Title: Estimation Following a Group Sequential Test for Distributions in the One-Parameter Exponential Family

Speaker: Aiyi Liu, Ph.D.
Principal Investigator/Mathematical Statistician
Biometry and Mathematical Statistics Branch
National Institute of Child Health and Human Development
National Institutes of Health
Bethesda, MD

Abstract: We consider unbiased estimation following a group sequential test for distributions in a one-parameter exponential family. We show that, for an estimable parameter function, there exists uniquely an unbiased estimator depending on the sufficient statistic and based on the truncation-adaptation criterion (Liu and Hall (1999)); moreover, this estimator is identical to one based on the Rao-Blackwell method. When completeness fails, we show that the uniformly minimum-variance unbiased estimator may not exist or might possess undesirable performance. A Phase-II clinical trial application with exponentially distributed responses is included.

Date: Friday, September 16, 2005

Time: 11:00-12:00 noon

Location: Rome Hall, Room 351

Title: Testable and Model-Preserving Parametric Constraints in a Parametric Probability Model

Speakers:

Dr. Somesh Das Gupta
Indian National Science Academy
New Delhi, India
Formerly of Indian Statistical Institute, Calcutta, India

and

Dr. Abhijit Das Gupta
Division of Cancer Epidemiology and Genetics
National Cancer Institute
Bethesda, MD

Abstract: We shall first introduce two basic concepts , namely "testable" parametric constraints and "model-preserving" parametric constraints. Some general results on these concepts are presented along with some examples to illustrate them. It will be noted that even when a hypothesis is stated in terms of a non-testable parametric constraint, some statistical inference can still be drawn on this by considering the ``equivalent" testable version of this hypothesis. Next, some of the results are specialized for the linear model. Lastly, a necessary and sufficient condition is obtained for a linear parametric constraint to be model-preserving.

Date: Friday, September 23, 2005

Time: 4:00-5:00 pm

Location: Rome Hall, Room 351

Second Symposium on Frontiers of Statistical, Mathematical and Computational Sciences

Titles and Speakers:

1. (9:00-9:50) Towards a generalized theory of uncertainty
   Professor Lofti Zadeh, Division of Computer Science, UC Berkeley
   
   
2. (9:50-10:40) Hierarchical structure in vision and language
   Professor Stuart Geman, Department of Applied Mathematics, Brown University
   
   
3. (11:10-12:00) Numerical range, and applications of anti-eigen/anti-singular values in statistics and physics
   Professor C. R. Rao, Department of Statistics, Pennsylvania State University
   
   
4. (1:30-2:20) Conditional distributions, reference measures, and nonlinear filtering
   Professor Thomas Kurtz, Department of Mathematics, University of Wisconsin
   
   
5. (2:20-3:10) Inference when current data restrict the range of future data
   Professor Jayaram Sethuraman , Department of Statistics, Florida State University and Indian Institute of Technology, Chennai, India
   
   
6. (3:10-4:00) Stochastic calculus, option pricing, and empirical behavior of asset prices
   Professor Michael Steele, Wharton School of Business, University of Pennsylvania
   
   

Date: Friday, September 30, 2005

Time: 8:45 am-4:10 pm

Location: 1957 E Street NW, Room 113

Title: Testing Degenerate Tensors in Diffusion Tensor Images

Speaker: Professor Hongtu Zhu
MRI unit, Department of Psychiatry
Columbia College of Physicians and Surgeons
and The New York State Psychiatric Institute

Abstract : Diffusion tensor (DT) images are used to map accurately the structure and orientation of fiber tracts in the white matter of the human brain in vivo. The directional dependence of diffusion is characterized by a matrix of the effective diffusion of water, denoted by D. Tractography algorithms have been developed to connect consecutive directions of maximal diffusion in order to reconstruct white matter tracts in the human brain in vivo. However, the performance of these algorithms is strongly influenced by the amount of noise in the images and by the number and prevalence of degeneracy in the brain where maximal diffusion is poorly defined. We propose a simple procedure for searching for degeneracy that uses rigorous test statistics based on invariant measures of diffusion tensors, such as fractional anisotropy. Our procedure effectively identifies singularities while accounting for the effects of noise. Examining DT images in human subjects, we demonstrate that this new procedure readily classifies diffusion tensors at each voxel into standard types (nondegenerate, oblate, prolate, and isotropic) without resorting to tensor characteristics at neighboring voxels. We also study the effects of singularities on the reconstructing fiber tracts in specific anatomical regions.

