Methods of evaluating and comparing the performance of diagnostic tests are of increasing importance as new tests are developed and marketed. When a test is based on an observed variable that lies on a continuous or graded scale, an assessment of the overall value of the test can be made through the use of a receiver operating characteristic (ROC) curve. The curve is constructed by varying the cutpoint used to determine which values of the observed variable will be considered abnormal and then plotting the resulting sensitivities against the corresponding false positive rates. When two or more empirical curves are constructed based on tests performed on the same individuals, statistical analysis on differences between curves must take into account the correlated nature of the data. This paper presents a nonparametric approach to the analysis of areas under correlated ROC curves, by using the theory on generalized U-statistics to generate an estimated covariance matrix.

Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach.

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature The book is supported by a website that provides all data sets, questions for each chapter and links to software

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Experimental Design and Data Analysis for Biologists

Benjamini and Hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems. A simple procedure was given there as an FDR controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate. We prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses. This condition for positive dependency is general enough to cover many problems of practical interest, including the comparisons of many treatments with a single control, multivariate normal test statistics with positive correlation matrix and multivariate $t$. Furthermore, the test statistics may be discrete, and the tested hypotheses composite without posing special difficulties. For all other forms of dependency, a simple conservative modification of the procedure controls the false discovery rate. Thus the range of problems for which a procedure with proven FDR control can be offered is greatly increased.

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The control of the false discovery rate in multiple testing under dependency

The least squares estimator of a regression coefficient β is vulnerable to gross errors and the associated confidence interval is, in addition, sensitive to non-normality of the parent distribution. In this paper, a simple and robust (point as well as interval) estimator of β based on Kendall's [6] rank correlation tau is studied. The point estimator is the median of the set of slopes (Yj - Yi )/(tj-ti ) joining pairs of points with ti ≠ ti , and is unbiased. The confidence interval is also determined by two order statistics of this set of slopes. Various properties of these estimators are studied and compared with those of the least squares and some other nonparametric estimators.

Estimates of the Regression Coefficient Based on Kendall's Tau

Weak convergence of u-statistics and von mises'

Nonparametric methodologies are proposed to assess college students' performance. Emphasis is given to gender and sector of High School. The application concerns the University of Campinas, a research university in Southeast Brazil. In Brazil college is based on a somewhat rigid set of subjects for each major. Thence a student's relative performance can not be accurately measured by the Grade Point Average or by any other single measure. We then define individual vectors of course grades. These vectors are used in pairwise comparisons of common subject grades for individuals that entered college in the same year. The relative college performances of any two students is compared to their relative performances on the Entrance Exam Score. A test based on generalized U-statistics is developed for homogeneity of some predefined groups. Asymptotic normality of the test statistic is true for both null and alternative hypotheses. Maximum power is attained by employing the union intersection principle.

A nonparametric approach to assess undergraduate performance

For diabetes and some other chronic diseases or disorders usually some nondegradation stochastic processes are encountered in quality of life (QoL) studies These processes may not exhibit the degradation phenomenon until some other complications arise, as illustrated with two notable examples The biology of these disorders is outlined and along with the formulation of degradation and nondegradation stochastic processes, QoL perspectives are emphasized The concept of adjusted quality-adjusted survival analysis underlies our discussion A small simulation study is also appended

Quality of Life Perspectives in Chronic Disease and Disorder Studies

Stochastic approximation aims to estimate efficiently level crossing or extermal points of a nonparametric regression function in a parametric or nonparametric manner. For bundle strength of parallel filaments (with stochastic length, cross section etc.,) and in some other problems, one has an extended statistical functional where ψ is a suitable function and G(x|y) stands for a conditional distribution function of X, the dependent variate, given the independent variate Y=y. For a compact set C chosen from extraneous considerations, the problem of interest is to locate an optimal y0∊C, in the sense that . Nonparametric estimation of the conditional distribution G(.|y), nonlinear nature of the functional θ(·), and the fact that y is in continuum in C add complexity to possible statistical resolutions and create impasses for a direct application of the well known Bechhofer-Gupta-Sobel methodology. General asympotics for the selection procedures arising in this context are considered with due emphasis on a s...

Stochastic approximation and selection of a conditional extermal function in continuum

SUMMARY This paper deals with the statistical analysis (both parametric and non-parametric) of 'mixed model' experiments. The general structure of such experiments involves n randomly chosen subjects who respond once to each of p distinct treatments. Thus the subject or block effects are random and treatment effects are fixed. The hypothesis of no treatment effects is considered under several different combinations of assumptions concerning the joint distribution of the observations corresponding to each of the particular subjects. For each situation, an appropriate test procedure is discussed and its properties studied. The different methods considered in the paper are illustrated in detail in two numerical examples. These examples have been chosen to illustrate the relative performances of the different test criteria for a situation in which the null hypothesis is essentially true (Example 1) and for a situation in which the null hypothesis is essentially false (Example 2). The reader may wish to begin by studying these examples for a better understanding of the theory. Finally, the section on examples contains algorithms for the efficient computation of the various test criteria. A computer program based on these algorithms has been written and can be made available to any interested persons.

Pranab Kumar Sen

Papers

Weak convergence of u-statistics and von mises'

A nonparametric approach to assess undergraduate performance

Quality of Life Perspectives in Chronic Disease and Disorder Studies

Stochastic approximation and selection of a conditional extermal function in continuum

Of the 'mixed model'