A method for obtaining randomized block designs in preclinical studies with multiple quantitative blocking variables

A method is proposed for block randomization of treatments to experimental units that can accommodate both multiple quantitative blocking variables and unbalanced designs. Hierarchical clustering in conjunction with leaf‐order optimization is used to block experimental units in multivariate space. The method is illustrated in the context of a diabetic mouse assay. A simulation study is presented to explore the utility of the proposed randomization method relative to that of a completely randomized approach, both in the presence and absence of covariate adjustment. An example R function is provided to illustrate the implementation of the method. Copyright © 2010 John Wiley & Sons, Ltd.     

随机序列的可积性

本文给出了广鞅差随机序列一致可积性条件，及其一个非一致可积鞅的广鞅差序列的典型例子，说明右闭下鞅不一定一致可积。     

On the maximum number of constraints for s-symbol balanced arrays of strength t

Several upper bounds on the maximum number of constraints for s-symbol balanced arrays of strength t are given. Some bounds derived here include the results obtained by Rafter and Seiden (1974), Chopra (1982, 1983) and Saha, Mukerjee and Kageyama (1983).     

On Bayesian estimators in multistage binomial designs

A new class of Bayesian estimators for a proportion in multistage binomial designs is considered. Priors belong to the beta-J distribution family, which is derived from the Fisher information associated with the design. The transposition of the beta parameters of the Haldane and the uniform priors in fixed binomial experiments into the beta-J distribution yields bias-corrected versions of these priors in multistage designs. We show that the estimator of the posterior mean based on the corrected Haldane prior and the estimator of the posterior mode based on the corrected uniform prior have good frequentist properties. An easy-to-use approximation of the estimator of the posterior mode is provided. The new Bayesian estimators are compared to Whitehead's and the uniformly minimum variance estimators through several multistage designs. Last, the bias of the estimator of the posterior mode is derived for a particular case.     

On the analysis of multivariate repeated measures designs

The relationship between the mixed-model analysis and multivariate approach to a repeated measures design with multiple responses is presented. It is shown that by taking the trace of the appropriate submatrix of the hypothesis (error) sums of squares and crossproducts (SSCP) matrix obtained from the multivariate approach, one can get the hypothesis (error) SSCP matrix for the mixed-model analysis. Thus, when analyzing data from a multivariate repeated measures design, it is advantageous to use the multivariate approach because the result of the mixed-model analysis can also be obtained without additional computation.     

De-aliasing effects using semifoldover techniques

Semifoldover designs, obtained by semifolding a regular two-level factorial design, have been discussed recently in the literature. In this article, with the use of indicator functions, we investigate various semifoldover designs that are obtained from a general two-level factorial design. We discuss when a main factor or a two-factor interaction can be de-aliased from their aliased two-factor interactions, and extend some of the existing results from regular designs to non-regular designs. Finally, we present some examples to illustrate the results developed here.     

Generation of multivariate distributions by vertical density representation

Troutt (1991,1993) proposed the idea of the vertical density representation (VDR) based on Box-Millar method. Kotz, Fang and Liang (1997) provided a systematic study on the multivariate vertical density representation (MVDR). Suppose that we want to generate a random vector X[d]Rⁿthat has a density function ?(x). The key point of using the MVDR is to generate the uniform distribution on [D]_?(v) = {x :?(x) = v} for any v > 0 which is the surface in RⁿIn this paper we use the conditional distribution method to generate the uniform distribution on a domain or on some surface and based on it we proposed an alternative version of the MVDR(type 2 MVDR), by which one can transfer the problem of generating a random vector X with given density f to one of generating (X, X_n+i) that follows the uniform distribution on a region in Rⁿ⁺¹defined by ?. Several examples indicate that the proposed method is quite practical.     

A study of BIB designs through support matrices

This paper deals with the existence and nonexistence of BIB designs with repeated blocks. The approach is an algebraic one. The concept of a support matrix is introduced and some of its basic properties are noted. Some basic examples of support matrices are given when the block size is 3. The connection between full column rank proper support matrices and irreducible designs is explored and some examples of such matrices are given.     

On the equivalence of two approaches to simplicity in the analysis of block designs and some related results

Two seemingly different approaches to simplicity in the analysis of connected block designs, and their relationship to the concepts of balance are discussed.     

New balanced sampling plans excluding adjacent units

Hedayat et al. [1988a. Sampling plans excluding contiguous units. J. Statist. Plann. Inference 19, 159–170; 1988b. Designs in survey sampling avoiding contiguous units. In: Krishnaiah, P.R., Rao, C.R. (Eds.). Handbook of Statistics, vol. 6. Elsevier, Amsterdam, pp. 575–583] first introduced balanced sampling designs for the exclusion of contiguous units. Sampling plans that excluded the selection of contiguous units within a given sample, while maintaining a constant second-order inclusion probability for non-contiguous units, were investigated for finite populations of N units arranged in a circular, one-dimensional ordering. There remain many open questions about the existence of such plans and their extension to plans excluding adjacent units. We present new generation techniques and new balanced sampling plans for the exclusion of adjacent units under finite, one-dimensional, circularly and linearly ordered populations.