Date: Friday, October 14, 2005

Time: 11:00 am-12:00 pm

Location: Rome Hall, Room 351

Title: Augmented designs to assess immune response in vaccine trials

Speaker: Dean Follmann Ph.D.
Assistant Director for Biostatistics, NIAID
Chief Biostatistics Research Branch
National Institute of Allergy and Infectious Diseases

Abstract : This paper introduces methods for use in vaccine clinical trials to help determine if
the immune response to a vaccine is actually causing a reduction in the infection rate.
This is not easy because immune response to the (say HIV) vaccine is only observed in
the HIV vaccine arm. If we knew what the HIV-specific immune response in placebo
recipients would have been, had they been vaccinated, this immune response could be
treated essentially like a baseline covariate and an interaction with treatment could be
evaluated. Relatedly, the rate of infection by this baseline covariate could be compared
between the two groups and a causative role of immune response would be supported if
infection risk decreased with increasing HIV immune response only in the vaccine group.
We introduce two methods for inferring this HIV-specific immune response. The first
involves vaccinating everyone before baseline with an irrelevant vaccine, e.g. rabies.
Randomization ensures that the relationship between the immune responses to the rabies
and HIV vaccines observed in the vaccine group is the same as what would have been seen
in the placebo group. We infer a placebo volunteer's response to the HIV vaccine using
their rabies response and a prediction model from the vaccine group. The second method
entails vaccinating all uninfected placebo patients at the closeout of the trial with the
HIV vaccine and recording immune response. We pretend this immune response at closeout is
what they would have had at baseline. We can then infer what the distribution of immune
response among placebo infecteds would have been. Such designs may help elucidate the
role of immune response in preventing infections. More pointedly, they could be helpful
in the decision to improve or abandon an HIV vaccine with mediocre performance in a phase
III trial.

Date: Friday, October 28, 2005

Time: 4:00-5:00 pm

Location: Rome Hall, Room 351

Title: Composite Likelihood Inference in Spatial Generalized Linear Mixed Models

Speaker: Professor Tatiyana V. Apanasovich
School of Operations Research and Industrial Engineering
Cornell University

Abstract: Spatial GLMMs (Diggle, et al. 1998) are flexible models for a variety of applications where we have observations of spatially dependent and non-Gaussian random variables. As in a standard GLMM (Breslow and Clayton, 1993) given the random effects, which they model by a Gaussian random field, the observations are conditionally independent and follow a generalized linear model. In a number of applications, neither Bayesian nor maximum likelihood approaches appear practical for large sets of correlated data. To gain computational efficiency, one may approximate the objective function. Instead of the likelihood, we consider a composite likelihood (Lindsay, 1988), which is the product of likelihoods for subsets of data, and estimate parameters by maximizing this product. The asymptotic properties of such estimators will be outlined. The application of the methods to the data from the experiment on aberrant crypt foci (ACF), which are precursors of colon cancer, will be presented.

Date: Friday, November 11, 2005

Time: 11:00 am-12:00 noon

Location: Rome Hall, Room 351

Title: Bayesian Social Network Models with Acute Outcomes

Speaker: Dr. Yasmin H. Said
George Mason University

Abstract: I begin by introducing the concept of DALYs, Disability Adjusted Life Years and indicate that alcohol abuse is a major risk factor in public health. I give an illustration of exploratory analysis of the consequences of alcohol abuse using some contemporary visualization software. Alcohol abuse also leads to violence related acute outcomes for both society and individuals. Among these, I identify DWI crashes with fatalities, assault and battery, suicide, murder, sexual assault, domestic violence, and child abuse. Alcohol abusers are embedded in a social network that involves the user, family and friends, producers and distributors of alcohol products, law enforcement, the judiciary, remediation, education, detox and treatment facilities, which are coupled to insurance and managed-care programs. This complex network is reminiscent of more traditional biologic ecology systems, hence the name. The basic idea is to formulate a model of this network with the goal of exploring short- and long-term interventions that reduce the overall probability of acute outcomes. The framework that is being pursued is a dynamic agent-based simulation. The basic model is a stochastic directed-graph model that follows agents (sometimes referred to as actors or individuals) through a 24-hour period. The stochastic directed graph has two major features that are being developed. First, I engage in what I call scenario development. This involves development of scenarios of typical behaviors throughout a day for nonusers, casual drinkers, alcohol abusers, and alcoholics. Associated with these scenarios, I am developing methods for estimation of transition probabilities from state to state during the day reflecting different behaviors and specific to both ethnic groups and geographic location. It is clear that models of this type can be used to investigate negative effects of drugs post FDA approval. Also, it is clear that a similar model structure of social networks can be applied to terrorists networks with the same ability to examine interventions in order to assess their effectiveness.

Date: Friday, December 2, 2005

Time: 4:00-5:00pm

Location: Rome Hall, Room 351

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Location: Rome Hall, Room 351