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Pranab Kumar Sen

Bio: Pranab Kumar Sen is an academic researcher from University of North Carolina at Chapel Hill. The author has contributed to research in topics: Estimator & Nonparametric statistics. The author has an hindex of 51, co-authored 570 publications receiving 19997 citations. Previous affiliations of Pranab Kumar Sen include Indian Statistical Institute & Academia Sinica.


Papers
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01 Jan 1997
TL;DR: In this article, the authors developed methods which bring together models for multivariate failure time data and competing risks under a unified framework, where observation continues past the first failure so that the remaining failures can be observed as one of generalized competing risks.
Abstract: SUMMARY. This research develops methods which bring together models for multivariate failure time data and competing risks under a unified framework. We refer to the situation where observation continues past the first failure so that the remaining failures can be observed as one of generalized competing risks. Under this more general setup, event-specific proportional hazards models for the first failure are formulated, and given the time and type of the first failure, conditional proportional hazards models for the remaining failures are similarly formulated. Estimation involves cross-classifying subjects into disjoint sets and the (conditional) stratum-specific partial likelihoods are pooled across strata to yield a total (conditional) partial likelihood for the first two failures. Maximum partial likelihood estimators (MPLEs) are obtained and their large-sample properties are examined. Weak convergence results for martingale stochastic processes are used to establish the weak consistency and asymptotic normality of the MPLEs and statistical tests are derived to assess the significance of the dependence of failure times on previous failures and on realized random covariates.

6 citations

01 May 1977
TL;DR: In this article, a class of analysis of covariance tests based on suitable linear rank statistics is proposed and studied, and some invariance principles for certain (multivariate) progressively censored rank order processes are established and incorporated in the study of the proposed tests.
Abstract: : In the context of survival analysis under a progressive censoring scheme, a class of analysis of covariance tests based on suitable linear rank statistics is proposed and studied. Some invariance principles for certain (multivariate) progressively censored rank order processes are established and incorporated in the study of the asymptotic properties of the proposed tests. (Author)

6 citations

01 Jan 2001
TL;DR: The present study aims to provide a general appraisal of survival analysis with due emphasis on clinical trials as well as pharmacogenomics.
Abstract: Summary Survival analysis with genesis in biometry and reliability analysis evolved with statistical modeling and analysis of life time data and survival distributions. During the past three decades, the advent of clinical trials has expanded its domain to clinical epidemiology, biomedical sciences, and public health disciplines, encompassing a variety of regression and noncompliance models. In this evolutionary process, parametrics gave way to more robust nonparametreics and semiparametrics where counting processes have stolen the methodoloic limelights. The past few years have witnessed a phenomenal growth of research in genomic sciences. From drug research and developmental perspectives, in pharmacogenoimcs there is a genuine need to incorporate survival analysis (albeit in a somewhat different form) in genomic clinical trials (involving biomarkers). The present study aims to provide a general appraisal of survival analysis with due emphasis on clinical trials as well as pharmacogenomics.

5 citations

Journal ArticleDOI

5 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered distribution free tests based on simple linear rank statistics and the classical union intersection principle in a progressively censored setup, and the main emphasis was laid on the development of the relevant asymptotic theory, and some (sub) martingale characterizations of progressively censored rank.
Abstract: Nonparametric testing procedures under progressive censoring schemes are often adopted in clinical trials and life testing experimentations. In a variety of situations, a null hypothesis (of the homogeneity of distributions) may be tested against a restricted viz., orthant or ordered alternative. Though such tests in a general setup have been considered in a complete sample or a single point censored (or truncated) experimental scheme, there has not been much progress with these tests in a progressively censored setup. Genuinely distribution free tests based on simple linear rank statistics and the classical union intersection principle are considered. The theory of such time sequential tests rests heavily on some basic invariance principles, and these are studied as well. The case of proportional hazard models is also treated briefly. The main emphasis is laid on the development of the relevant asymptotic theory, and in this context, some (sub) martingale characterizations of progressively censored rank ...

5 citations


Cited by
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Journal ArticleDOI
TL;DR: A nonparametric approach to the analysis of areas under correlated ROC curves is presented, by using the theory on generalized U-statistics to generate an estimated covariance matrix.
Abstract: 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.

16,496 citations

Journal Article
TL;DR: 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.
Abstract: 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

13,333 citations

Book
21 Mar 2002
TL;DR: An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data is as discussed by the authors, 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.
Abstract: 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

9,509 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that a simple FDR controlling procedure for independent test statistics can also control the false discovery rate when test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses.
Abstract: 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.

9,335 citations

Journal ArticleDOI
TL;DR: In this article, a simple and robust estimator of regression coefficient β based on Kendall's rank correlation tau is studied, where the point estimator is the median of the set of slopes (Yj - Yi )/(tj-ti ) joining pairs of points with ti ≠ ti.
Abstract: 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.

8,409 citations