A sequential design for maximizing the probability of a favourable response

Consider the situation in which subjects arrive sequentially for a treatment and in which there are two distinct ways in which the treatment may fail. Treatments are given at different dosages, and the probabilities of the two failure types vary with dose. Assuming that decreasing the chances of one failure type increases the chances of the other, we say the failures oppose each other. Also assume that one failure type is primary in that, if it occurs, it censors the trial, so that observation of the secondary failure type is contingent on no failure of the primary type. We are interested in designs that provide information about the dose that maximizes the probability of success, i.e., the optimal dose, while treating very few subjects at dosages that have high risks of failure. Assuming that dosages belong to a discrete set, we show that a randomized version of the Pólya urn scheme causes dose selection to be progressively biased so as to favour those doses that produce success with higher probability.     

Some robust design strategies for percentile estimation in binary response models

For the problem of percentile estimation of a quantal response curve, the authors determine multiobjective designs which are robust with respect to misspecifications of the model assumptions. They propose a maximin approach based on efficiencies which leads to designs that are simultaneously efficient with respect to various choices of link functions and parameter regions. Furthermore, the authors deal with the problems of designing model and percentile robust experiments. They give various examples of such designs, which are calculated numerically.     

Some aspects of the design and analysis of cluster randomization trials

Trials which randomize intact social groups, or clusters, to different interventions are becoming increasingly widespread. Although statistically less efficient than trials which randomize individuals, such designs are often preferred from a practical or ethical point of view, particularly in the evaluation of health care or educational strategies. We discuss selected issues that arise in the conduct of such trials, including the choice of design, ethical implications, sample size estimation and approaches to the analysis. The discussion is closely tied to methodological issues that have arisen in a recent evaluation trial of a new antenatal care programme, as sponsored by the Special Programme of Research, Development and Research Training in Human Reproduction of the World Health Organization.     

On using non identical and independent Bernoulli trials in human surveys

Unlike the usual randomized response techniques, as a pioneering attempt, this article focuses on using non identical independent Bernoulli trials in sensitive surveys. For this purpose, a general class of randomized response techniques is considered. The usual randomized response techniques are based on a fixed probability of having a yes answer. Contrary to usual techniques, in the proposed technique every respondent has a different probability of reporting a yes answer. With this setting, in most of the situations, the proposed technique is observed performing better in terms of variability. To illustrate and support the superiority of the proposed technique it is compared with models such as Warner (1965), Greenberg et al. (1969), Mangat and Singh (1990), and Mangat (1994) using identical Bernoulli trials. Relative efficiency and privacy protection are studied in detail using Warner (1965) and Mangat (1994) models.     

On comutativity of design and model expectations in randomized response surveys

Interchangability of the order of design expectation ( E_p ) and model expectation ( E_R ) under randomized response ( RR ) surveys for finding expectation and mean-square error of a linear estimator e found to be permissible for a non-informative sampling design. The non-comutative property established by Chaudhuri & Adhikary ( 1990 ) under probability proportional to size with replacement ( PPSWR ) sampling is disproved.     

Interval robust design under contaminated and non normal data

Abstract

Robust parameter design (RPD) is an effective tool, which involves experimental design and strategic modeling to determine the optimal operating conditions of a system. The usual assumptions of RPD are that normally distributed experimental data and no contamination due to outliers. And generally the parameter uncertainties in response models are neglected. However, using normal theory modeling methods for a skewed data and ignoring parameter uncertainties can create a chain of degradation in optimization and production phases such that misleading fit, poor estimated optimal operating conditions, and poor quality products. This article presents a new approach based on confidence interval (CI) response modeling for the process mean. The proposed interval robust design makes the system median unbiased for the mean and uses midpoint of the interval as a measure of location performance response. As an alternative robust estimator for the process variance response modeling, using biweight midvariance is proposed which is both resistant and robust of efficiency where normality is not met. The results further show that the proposed interval robust design gives a robust solution to the skewed structure of the data and to contaminated data. The procedure and its advantages are illustrated using two experimental design studies.     

Correlation coefficient of response variances in compound noise and product array experiments

In robust parameter design, a compound noise experiment has been frequently used for reducing the number of experimental runs compared to a product array experiment. However, the results obtained by the compound noise experiment and the product array experiment are often much different. This paper derives an expression of the correlation coefficient of response variances in the compound noise and the product array experiments, which gives an explanation of that difference.     

Survival trial design and monitoring using historical controls

In this paper, we propose a multistage group sequential procedure to design survival trials using historical controls. The formula for the number of events required for historical control trial designs is derived. Furthermore, a transformed information time is proposed for trial monitoring. An example is given to illustrate the application of the proposed methods to survival trial designs using historical controls. Copyright © 2016 John Wiley & Sons, Ltd.