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

Bioinformatics is an emerging field of science emphasizing the application of mathematics, statistics, and informatics to study and analysis of very large molecular biological (mostly, genetic and genomic) systems (data sets). In a comparatively broader setup of large biological systems without necessarily having a predominant genetic undercurrent, and having genesis in biometry to biostatistics, biostochastics has evolved as the primary vehicle for the much needed statistical reasoning. It is intended to point out the genuine need for statistical reasoning in this evolving interdisciplinary field, and in that way, to appraise the limitations of current (mostly, algorithm based) statistical resolutions.

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Bioinformatics to Biostochastics: Statistical Perspectives and Tasks Ahead

*Reprinted from Handbook of Sequential Analysis; Ghosh, B.K., Sen, P.K., Eds.; Marcel Dekker, Inc.: New York, 1991, 169–198.

Repeated significance tests in frequency and time domains

The problem of testing a general parametric hypothsis following a preliminary test on some other parametric restraints is considered. These tests are based on appropriate likelihood ratio statistics. The effect of the preliminary test on the size and power of the ultimate test is studied. In this context, some asymptotic distributional properties of some likelihood ratio statistics are studied and incorporated in the study of the main results. 1 . Introduction In a parametric model, the underlying distribution are of assumed forms and the parameter θ belongs to a parameter * Work supported by the National Heart, Lung and Blood Institute, Contract NIH-NHLBI-71-2243-L from the National Institutes of Health. AMS 1980 classifications. 62 Ε 20

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Asymptotic properties of likelihood ratio tests based on conditional specification

where # is the mean-effect, i l l , . . . , fin are the block effects (nuisance parameters for the f ixed effects model or random variables for the mixed effects model), "q, .. . , zc are the treatments effects, and the e~, are the error components. It is assumed that n, = (el,, . . . , e J , e 1 . . . . , n are independent and identically distributed stochastic vectors with a continuous cumulative distribution function (cdf) F(~), ~ R c (the real c space), where F(~) is symmetric in its c arguments, that is, for any ~ R c and any permutat ion (il, . . . , ic) of (1, .. . , c)

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Pranab Kumar Sen

Papers

Bioinformatics to Biostochastics: Statistical Perspectives and Tasks Ahead

Repeated significance tests in frequency and time domains

Asymptotic properties of likelihood ratio tests based on conditional specification

On some selection procedures in two-way layouts

Burden of bioinformatics in medical research: Statistical perspectives and controversies