Multivariate Concordance Correlation Coefficient
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Multivariate Concordance Correlation Coefficient
In many clinical studies, the Lin's concordance correlation coefficient (CCC) is a common tool to assess the agreement of a continuous response measured by two raters or methods. However, the need of measures of agreement may arise for more complex situations, such as when the responses are measured on more than one occasion by each rater or method. In this work, we propose a new CCC in the presence of repeated measurements, called the multivariate concordance correlation coefficient. We constructed the multivariate CCC based on a matrix that possesses the properties needed to characterize the level of agreement between two p x 1 vectors of random variables. For ease of interpretation, we transformed this matrix to a scalar whose value is scaled to range between -1 and 1 by using three distinct functions, namely trace, highest eigenvalue, and determinant. It can be shown that the multivariate CCC reduces to Lin's CCC when p = 1. For inference, we proposed an asymptotically unbiased estimator based on U-statistics and derived its asymptotic distribution for each form of the function. The proposed estimators are proven to be asymptotically normal and their performances are evaluated via simulation studies. To obtain a confidence interval or a test statistic, we considered a sample moment estimator of the asymptotic variance and the Z-transformation to improve the normal approximation and bound the confidence limits. The simulation studies confirmed that overall in terms of accuracy, precision, and the coverage probabilities, the estimator of the multivariate CCC based on the determinant function works relatively well in general cases even with small samples. However, for a skewed underlying distribution with moderate or weaker correlation between the two variables, the trace multivariate CCC is slightly more robust. Finally, We used real data from an Asthma Clinical Research Network(ACRN) study and the Penn State Young Women's Health Study for demonstration.
Distributions With Given Marginals and Statistical Modelling
Author: Carles M. Cuadras
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-11-11
This volume contains the papers presented at the meeting "Distributions with given marginals and statistical modelling", held in Barcelona (Spain), July 17- 20, 2000. This is the fourth meeting on given marginals, showing that this topic has aremarkable interest. BRIEF HISTORY The construction of distributions with given marginals started with the seminal papers by Hoeffding (1940) and Fn!chet (1951). Since then, many others have contributed on this topic: Dall' Aglio, Farlie, Gumbel, Johnson, Kellerer, Kotz, Morgenstern, Marshali, Olkin, Strassen, Vitale, Whitt, etc., as weIl as Arnold, Cambanis, Deheuvels, Genest, Frank, Joe, Kirneldorf, Nelsen, Rüschendorf, Sampson, Scarsini, Tiit, etc. In 1957 Sklar and Schweizer introduced probabilistic metric spaces. In 1975 Kirneldorf and Sampson studied the uniform representation of a bivariate dis tribution and proposed the desirable conditions that should be satisfied by any bivariate family. In 1991 Darsow, Nguyen and Olsen defined a natural operation between cop ulas, with applications in stochastic processes. In 1993, AIsina, Nelsen and Schweizer introduced the notion of quasi-copula
Repeated Measurements and Cross-Over Designs
Author: Damaraju Raghavarao
language: en
Publisher: John Wiley & Sons
Release Date: 2014-04-14
An introduction to state-of-the-art experimental design approaches to better understand and interpret repeated measurement data in cross-over designs. Repeated Measurements and Cross-Over Designs: Features the close tie between the design, analysis, and presentation of results Presents principles and rules that apply very generally to most areas of research, such as clinical trials, agricultural investigations, industrial procedures, quality control procedures, and epidemiological studies Includes many practical examples, such as PK/PD studies in the pharmaceutical industry, k-sample and one sample repeated measurement designs for psychological studies, and residual effects of different treatments in controlling conditions such as asthma, blood pressure, and diabetes. Utilizes SAS(R) software to draw necessary inferences. All SAS output and data sets are available via the book's related website. This book is ideal for a broad audience including statisticians in pre-clinical research, researchers in psychology, sociology, politics, marketing, and engineering.