Statistics Seminar Series

Department of Mathematical Sciences
Center for Applied Mathematics and Statistics

New Jersey Institute of Technology

Fall 2008


All seminars are 4:00 - 5:00 p.m., in Cullimore Hall Room 611 (Math Conference Room) unless noted otherwise. Refreshments are usually served at 3:30 p.m., and talks start at 4:00 p.m. If you have any questions about a particular seminar, please contact the person hosting the speaker.


Speaker and Title

September 11, 2008

Dr. Kaifeng Lu, Merck Laboratories, Rahway, NJ
Sample Size Calculations for the Constrained Longitudinal Data Analysis Model

Sundar Subramanian

September 25, 2008
425 Fenster Hall 4:00PM

Dr. Ying Wei, Department of Biostatistics, Columbia University
Quantile Regression and its Application in Medical Sciences (abstract)
Sundar Subramanian

November 13, 2008

Dr. Bin Cheng, Department of Biostatistics, Columbia University
Statistical Assessment and Sample Size Calculation in QT/QTc Prolongation Studies
Chung Chang

December 4, 2008

Nan Kong, Educational Testing Services
K-Dependence Coefficient and L-Multivariate Association Coefficient
Chung Chang 




Sample Size Calculations for the Constrained Longitudinal Data Analysis Model:

The longitudinal data analysis model proposed by Liang & Zeger (2000) uses baseline as well as post-baseline values as dependent variables, and the baseline means are constrained to be the same across treatment groups due to randomization. We would like to address the issue of sample size calculations for this model. General results on the sample size calculations will be shown. The sensitivity of the sample size requirement to the configuration of the correlation structure and drop-out pattern will be assessed for both normal and continuous non-normal data using simulations. The performance of several ad-hoc approximations for sample size calculations will also be evaluated.

Recommendations under various conditions and implementation using a SAS macro will be discussed. Examples from two phase III clinical trials will be used for illustration.

Dr. Kaifeng Lu ~ September 11, 2008

Quantile Regression and its Application in Medical Sciences:

Classical least square regression explores the relationship between a response variable Y and its covariates X solely on estimating the covariate effect on the conditional mean E(Y|X). In contrast, quantile regression describes the covariates effect on the conditional quantilesQ(Y|X), such as the median, 0.1th or 0.9th quantile. This way, quantile regression provides a more complete picture of the relationship between Y and X. It can be particularly useful when the upper and lower tails of the conditional quantile functions behave very differently from thecentral trend, and the research interest is more focused on the tails of a distribution. The talk consists of two parts: 1) an introduction to the fundamental theories of quantile regression, including estimation,inference tools and goodness-of-fit methods. 2) Illustrative examples of its application in medical science, including exploration of early life risk factors for adult obesity based on a New York cohort, and construction of longitudinal growth chart to incorporate with anindividuals prior path.

Dr. Ying Wei ~ September 25, 2008

Statistical Assessment and Sample Size Calculation in QT/QTc Prolongation Studies:

To establish non-inferiority in QT/QTc prolongation of a test drug with respect to either a placebo or an active control, a thorough QT/QTc study is recommended by ICH (ICH E14, 2005) which concerns statistical inference on the maximal time-matched drug effect. The existing statistical methods for assessing such effects suffer either power loss or parameter restriction. We propose a new asymptotic test with small sample correction based on distribution of maximum of correlated random variables under both a parallel- group design and a crossover design. Simulations indicate that our proposed test has adequate powers. For design purpose, the impact on power and sample size calculation for routine QT studies with ECG recording replicates under a parallel-group design and a crossover design is examined. Formulas for sample size calculations with and without adjustment for covariates were derived under both the parallel-group design and the crossover design. The results indicate that the approach of replicates may require a smaller sample size for achieving the same power when the correlation coefficient between the recording replicates (or repeated measures) is close to 0 (i.e., these replicate ECGs are almost independent). On the other hand, if the correlation coefficient is close to 1, then there is not much gain regardless whether replicate ECGs are considered. In this paper, an approach to identifying optimal allocation between the number of subjects and the number of replicates per subject is proposed for achieving the maximum power under a fixed budget constraint. The proposed approach can also be applied to minimize the cost for a given power.

Dr. Bin Cheng ~ November 13, 2008

K-Dependence Coefficient and L-Multivariate Association Coefficient:

Given a system of multiple random variables, a new measure called the L-multivariate association coefficient is defined using (conditional) entropy. Unlike traditional correlation measures, the L-multivariate association coefficient measures the multiassociations or multirelations among the multiple variables in the given system; that is, the L-multivariate association coefficient measures the degree of the association for the given system. The L-multivariate association coefficient for the system of two random variables is also called the L-bivariate association coefficient. The association measured by the L-multivariate association coefficient is a general type of association, not any specific type of a linear or nonlinear association. Unlike the K-dependence coefficient, which is an asymmetrical measure, the L-multivariate association coefficient is a symmetrical measure. A direct application of the L-multivariate association coefficient is in variables selection or variables reduction. This paper also explores the relationship between the L-multivariate association coefficient and the K-dependence coefficient.

Nan Kong ~ December 4, 2008