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

In dose-response models, there are cases where only a portion of the administered dose may have an effect. This results in a stochastic compliance of the administered dose. In a previous paper (Chen-Mok and Sen, 1999), we developed suitable adjustments for compliance in the logistic model under the assumption of nondifferential measurement error. These compliance-adjusted models were categorized into three types: (i) Low (or near zero) dose levels, (ii) moderate dose levels, and (iii) high dose levels. In this paper, we analyze a set of data on the atomic bomb survivors of Japan to illustrate the use of the proposed methods. In addition, we examine the performance of these methods under different conditions based on a simulation study. Among all three cases, the adjustments proposed for the moderate dose case do not seem to work adequately. Both bias and variance are larger when using the adjusted model in comparison with the unadjusted model. The adjustments for the low dose case seem to work in reducing...

Nondifferentiable errors in beta-compliance integrated logistic models: numerical results

Exposure assessment is an important task in environmental risk assessment and should be done prior to formulating any dose response relationship. Understanding the presence or absence of an agent, and its concentration and distribution is the primary focus of an exposure assessment. Predictive models and environmental monitoring can be used to determine the levels of exposure at different points. Spatial prediction and interpolation of pollutant concentrations is considered here as a mode of exposure assessment. Models based on spatial covariance matrices with unknown elements are considered to construct a predictor of pollutant concentrations at points of interests. Bayesian approach with Markov Chain Monte Carlo (MCMC) techniques is implemented to estimate model parameters. An extensive simulation analysis is conducted to demonstrate the whole process of kriging for predicting the arsenic concentration in ground water used for personal usage.

Location Mapping Implications for Spatial Prediction of Low-Concentration Pollutants and the Arsenic Problem

Large-Sample Theory with Emphasis on Biostatistics†

reverse martingale, a Hajek-Renyi type inequality is derived, and its applications in some problems of simultaneous confidence regions are stressed. 1. Statement of the result. A variety of multivariate Chebyshev inequalities is available in the literature; we refer to Karlin and Studden (1966) and to Mudholkar and Rao (1967) which include earlier references. In the present note, for stochastic vectors, a simultaneous inequality comparable to Chow's (1960) semi-martingale extension of the H'ajek-Renyi (1955) inequality is considered. Let {Z., i > 1} be a sequence of stochastic p-dimensional column vectors,

A hajek-renyi type inequality for stochastic vectors

Pitman estimators of location are unbiased, translation-equivariant and possess some optimality properties under quadratic loss. Similar optimality properties of Pitman estimators are studied with respect to the measure of Pitman closeness of estimators.

Pranab Kumar Sen

Papers

Nondifferentiable errors in beta-compliance integrated logistic models: numerical results

Location Mapping Implications for Spatial Prediction of Low-Concentration Pollutants and the Arsenic Problem

Large-Sample Theory with Emphasis on Biostatistics†

A hajek-renyi type inequality for stochastic vectors

On Pitman closeness of Pitman estimators