence of a test formulation and a reference formulation of a specific drug by establishing their equivalence in bioavailability. These studies are typically run as crossover studies. In the planning phase of such trials, investigators and sponsors are often faced with a high variability in the coefficients of variation of the typical pharmacokinetic endpoints such as the area under the concentration curve or the maximum plasma concentration. Adaptive designs have recently been considered to deal with this uncertainty by adjusting the sample size based on the accumulating data. Because regulators generally favor sample size re‐estimation procedures that maintain the blinding of the treatment allocations throughout the trial, we propose in this paper a blinded sample size re‐estimation strategy and investigate its error rates. We show that the procedure, although blinded, can lead to some inflation of the type I error rate. In the context of an example, we demonstrate how this inflation of the significance level can be adjusted for to achieve control of the type I error rate at a pre‐specified level. Furthermore, some refinements of the re‐estimation procedure are proposed to improve the power properties, in particular in scenarios with small sample sizes. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

    

Athanasios C. Rakitzis  Philippe Castagliola 《统计学通讯:理论与方法》2013,42(14):4194-4214

ABSTRACT

Zero-inflated probability models are used to model count data that have an excessive number of zeros. Shewhart-type control charts have been proposed for the monitoring of zero-inflated processes. Usually their performance is evaluated under the assumption of known process parameters. However, in practice, their values are rarely known and they have to be estimated from an in-control historical Phase I sample. In the present paper, we investigate the performance of Shewhart-type control charts for zero-inflated processes with estimated parameters and propose practical guidelines for the statistical design of the examined charts, when the size of the preliminary sample is predetermined.  相似文献   

    

H. Ogasawara 《统计学通讯:理论与方法》2013,42(17):5166-5178

ABSTRACT

For interval estimation of a binomial proportion and a Poisson mean, matching pseudocounts are derived, which give the one-sided Wald confidence intervals with second-order accuracy. The confidence intervals remove the bias of coverage probabilities given by the score confidence intervals. Partial poor behavior of the confidence intervals by the matching pseudocounts is corrected by hybrid methods using the score confidence interval depending on sample values.  相似文献   

    

Andrew C. Leon  Hakan Demirtas  Chunshan Li  Donald Hedeker 《Pharmaceutical statistics》2013,12(5):268-274

In a cluster randomized controlled trial (RCT), the number of randomized units is typically considerably smaller than in trials where the unit of randomization is the patient. If the number of randomized clusters is small, there is a reasonable chance of baseline imbalance between the experimental and control groups. This imbalance threatens the validity of inferences regarding post‐treatment intervention effects unless an appropriate statistical adjustment is used. Here, we consider application of the propensity score adjustment for cluster RCTs. For the purpose of illustration, we apply the propensity adjustment to a cluster RCT that evaluated an intervention to reduce suicidal ideation and depression. This approach to adjusting imbalance had considerable bearing on the interpretation of results. A simulation study demonstrates that the propensity adjustment reduced well over 90% of the bias seen in unadjusted models for the specifications examined. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

    

Johannes Forkman 《Journal of applied statistics》2013,40(12):2681-2698

In a series of crop variety trials, ‘test varieties’ are compared with one another and with a ‘reference’ variety that is included in all trials. The series is typically analyzed with a linear mixed model and the method of generalized least squares. Usually, the estimates of the expected differences between the test varieties and the reference variety are presented. When the series is incomplete, i.e. when all test varieties were not included in all trials, the method of generalized least squares may give estimates of expected differences to the reference variety that do not appear to accord with observed differences. The present paper draws attention to this phenomenon and explores the recurrent idea of comparing test varieties indirectly through the use of the reference. A new ‘reference treatment method’ was specified and compared with the method of generalized least squares when applied to a five-year series of 85 spring wheat trials. The reference treatment method provided estimates of differences to the reference variety that agreed with observed differences, but was considerably less efficient than the method of generalized least squares.  相似文献   

    

Erin Donahue  Roy T. Sabo 《Pharmaceutical statistics》2021,20(3):563-572

Response-adaptive (RA) allocation designs can skew the allocation of incoming subjects toward the better performing treatment group based on the previously accrued responses. While unstable estimators and increased variability can adversely affect adaptation in early trial stages, Bayesian methods can be implemented with decreasingly informative priors (DIP) to overcome these difficulties. DIPs have been previously used for binary outcomes to constrain adaptation early in the trial, yet gradually increase adaptation as subjects accrue. We extend the DIP approach to RA designs for continuous outcomes, primarily in the normal conjugate family by functionalizing the prior effective sample size to equal the unobserved sample size. We compare this effective sample size DIP approach to other DIP formulations. Further, we considered various allocation equations and assessed their behavior utilizing DIPs. Simulated clinical trials comparing the behavior of these approaches with traditional Frequentist and Bayesian RA as well as balanced designs show that the natural lead-in approaches maintain improved treatment with lower variability and greater power.  相似文献