Amplification of Sensitivity Analysis in Matched Observational Studies

A sensitivity analysis displays the increase in uncertainty that attends an inference when a key assumption is relaxed. In matched observational studies of treatment effects, a key assumption in some analyses is that subjects matched for observed covariates are comparable, and this assumption is relaxed by positing a relevant covariate that was not observed and not controlled by matching. What properties would such an unobserved covariate need to have to materially alter the inference about treatment effects? For ease of calculation and reporting, it is convenient that the sensitivity analysis be of low dimension, perhaps indexed by a scalar sensitivity parameter, but for interpretation in specific contexts, a higher dimensional analysis may be of greater relevance. An amplification of a sensitivity analysis is defined as a map from each point in a low dimensional sensitivity analysis to a set of points, perhaps a 'curve,' in a higher dimensional sensitivity analysis such that the possible inferences are the same for all points in the set. Possessing an amplification, an investigator may calculate and report the low dimensional analysis, yet have available the interpretations of the higher dimensional analysis.     

Gibbs sampling for marginal posterior expectations

In earlier work (Gelfand and Smith, 1990 and Gelfand et al, 1990) a sampling based approach using the Gibbs sampler was offered as a means for developing marginal posterior densities for a wide range of Bayesian problems several of which were previously inaccessible. Our purpose here is two-fold. First we flesh out the implementation of this approach for calculation of arbitrary expectations of interest. Secondly we offer comparison with perhaps the most prominent approach for calculating posterior expectations, analytic approximation involving application of the LaPlace method. Several illustrative examples are discussed as well. Clear advantages for the sampling based approach emerge.     

Construction of Confidence Intervals for the IVIean of a Population Containing Many Zero Values

The likelihood ratio method is used to construct a confidence interval for a population mean when sampling from a population with certain characteristics found in many applications, such as auditing. Specifically, a sample taken from this type of population usually consists of a very large number of zero values, plus a small number of nonzero values that follow some continuous distribution. In this situation, the traditional confidence interval constructed for the population mean is known to be unreliable. This article derives confidence intervals based on the likelihood-ratio-test approach by assuming (1) a normal distribution (normal algorithm) and (2) an exponential distribution (exponential algorithm). Because the error population distribution is usually unknown, it is important to study the robustness of the proposed procedures. We perform an extensive simulation study to compare the percentage of confidence intervals containing the true population mean using the two proposed algorithms with the percentage obtained from the traditional method based on the central limit theorem. It is shown that the normal algorithm is the most robust procedure against many different distributional error assumptions.     

Comparing mean ranks for repeated measures data

Rank tests are considered that compare t treatments in repeated measures designs. A statistic is given that contains as special cases several that have been proposed for this problem, including one that corresponds to the randomized block ANOVA statistic applied to the rank transformed data. Another statistic is proposed, having a null distribution holding under more general conditions, that is the rank transform of the Hotelling statistic for repeated measures. A statistic of this type is also given for data that are ordered categorical rather than fully rankedo Unlike the Friedman statistic, the statistics discussed in this article utilize a single ranking of the entire sample. Power calculations for an underlying normal distribution indicate that the rank transformed ANOVA test can be substantially more powerful than the Friedman test.     

Book Reviews

Statistics for Engineering Problem Solving.: Stephen B. Vardeman. Boston, MA: PWS Publishing, 1994. 840 pp. $59.95. Reviewed by Soren Bisgaard

A Data-Based Approach to Statistics.: Ronald L. Iman. Belmont, CA: Wadsworth Publishing, 1994. xiv + 898 pp. $51.95. Reviewed by Katherine Halvorsen

Concepts in Probability and Stochastic Modeling.: James J. Higgins and Sallie Keller-McNulty. Belmont, CA: Duxbury Press, 1995. xi + 420 pp. $67.43. Reviewed by David M. Nickerson

Statistics (6th ed.).: James T. McClave and Frank H. Dietrich II. New York: Dellen/Macmillan College Publishing, 1994. xix + 967 pp. $66.00. Reviewed by Katherine Halvorsen

Data Analysis for Monitoring Human Rights.: Herbert Spirer and Louise Spirer. Washington, DC: American Association for the Advancement of Science, 1994. xiv + 126 pp. $15.00. Reviewed by Diane G. Saphire     

Do taboo trade-offs explain the difficulty in valuing health and social interventions?

Persistent anomalies in the results of willingness to pay studies, despite improvements in measurement technique, challenge the assumption in economics that all sources of value are commensurable. Two sources of incommensurability have been identified: interdimensional incommensurability, which refers to the cognitive difficulty that people encounter when trying to assign a monetary value to health; and constitutive incommensurability, which arises when some forms of trade-off are regarded as ‘taboo’. In this paper we explore whether the notion of taboo trade-offs might explain some of the difficulties experienced in health-related willingness to pay studies.     

Immigrants and Employer-provided Training

Much has been written about the labour market outcomes for immigrants in their host countries, particularly with regard to earnings, employment and occupational attainment. However, much less attention has been paid to the question of whether immigrants are as likely to receive employer-provided training relative to comparable natives. As such training should be crucial in determining the labour market success of immigrants in the long run it is a critically important question. Using data from a large-scale survey of employees in Ireland, we find that immigrants are less likely to receive training from employers, with immigrants from the New Member States of the EU experiencing a particular disadvantage. The immigrant training disadvantage arises in part from a failure on the part of immigrants to get employed by training-oriented firms. However, they also experience a training disadvantage relative to natives within firms where less training is provided.