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

Bounded risk estimation of the mean of a finite population is considered under three simple random sampling strategies: (i) with replacement, mean per unit estimation, (ii) with replacement, mean per distinct unit estimation, and (iii) without replacement, mean per unit estimation. It is well known that in the fixed sample size scheme, (iii) fares better than (ii) and (ii) better than (i). However, in the current context, the sample sizes are dictated by (possibly, degenerate) stopping times, and visualizing the cost (due to measurements/recording, etc.) as a function of the number of distinct units in the sample, it is shown that the second strategy still fares better than the first, although the third strategy may not perform better than the second one. Actually, in the case of known population variance, it is shown that in the light of the number of distinct units, the difference of ASN for the second and third strategies can never be greater than two or less than minus one. A similar relationship also...

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Bounded risk estimation of a finite population mean optimal strategies

Publisher Summary A sound statistical planning (design) of the experiment constitutes the first and foremost task in experimental studies. In a conventional setup, it is generally assumed that the response distribution is continuous, and further that it can be taken as normal whose mean (location parameter) depends linearly on the model based parameters, while the variance is a constant under varied experimental setups. The linearity of the model—that is, the additivity of the effects—homoscedasticity, and normality of the errors are the three basic regularity assumptions underlying the traditional parametric statistical analysis of experimental outcomes. In biological assays, biomedical and clinical experiments, the response variable is typically nonnegative and has a positively skewed distribution. Nonparametric and robust statistical procedures have their genesis in robustness and validity complex. Pedagogically, developments in nonparametrics started in the hypotheses testing sector, where under suitable hypotheses of invariance, the sample observations have a joint distribution which remains invariant under appropriate groups of transformations which map the sample space onto itself. This characterization of the null hypothesis generates exactly distribution-free (EDF) tests for some simple hypotheses testing problems.

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4 Design and analysis of experiments: Nonparametric methods with applications to clinical trials

Staggering entry, random withdrawal and progressive censoring schemes: Some nonparametric procedures

Nonparametric repeated significance tests for one-way anova with adoptation to multiple comparisons

In a stochastic environment, a degradation process, inspite of showing a mono- tone trend, may contain stochastic variations which may camouflage the statistical picture to a certain extent. There are, however, some other processes which may not exhibit a degradation phenomenon. For some of these nondegradation stochas- tic processes, associated aging perspectives are appraised, without being confined to a semiparametric fashion, and their application in health related quality of life assessment are considered.

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Pranab Kumar Sen

Papers

Bounded risk estimation of a finite population mean optimal strategies

4 Design and analysis of experiments: Nonparametric methods with applications to clinical trials

Staggering entry, random withdrawal and progressive censoring schemes: Some nonparametric procedures

Nonparametric repeated significance tests for one-way anova with adoptation to multiple comparisons

Aging perspectives in some nondegradation stochastic processes