Randomization of neighbour balanced generalized Youden designs

If a crossover design with more than two treatments is carryover balanced, then the usual randomization of experimental units and periods would destroy the neighbour structure of the design. As an alternative, Bailey [1985. Restricted randomization for neighbour-balanced designs. Statist. Decisions Suppl. 2, 237–248] considered randomization of experimental units and of treatment labels, which leaves the neighbour structure intact. She has shown that, if there are no carryover effects, this randomization validates the row–column model, provided the starting design is a generalized Latin square. We extend this result to generalized Youden designs where either the number of experimental units is a multiple of the number of treatments or the number of periods is equal to the number of treatments. For the situation when there are carryover effects we show for so-called totally balanced designs that the variance of the estimates of treatment differences does not change in the presence of carryover effects, while the estimated variance of this estimate becomes conservative.     

Efficient circular neighbour designs for spatial interference model

We consider circular block designs for field-trials when there are two-sided spatial interference between neighbouring plots of the same blocks. The parameter of interest is total effects that is the sum of direct effect of treatment and neighbour effects, which correspond to the use of a single treatment in the whole field. We determine universally optimal approximate designs. When the number of blocks may be large, we propose efficient exact designs generated by a single sequence of treatment. We also give efficiency factors of the usual binary block neighbour balanced designs which can be used when the number of blocks is small.     

Optimal Circular Block Designs for Neighbouring Competition Effects

Competition or interference occurs when the responses to treatments in experimental units are affected by the treatments in neighbouring units. This may contribute to variability in experimental results and lead to substantial losses in efficiency. The study of a competing situation needs designs in which the competing units appear in a predetermined pattern. This paper deals with optimality aspects of circular block designs for studying the competition among treatments applied to neighbouring experimental units. The model considered is a four-way classified model consisting of direct effect of the treatment applied to a particular plot, the effect of those treatments applied to the immediate left and right neighbouring units and the block effect. Conditions have been obtained for the block design to be universally optimal for estimating direct and neighbour effects. Some classes of balanced and strongly balanced complete block designs have been identified to be universally optimal for the estimation of direct, left and right neighbour effects and a list of universally optimal designs for v<20 and r<100 has been prepared.     

On the Construction of Nearest–Neighbour Balanced Row–Column Designs

Nearest–neighbour balance is considered a desirable property for an experiment to possess in situations where experimental units are influenced by their neighbours. This paper introduces a measure of the degree of nearest–neighbour balance of a design. The measure is used in an algorithm which generates nearest–neighbour balanced designs and is readily modified to obtain designs with various types of nearest–neighbour balance. Nearest–neighbour balanced designs are produced for a wide class of parameter settings, and in particular for those settings for which such designs cannot be found by existing direct combinatorial methods. In addition, designs with unequal row and column sizes, and designs with border plots are constructed using the approach presented here.     

Characterization of Admissible Linear Estimators in Multivariate Linear Model with Respect to Inequality Constraints under Matrix Loss Function

In this article, we study the characterization of admissible linear estimators in a multivariate linear model with inequality constraint, under a matrix loss function. In the homogeneous class, we present several equivalent, necessary and sufficient conditions for a linear estimator of estimable functions to be admissible. In the inhomogeneous class, we find that the necessary and sufficient conditions depend on the rank of the matrix in the constraint. When the rank is greater than one, the necessary and sufficient conditions are obtained. When the rank is equal to one, we have necessary conditions and sufficient conditions separately. We also obtain the necessary and sufficient conditions for a linear estimator of inestimable function to be admissible in both classes.     

Optimal Bayesian Randomization

Randomization is a puzzle for Bayesians. The intuitive need for randomization is clear, but there is a standard result that Bayesians need not randomize. In this paper we propose a model in which randomization is a strictly optimal procedure. The most important aspect of our model is that there are several parties who make different decisions and observe different data. The result also sheds light on the ethical considerations involving randomization in a clinical trial.     

Privacy protection measures for randomized response surveys on stigmatizing continuous variables

We consider the situation where sample surveys are to be undertaken on sensitive or stigmatizing issues. For such surveys, direct questioning methods usually lead to non-compliance or incorrect responses and so, the randomized response technique, where the responses are collected through some randomization device, is found to be useful. A majority of the literature on these techniques focus on dichotomous sensitive variables, while some techniques are also available for continuous sensitive variables. In this article, we focus on the extent of privacy protection available in sample surveys to respondents for continuous response variables. We also propose two measures of privacy protection. We demonstrate that the parameters of our randomization scheme can be so chosen as to achieve a pre-assigned level of privacy protection while at the same time yielding efficient estimates. We also show some numerical comparisons.     

