An application of a multi‐stage strategy involving confidence intervals to evaluate whether a response rate is favourable or not

In early clinical development of new medicines, a single‐arm study with a limited number of patients is often used to provide a preliminary assessment of a response rate. A multi‐stage design may be indicated, especially when the first stage should only include very few patients so as to enable rapid identification of an ineffective drug. We used decision rules based on several types of nominal confidence intervals to evaluate a three‐stage design for a study that includes at most 30 patients. For each decision rule, we used exact binomial calculations to determine the probability of continuing to further stages as well as to evaluate Type I and Type II error rates. Examples are provided to illustrate the methods for evaluating alternative decision rules and to provide guidance on how to extend the methods to situations with modifications to the number of stages or number of patients per stage in the study design. Copyright © 2004 John Wiley & Sons, Ltd.     

Monte Carlo exact methods used for analysing interethnic unions in Great Britain

The value of using exact rather than asymptotic tests to measure intermarriage in the United Kingdom is examined. "We develop Markov chain Monte Carlo methods for estimating the exact conditional p-value and the exact distribution of the residuals, for quasi-independence and quasi-symmetry. These methods are used to analyse a sparse 10 x 10 symmetric table of interethnic unions, extracted from the 1% household sample of anonymized records from the 1991 U.K. census. With the exception of Pakistani/White and Other Asian/White unions, there is no evidence against quasi-symmetry. We conclude that, with these exceptions, there are no gender differences in the affinities between ethnic groups."     

The menstrual cycle and personal space

Sixty undergraduate women were individually tested for interpersonal distance preferences by either a male or female confederate who approached each subject from six different directions using a procedure reported by Kinzel (1970). Randomly, each participated during either the four days prior to menstrual flow (premenstrual), the four days beginning with the first day of flow (menstrual), or the four days midway between the onset of their last period and the estimated beginning of the next (midcycle). Unexpectedly, interpersonal distance preferences were greater for males than for female testers only during the midcycle phase. Moos Menstrual Distress Questionnaire scores were not reliably correlated with interpersonal distance preferences, nor were questionnaire items tapping extent of sexual experience, usage of birth-control pills, or concern about menstrual odor. Ratings of the attractiveness of the person doing the testing was inversely related to the preferred interpersonal distance with the exception of midcycle subjects. Both negative affect and sexual interest interpretations of the effects of menstrual cycle on personal space are discussed.Edgar C. O'Neal is professor of psychology at Tulane; he received his Ph.D. in social psychology from the University of Missouri at Columbia. Janet Schultz is a M.S.W. candidate at Tulane's Graduate School of Social Work; she received her B.A. with honors in psychology from Newcomb College of Tulane University. Terry E. Christenson is associate professor of psychology and biology at Tulane and received his Ph.D. in psychology from the University of California at Berkeley. Address reprint requests to the first author, Department of Psychology, 2007 Percival Stern Hall, Tulane University, New Orleans, LA 70118-5698.     

Calculation of marginal densities for parameters of multinomial distributions

The full Bayesian analysis of multinomial data using informative and flexible prior distributions has, in the past, been restricted by the technical problems involved in performing the numerical integrations required to obtain marginal densities for parameters and other functions thereof. In this paper it is shown that Gibbs sampling is suitable for obtaining accurate approximations to marginal densities for a large and flexible family of posterior distributions—the family. The method is illustrated with a three-way contingency table. Two alternative Monte Carlo strategies are also discussed.     

Properties of the bridge sampler with a focus on splitting the MCMC sample

Computation of normalizing constants is a fundamental mathematical problem in various disciplines, particularly in Bayesian model selection problems. A sampling-based technique known as bridge sampling (Meng and Wong in Stat Sin 6(4):831–860, 1996) has been found to produce accurate estimates of normalizing constants and is shown to possess good asymptotic properties. For small to moderate sample sizes (as in situations with limited computational resources), we demonstrate that the (optimal) bridge sampler produces biased estimates. Specifically, when one density (we denote as $$p_2$$) is constructed to be close to the target density (we denote as $$p_1$$) using method of moments, our simulation-based results indicate that the correlation-induced bias through the moment-matching procedure is non-negligible. More crucially, the bias amplifies as the dimensionality of the problem increases. Thus, a series of theoretical as well as empirical investigations is carried out to identify the nature and origin of the bias. We then examine the effect of sample size allocation on the accuracy of bridge sampling estimates and discovered that one possibility of reducing both the bias and standard error with a small increase in computational effort is by drawing extra samples from the moment-matched density $$p_2$$ (which we assume easy to sample from), provided that the evaluation of $$p_1$$ is not too expensive. We proceed to show how the simple adaptive approach we termed “splitting” manages to alleviate the correlation-induced bias at the expense of a higher standard error, irrespective of the dimensionality involved. We also slightly modified the strategy suggested by Wang et al. (Warp bridge sampling: the next generation, Preprint, 2019. arXiv:1609.07690) to address the issue of the increase in standard error due to splitting, which is later generalized to further improve the efficiency. We conclude the paper by offering our insights of the application of a combination of these adaptive methods to improve the accuracy of bridge sampling estimates in Bayesian applications (where posterior samples are typically expensive to generate) based on the preceding investigations, with an application to a practical example.     

Comparing Varieties of Agency Theory in Economics, Political Science, and Sociology: An Illustration from State Policy Implementation

As rational choice theory has moved from economics into political science and sociology, it has been dramatically transformed. The intellectual diffusion of agency theory illustrates this process. Agency theory is a general model of social relations involving the delegation of authority, and generally resulting in problems of control, which has been applied to a broad range of substantive contexts. This paper analyzes applications of agency theory to state policy implementation in economics, political science, and sociology. After documenting variations in the theory across disciplinary contexts, the strengths and weaknesses of these different varieties of agency theory are assessed. Sociological versions of agency theory, incorporating both broader microfoundations and richer models of social structure, are in many respects the most promising. This type of agency theory illustrates the potential of an emerging sociological version of rational choice theory.