Statistical Properties of a Modified Accelerated Design for Phase I Cancer Clinical Trials

We consider the semiparametric profile likelihood inference for the distribution function under doubly censored data. For further developments of the statistical inference based on the profile likelihood ratio and alternative tools such as the score or Wald-type inference, we discuss the structures of the profile likelihood estimators and their derivatives included in the score function and the Fisher function of the profile likelihood, establishing the consistencies of their estimators.     

An Extension of Economic Design of x-Bar Control Charts for Non Normally Distributed Data Under Weibull Shock Models

Three parameters—sample size, sampling intervals, and the control limits—must be determined when the x bar chart to monitor a manufacturing process. The constant sampling intervals were widely employed because of its administrative simplicity. However, the variable sampling interval (VSI) has recently been shown to give substantially faster detection of most process shifts than fixed-sampling-interval (FSI) for x-bar charts. In addition, these measurements in the subgroup are assumed to be normally distributed. That assumption may not be tenable. This investigation compares the economic design of x-bar control charts for non normal data under Weibull shock models with various sampling avenues.     

Coherent Frequentism: A Decision Theory Based on Confidence Sets

By representing fair betting odds according to one or more pairs of confidence set estimators, dual parameter distributions called confidence posteriors secure the coherence of actions without any prior distribution. This theory reduces to the maximization of expected utility when the pair of posteriors is induced by an exact or approximate confidence set estimator or when a reduction rule is applied to the pair. Unlike the p-value, the confidence posterior probability of an interval hypothesis is suitable as an estimator of the indicator of hypothesis truth since it converges to 1 if the hypothesis is true or to 0 otherwise.     

Computer-Generated Change-Over Designs for Correlated Observations

Change-over designs with independently distributed errors in the model have been studied extensively in the literature. Martin and Eccleston (2001 Martin , R. J. , Eccleston , J. A. ( 2001 ). Optimal and near optimal designs for dependent observations . Statist. Applic. 3 : 101 – 116 . [Google Scholar]) gave an algorithm for the generation of efficient change-over designs when the errors are correlated. This article proposes an algorithm for the generation of efficient change-over designs for estimation of direct effects of treatments in the presence of first-order residual effects in the model and when the errors are correlated.     

Uniform Design for Experiments with Mixtures

The goal of uniform mixture design is to scatter the design points in the experimental region uniformly. The commonly used criteria, such as mean square distance, are based on the Euclidean distance. Based on the Lee distance, a new criterion is proposed in this article. And an algorithm, called NTLBG, is also proposed to refine the randomly generated design for the experimental design with mixtures. Some examples show that the design generated by the NTLBG algorithm has a lower criteria value.     

Adaptive Crossover Design for Normal Responses

In a response-adaptive design, we review and update the trial on the basis of outcomes in order to achive a specific goal. In clinical trials our goal is to allocate a larger number of patients to the better treatment. In the present paper, we use a response adaptive design in a two-treatment two-period crossover trial where the treatment responses are continuous. We provide probability measures to choose between the possible treatment combinations AA, AB, BA, or BB. The goal is to use the better treatment combination a larger number of times. We calculate the allocation proportions to the possible treatment combinations and their standard errors. We also derive some asymptotic results and provide solutions on related inferential problems. The proposed procedure is compared with a possible competitor. Finally, we use a data set to illustrate the applicability of our proposed design.     

A-optimal designs for heteroscedastic multifactor regression models

Abstract

This paper searches for A-optimal designs for Kronecker product and additive regression models when the errors are heteroscedastic. Sufficient conditions are given so that A-optimal designs for the multifactor models can be built from A-optimal designs for their sub-models with a single factor. The results of an efficiency study carried out to check the adequacy of the products of optimal designs for uni-factor marginal models when these are used to estimate different multi-factor models are also reported.     

Optimal block designs for double cross experiments

ABSTRACT

This paper presents systematic methods of construction of optimal block designs for a double cross experiments for both even and odd values of “p” parental lines. The both even and odd values of designs are derived by using initial block of unreduced balanced incomplete block designs and initial block of row–column designs given by Bose et al. (1953 Bose, R.C., Shrikhande, S.S., Bhattacharya, K.N. (1953). On the construction of group divisible incomplete block design. Ann. Math. Stat. 24:167–195.[Crossref] , [Google Scholar]) and Gupta and Choi (1998 Gupta, S., Choi, K.C. (1998). Optimal row-column designs for complete diallel crosses. Commun. Stat. Theory Methods 27(11):2827–2835.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), respectively. In this attempt we have found some new universally optimal block designs for double cross experiments.     

Admissibility of a variance estimator in finite population sampling under Warner's randomized response plan with multiple responses

ABSTRACT

Let P be the proportion of individuals in a finite population possessing a sensitive attribute. We consider the problem of unbiased estimation of (i) the variance of a linear unbiased estimator of P and (ii) the population variance P (1—P) for a given probability sampling design under Warner's (1965 Warner, S.L. (1965). Randomized response - A survey technique for eliminating evasive answer bias. J. Amer. Statist. Assoc. 60:63–69.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) randomized response (RR) plan when independent responses are obtained from each sampled individual as many times as he/she is selected in the sample and prove the admissibility of a quadratic unbiased estimator for each.