Real and quasi-experiments in capture-recapture studies

The three key elements of experimental design are randomization, replication, and variance identification and control. Capture-recapture experiments usually pay sufficient attention to the first two elements, but often do not pay sufficient attention to sources of variation. These include blocking factors and different sizes of experimental units. By casting capture-recapture studies in an experimental design framework, the various roles of these sources of variation become clear and the sources that are pooled when these experiments are analysed using existing software is also clear. This formulation also shows that care must be taken with pseudo-replication and different sized experimental units.     

ON THE DESIGN OF FIELD EXPERIMENTS UNDER A ONE-DIMENSIONAL NEIGHBOUR MODEL

This paper examines the effect of randomisation restrictions, either to satisfy conditions for a balanced incomplete block design or to attain a higher level of partial neighbour balance, on the average variance of pair-wise treatment contrasts under a neighbour model discussed by Gleeson & Cullis (1987). Results suggest that smaller average pairwise variances can be obtained by ignoring requirements for incomplete block designs and concentrating on achieving a higher level of partial neighbour balance. Field layout of the design, although often determined by practical constraints, e.g. size, shape of site, minimum plot size and experimental husbandry, may markedly affect average pairwise variance. For the one-dimensional (row-wise) neighbour model considered here, investigation of three different layouts suggests that for a rectangular array of plots, smaller average pairwise variances can generally be obtained from layouts with fewer rows and more plots per row.     

Randomization of Clusters Versus Randomization of Persons Within Clusters

Many experiments aim at populations with persons nested within clusters. Randomization to treatment conditions can be done at the cluster level or at the person level within each cluster. The latter may result in control group contamination, and cluster randomization is therefore oftenpreferred in practice. This article models the control group contamination, calculates the required sample sizes for both levels of randomization, and gives the degree of contamination for which cluster randomization is preferable above randomization of persons within clusters. Moreover, itprovides examples of situations where one has to make a choice between both levels of randomization.     

Monte-Carlo Sensitivity Analysis for Controlled Direct Effects Using Marginal Structural Models in the Presence of Confounded Mediators

In randomized trials, investigators are frequently interested in estimating the direct effect of a treatment on an outcome that is not relayed by intermediate variables, in addition to the usual intention-to-treat (ITT) effect. Even if the ITT effect is not confounded due to randomization, the direct effect is not identified when unmeasured variables affect the intermediate and outcome variables. Although the unmeasured variables cannot be adjusted for in the models, it is still important to evaluate the potential bias of these variables quantitatively. This article proposes a sensitivity analysis method for controlled direct effects using a marginal structural model that is an extension of the sensitivity analysis method of unmeasured confounding introduced in the context of observational studies. The proposed method is illustrated using a randomized trial of depression.     

Randomization with non-uniform allocations: fulfillment time distributions and bias properties

This article compares the properties of two balanced randomization schemes with several treatments under non-uniform allocation probabilities. According to the first procedure, the so-called truncated multinomial randomization design, the process employs a given allocation distribution, until a treatment receives its quota of subjects, after which this distribution switches to the conditional distribution for the remaining treatments, and so on. The second scheme, the random allocation rule, selects at random any legitimate assignment of the given number of subjects per treatment. The behavior of these two schemes is shown to be quite different: the truncated multinomial randomization design's assignment probabilities to a treatment turn out to vary over the recruitment period, and its accidental bias can be large, whereas the random allocation rule's this bias is bounded. The limiting distributions of the instants at which a treatment receives the given number of subjects is shown to be that of weighted spacings for normal order statistics with different variances. Formulas for the selection bias of both procedures are also derived.     

Effects of unstratified and centre‐stratified randomization in multi‐centre clinical trials

This paper deals with the analysis of randomization effects in multi‐centre clinical trials. The two randomization schemes most often used in clinical trials are considered: unstratified and centre‐stratified block‐permuted randomization. The prediction of the number of patients randomized to different treatment arms in different regions during the recruitment period accounting for the stochastic nature of the recruitment and effects of multiple centres is investigated. A new analytic approach using a Poisson‐gamma patient recruitment model (patients arrive at different centres according to Poisson processes with rates sampled from a gamma distributed population) and its further extensions is proposed. Closed‐form expressions for corresponding distributions of the predicted number of the patients randomized in different regions are derived. In the case of two treatments, the properties of the total imbalance in the number of patients on treatment arms caused by using centre‐stratified randomization are investigated and for a large number of centres a normal approximation of imbalance is proved. The impact of imbalance on the power of the study is considered. It is shown that the loss of statistical power is practically negligible and can be compensated by a minor increase in sample size. The influence of patient dropout is also investigated. The impact of randomization on predicted drug supply overage is discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Using partial ranking information in the design of small-sample comparisons

