A Unified Framework for the Prioritization of Organ Transplant Patients: Analytic Hierarchy Process,Sensitivity and Multifactor Robustness Study

Fair and equitable allocation of donor organs in the USA is a daunting yet necessary task, which can mean the difference between life and death for patients on transplant waiting lists. This paper proposes a multi‐criterion decision‐making model using the analytic hierarchy process to allow for an allocation decision to be made on the basis of urgency, efficiency, benefit and equity. These four perspectives and objectives can be broken down into both quantitative and qualitative measures, which can be easily combined and weighted through group consensus. The proposed model overcomes the limitations of a single type of system, integrates the views of many organ allocation philosophies, improves the decision maker's ability to collaborate, helps justify the decision and reaches the optimal result. In addition, the proposed profile matrix allows decision makers to graphically trade off criteria against each other and to clearly articulate the decision rationale. Our computational study suggests that the proposed model not only satisfactorily serves the objectives of many constituents, but also remains noticeably robust under various criteria‐weight‐change scenarios. It improves stakeholder confidence in the organ allocation procedure, maximizes the usefulness of the organ and enhances welfare to society. Copyright © 2012 John Wiley & Sons, Ltd.     

Asymptotic distributions of the estimators of communalities in factor analysis

Asymptotic distributions of the estimators of communalities are derived for the maximum likelihood method in factor analysis. It is shown that the common practice of equating the asymptotic standard error of the communality estimate to the unique variance estimate is correct for standardized communality but not correct for unstandardized communality. In a Monte Carlo simulation the accuracy of the normal approximation to the distributions of the estimators are assessed when the sample size is 150 or 300. This study was carried out in part under the ISM Cooperative Research Program (90-ISM-CRP-9).     

The robustness of the usual correction for restriction in range due to explicit selection

Corrections for restriction in range due to explicit selection assume the linearity of regression and homoscedastic array variances. This paper develops a theoretical framework in which the effects of some common forms of violation of these assumptions on the estimation of the unrestricted correlation can be investigated. Simple expressions are derived for both the restricted and corrected correlations in terms of the target (unrestricted) correlation in these situations.The author is grateful to D. Holt, C. J. Skinner and T. M. F. Smith (all University of Southampton) for their helpful comments. Research was initially supported by grant No. HR7152 from the Economic and Social Research Council.     

The comparison of interdependent correlations between optimal linear composites

A general procedure is provided for comparing correlation coefficients between optimal linear composites. The procedure allows computationally efficient significance tests on independent or dependent multiple correlations, partial correlations, and canonical correlations, with or without the assumption of multivariate normality. Evidence from some Monte Carlo studies on the effectiveness of the methods is also provided.This research was supported in part by an operating grant (#67-4640) to the first author from the National Sciences and Engineering Research Council of Canada. The authors would also like to acknowledge the helpful comments and encouragement of Alexander Shapiro, Stanley Nash, and Ingram Olkin.     

Tests for linear trend in the smallest eigenvalues of the correlation matrix

A test for linear trend among a set of eigenvalues of a correlation matrix is developed. As a technical implementation of Cattell's scree test, this is a generalization of Anderson's test for the equality of eigenvalues, and extends Bentler and Yuan's work on linear trends in eigenvalues of a covariance matrix. The power of minimumx ² and maximum likelihood ratio tests are compared. Examples show that the linear trend hypothesis is more realistic than the standard hypothesis of equality of eigenvalues, and that the hypothesis is compatible with standard decisions on the number of factors or components to retain in data analysis.This work was supported by National Institute on Drug Abuse Grants DA01070 and DA00017. The assistance of Maia Berkane and several anonymous reviewers is gratefully acknowledged.     

Some standard errors in item response theory

The mathematics required to calculate the asymptotic standard errors of the parameters of three commonly used logistic item response models is described and used to generate values for some common situations. It is shown that the maximum likelihood estimation of a lower asymptote can wreak havoc with the accuracy of estimation of a location parameter, indicating that if one needs to have accurate estimates of location parameters (say for purposes of test linking/equating or computerized adaptive testing) the sample sizes required for acceptable accuracy may be unattainable in most applications. It is suggested that other estimation methods be used if the three parameter model is applied in these situations.The research reported here was supported, in part, by contract #F41689-81-6-0012 from the Air Force Human Resources Laboratory to McFann-Gray & Associates, Benjamin A. Fairbank, Jr., Principal Investigator. Further support of Wainer's effort was supplied by the Educational Testing Service, Program Statistics Research Project.     

Approximate confidence intervals for a robust scale parameter

A recent paper by Wainer and Thissen has renewed the interest in Gini's mean difference,G, by pointing out its robust characteristics. This note presents distribution-free asymptotic confidence intervals for its population value,γ, in the one sample case and for the difference Δ=(γ ₁?γ ₂) in the two sample situations. Both procedures are based on a technique of jackknifingU-statistics developed by Arvesen.     

The Map and the Territory: Complexity in Biology

In business administration or in economics it is absolutely relevant not to consider indexes like profit growth rate or gross domestic product as exhaustive indexes for economic wealth. Likewise, in biology it is important not to confuse the representation of life with life itself. The most important concepts in biology are information, memory, structure, plasticity, and robustness. Information is the difference that makes the difference. Memories are information registered in an organism. Plasticity is the capacity of a living organism to change its own structure/sets of behaviors for having a competitive advantage. Robustness is the ability of a living organism to resist environmental changes without changing its own structure/sets of behavior, and fragility is when a living organism undergoes changes in its own structure without being able to resist non-adaptive changes.     

On robusiness of the normal-theory based asymptotic distributions of three reliability coefficient estimates

This paper studies the asymptotic distributions of three reliability coefficient estimates: Sample coefficient alpha, the reliability estimate of a composite score following a factor analysis, and the estimate of the maximal reliability of a linear combination of item scores following a factor analysis. Results indicate that the asymptotic distribution for each of the coefficient estimates, obtained based on a normal sampling distribution, is still valid within a large class of nonnormal distributions. Therefore, a formula for calculating the standard error of the sample coefficient alpha, recently obtained by van Zyl, Neudecker and Nel, applies to other reliability coefficients and can still be used even with skewed and kurtotic data such as are typical in the social and behavioral sciences.This research was supported by grants DA01070 and DA00017 from the National Institute on Drug Abuse and a University of North Texas faculty research grant. We would like to thank the Associate Editor and two reviewers for suggestions that helped to improve the paper.     

On computing ELECTRE's credibility indices under partial information

The ELECTRE family of decision aid methods is a well‐known approach to help decision makers (DMs) advance in a decision process. Among the most recent methods in the family, ELECTRE IS, III, and TRI compute fuzzy indices for the credibility of a given action outranking some other. We consider the case when the DMs are unsure which values each parameter should take, which may result from insufficient, imprecise or contradictory information, as well as from different preferences among a group of DMs. In the framework of a robustness analysis approach, where DMs provide only partial information on the parameter values (through constraints on acceptable combinations), we study how to find whether an outranking among two actions in an ELECTRE method is robust. In this context, we study the resulting nonlinear problems of optimizing a credibility index (under the type of constraints that we consider to appear in practice) and present some examples. Copyright © 1999 John Wiley & Sons, Ltd.