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

/pdf/experimental-design-and-data-analysis-for-biologists-8ybva8d53x.pdf

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.

/pdf/the-control-of-the-false-discovery-rate-in-multiple-testing-426hrdkyhb.pdf

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

Bivariate high-level exceedance and the Chen-Stein theorem in genomics multiple hypothesis testing perspectives

A CLASS of nonparametric tests based on Hoeffding's (1948) U-statisticsis shown to be robust for heterogeneity of the distributions of the sample observations ; the theory is illustrated by means of some known tests. Let X10 • •• , Xn be independent (real or vector valued) random variables having cumulative distribution functions (cdf's) F1(x), ... Fn(x) respectively. Let n be the set of all cdf's closed under the following (countable) set operation: if FidJ. for i = 1, 2, ... , then (1/n)Lt~tFtt:!2 for all n;>l. It is assumed that Fn = (F1, ••. , Fn) is an element of the product set Qn, and the null hypothesis states that

/pdf/on-a-robustness-property-of-a-class-of-nonparametric-tests-2c5dc4zdjf.pdf

On a Robustness Property of a Class of Nonparametric Tests Based on U­Statistics*

On sequential nonparametric estimation of multivariate location

Isotonic M-estimation of location parameters in the multivariate simple location model is considered under an orthant restriction on the parameters. The union-intersection principle and theory of M-estimation of location are incorporated in the formulation of some robust preliminary test and the derived estimator is studied under the null hypothesis as well as a sequence of local alternatives.

On Preliminary Test Isotonic M-Estimation of Multivariate Location Parameters

In a classical measurement error model, true regressors, though unknown, vary stochastically around the true level. In inhalation toxicology, environmental epidemiology, and some other problems, the administered dose may not be completely absorbed into the system, resulting in a stochastic compliance where the actual dose intake is smaller in magnitude, so the classical measurement error models may not be tenable. We introduce some logistic models for stochastic compliance of various types incorporating a Beta-compliance distribution. These compliance-adjusted models are categorized into three types: (i) Low (or near zero) dose levels, (ii) moderate dose levels, and (iii) high dose levels, resulting in different forms. The bootstrap method is incorporated to draw statistical conclusions based on BAN estimators.

Pranab Kumar Sen

Papers

Bivariate high-level exceedance and the Chen-Stein theorem in genomics multiple hypothesis testing perspectives

On a Robustness Property of a Class of Nonparametric Tests Based on UStatistics*

On sequential nonparametric estimation of multivariate location

On Preliminary Test Isotonic M-Estimation of Multivariate Location Parameters

Nondifferentiable errors in beta-compliance integrated logistic models

Pranab Kumar Sen

Papers

Bivariate high-level exceedance and the Chen-Stein theorem in genomics multiple hypothesis testing perspectives

On a Robustness Property of a Class of Nonparametric Tests Based on U­Statistics*

On sequential nonparametric estimation of multivariate location

On Preliminary Test Isotonic M-Estimation of Multivariate Location Parameters

Nondifferentiable errors in beta-compliance integrated logistic models

On a Robustness Property of a Class of Nonparametric Tests Based on UStatistics*