Random assignment of experimental units to treatment and control groups is a conventional device tob create unbiased comparisons. However, when sample sizes are small and the units differ considerably, there is a significant risk that randomization will create seriously unbalanced partitions of the units into treatment and control groups. We develop and evaluate an alternative to complete randomization for small-sample comparisons involving ordinal data with partial information on ranks of units. For instance, we might know that, of eight units, Rank (A) < Rank (C), Rank (A) < Rank (E) and Rank(D) < Rank(H). We develop an efficient computational procedure to use such information as the basis for restricted randomization of units to the treatment group. We compare our methods to complete randomization in the context of the Mann-Whitney test. With sufficient ranking information, the restricted randomization results in more powerful comparisons.     

Conditions for Non-confounding and Collapsibility without Knowledge of Completely Constructed Causal Diagrams

In this paper, we discuss several concepts in causal inference in terms of causal diagrams proposed by Pearl (1993 , 1995a , b ), and we give conditions for non-confounding, homogeneity and collapsibility for causal effects without knowledge of a completely constructed causal diagram. We first introduce the concepts of non-confounding, conditional non-confounding, uniform non-confounding, homogeneity, collapsibility and strong collapsibility for causal effects, then we present necessary and sufficient conditions for uniform non-confounding, homegeneity and collapsibilities, and finally we show sufficient conditions for non-confounding, conditional non-confounding and uniform non-confounding.     

Families of neighbour designs and their analysis

Several methods of construction of generalised neighbour designs of equal and unequal block sizes are presented alongwith examples. Some methods for constructing neighbour designs of Rees are also given. The outline of analysis of generalised neighbour design has also been suggested.     

Robustness of designed experiments against missing data

This paper investigates the robustness of designed experiments for estimating linear functions of a subset of parameters in a general linear model against the loss of any t( ≥1) observations. Necessary and sufficient conditions for robustness of a design under a homoscedastic model are derived. It is shown that a design robust under a homoscedastic model is also robust under a general heteroscedastic model with correlated observations. As a particular case, necessary and sufficient conditions are obtained for the robustness of block designs against the loss of data. Simple sufficient conditions are also provided for the binary block designs to be robust against the loss of data. Some classes of designs, robust up to three missing observations, are identified. A-efficiency of the residual design is evaluated for certain block designs for several patterns of two missing observations. The efficiency of the residual design has also been worked out when all the observations in any two blocks, not necessarily disjoint, are lost. The lower bound to A-efficiency has also been obtained for the loss of t observations. Finally, a general expression is obtained for the efficiency of the residual design when all the observations of m ( ≥1) disjoint blocks are lost.     

Bayesian randomized clinical trials: A decision‐theoretic sequential design

The authors propose a Bayesian decision‐theoretic framework justifying randomization in clinical trials. Noting that the decision maker is often unable or unwilling to specify a unique utility function, they develop a sequential myopic design that includes randomization justified by the consideration of a set of utility functions. Randomization is introduced over all nondominated treatments, allowing for interim removal of treatments and early stopping. The authors illustrate their approach in the context of a study to find the optimal dose of pegylated interferon for platinum resistant ovarian cancer. They also develop an algorithm to implement their methodology in a phase II clinical trial comparing several competing experimental treatments.     

Semiparametric Time-Varying Coefficients Regression Model for Longitudinal Data

Abstract.  In this paper, we consider a semiparametric time-varying coefficients regression model where the influences of some covariates vary non-parametrically with time while the effects of the remaining covariates follow certain parametric functions of time. The weighted least squares type estimators for the unknown parameters of the parametric coefficient functions as well as the estimators for the non-parametric coefficient functions are developed. We show that the kernel smoothing that avoids modelling of the sampling times is asymptotically more efficient than a single nearest neighbour smoothing that depends on the estimation of the sampling model. The asymptotic optimal bandwidth is also derived. A hypothesis testing procedure is proposed to test whether some covariate effects follow certain parametric forms. Simulation studies are conducted to compare the finite sample performances of the kernel neighbourhood smoothing and the single nearest neighbour smoothing and to check the empirical sizes and powers of the proposed testing procedures. An application to a data set from an AIDS clinical trial study is provided for illustration.     

A Note on the Use of Some Functions of Spacings in the Estimation of Common Scale Parameter of Several Symmetric Distributions

In this article, we consider the problem of best linear unbiased estimation and best linear invariant estimation of the common scale parameter of several symmetric distributions using some functions of spacings of all observations taken from individual samples. We also proved a sufficient condition for the non negativity of the common scale estimator obtained by the above method. Furthermore, we obtained necessary and sufficient conditions for the derived estimators to be constant multiple of the sum of first and last spacings of the pooled sample.