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.

/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

In the multivariate one-sample location model, only L-estimators are affine equivariant; we propose a class of flexible robust, affine equivariant L-estimators of location, for distributions invoking affine-invariance of Mahalanobis distances of individual observations. An involved iteration process for their computation is numerically illustrated.

/pdf/affine-equivariant-rank-weighted-l-estimation-of-2gop1lb5o6.pdf

Affine Equivariant Rank-Weighted L-Estimation of Multivariate Location

During the past four decades, clinical trials, having their genesis in biometric and epidemiologic studies, have been going through an evolutionary transition from simple biometric type to (randomized) multiphase placebo-controlled trials to active controlled equivalence trials to adaption of dynamic treatment regimens, all generally relating to symptomatic diagnostics. In this scenario, a newcomer is bioinformatics with its battery of thousands of genes, interacting with the disease/disorder complexities as well as with environmental Stressors of diverse types. Although the impact of genomics is not yet totally clear, statistical challenges are mounting, and there is a dire need for development of novel and largely nonstandard methodology to cope with the basic statistical modeling and inference tasks. Some of these perspectives are appraised here with due consideration of their impact on modern clinical trials.

Clinical Trials and the Genomic Evolution: Some Statistical Perspectives

Asymptotics via sub-sampling Bahadur-type representations

On a class of rank order estimators of contrasts in manova

In a simple multivariate measurement error regression model, the classical least squares estimator does not consistently estimate the vector of the slope parameters. Under multinormality, linear regression stands valid, although with some discount factor. The situation is entirely different when the multinormality assumption is dispensed with. In genomics studies. data models relate to excessively high dimensions where the multinormality assumption may rarely be tenable, and in addition, measurement errors in the regressor is universally anticipated. As such, robustness perspectives call for other estimators which may require less stringent distributional regularity assumptions. The Theil-Sen estimator in high-dimentional measurement error setups is studied here with due emphasis on genomics studies.

http://csa.sagepub.com/content/63/1-4/37.full.pdf

Pranab Kumar Sen

Papers

Affine Equivariant Rank-Weighted L-Estimation of Multivariate Location

Clinical Trials and the Genomic Evolution: Some Statistical Perspectives

Asymptotics via sub-sampling Bahadur-type representations

On a class of rank order estimators of contrasts in manova

The Theil-Sen Estimator in Genomic High Dimensional Mearsurement Error Models Perspectives