SCHEDULE OF TALKS

TITLES AND ABSTRACTS

A Test for Individual Bioequivalence
Thomas Mathew
University of Maryland-Baltimore

The concept of individual bioequivalence is important in the context of testing the equivalence of a generic drug product to a brand name drug. The data for testing bioequivalence consist of the area under the time-concentration curve, or simply the area under the curve (AUC), for a group of individuals who receive both the generic drug and the brand name drug. A crossover design is used to collect the data. Typically, AUC follows a lognormal distribution. The individual bioequivalence criterion is simply the expected value of the squared difference between the log(AUC) for the brand name drug and that for the generic drug, for the same individual. The criterion is scaled suitably, and we conclude individual bioequivalence if the criterion is less than a specified threshold. Thus the problem of testing individual bioequivalence consists of testing if the criterion is less than the threshold. The tests that are currently available for the problem are quite conservative. In the talk, I will explain the individual bioequivalence criterion, the mixed models that are used to model the log(AUC) data, and I will introduce a new test that is less conservative. Numerical results concerning the performance of the test will be reported and the results will be illustrated with examples.

Optimization of Governmental Decisions
Ginta Uzulina
Purdue University

The report presents some of the outcomes of research on Quantitative Methods of Analysis for the Drafts of Governmental Decisions, which discusses the role of impact assessment and evaluation of governmental decisions, as well as the role of one of the traditional statistical methods in solving applied problems of economic policy. The objective of the report is to highlight one of the possible methods how to find optimal allocation of finance for governmental policy measures to provide higher expected gains as a result of the chosen set of allocation. According to the decision theory we assume that a policy maker does not know the real state of nature at the moment of taking decision and therefore the policy maker does not know the actual consequences as a result of the action. If the policy maker chooses an action then the actual consequences are not certain because the state of nature is not known. It means that if the policy maker makes an action allocating finance for certain measures, then he or she does not know what the exact consequences will be. There is no clear answer or guarantee in policy making that the policy maker has made the optimal allocation of finances and that it will provide the highest value of gains. The possibilities of allocation are unlimited. Therefore, to find the optimal action of allocation the policy maker should predict what consequences could be as a result of this action. Allocation is closely linked with the number of support recipients for each measure. On one hand the policy maker does not known the actual number of potential beneficiaries, but on the other hand he or she must fix it with specific criteria of eligibility in order to target financial support to the specific target groups. These criteria should be targeted to achieve specific objectives of each measure. The criteria have an important role in policy making because they influence results of the actions. If a target group or number of recipients will be defined by weak criteria then policy and allocated finance may not reach the specific target group, where problems exist. If the number of recipients will be too limited by these criteria then some parts of the target group could be outside of beneficiaries. If criteria will not be set effectively then there could be a shortage of finance or a surplus of finance for some measures. How to find the balance in estimation of recipients according to fixed criteria? Precise estimation of the number of recipients is necessary. This, however, is unknown for the decision-maker, because the behavior of a human is not predictable. The policy maker has a certain level of uncertainty because some of the eligible recipients could not apply for state support or other privileges due to their preferences or any other reason, which are also not predictable. In this case there is several unsolved problems for the policy maker - how to estimate the number of recipients, how to allocate funds? In order to answer the above-mentioned questions, a statistical model is developed as a support tool for the decision-maker to choose the best action in the available set of actions. Theory of decision is used as a statistical model in seeking solutions to various questions. The functions of the losses (gains) are defined on the basis of statistical data and practices, as well as the necessary distributions of probability are substantiated in the model of decision theory.

An Optimization Approach for the Parameter Estimation in Nonlinear Mixed Effects Models
Jing Wang
Louisiana State University

Nonlinear mixed-effects models (NLMM) have received a great deal of attention in the statistical literature in recent years because of the flexibility they offer in handling the unbalanced repeated-measurements data that arise in different areas of investigation, such as pharmacokinetics. We concentrate here on maximum likelihood estimation for the parameters in nonlinear mixed-effects models. A rather complex numerical issue for maximum likelihood estimation in nonlinear mixed-effects models is the evaluation of the likelihood, which is given in the form of a multiple integral that, in most cases, does not have a closed-form expression. We restrict our attention in this article on numerical methods that are based on approximation for the likelihood. In addition, for a general optimization problem, iterative methods are usually required to update the parameter estimates iteratively. The objective of this paper is to propose an optimization approach for the parameter estimation in nonlinear mixed-effects models. This optimization method implements Importance Sampling for approximating likelihood and a stochastic recursive procedure for updating parameter estimates in NLMM. Simulations are performed in order to compare this approach to the other optimization methods.

Breast Cancer Detection Using Rank Nearest Neighbor Classification Rules
Subhash C. Bagui
The University of West Florida

In this talk, we propose a new generalization of the rank nearest neighbor (RNN) rule for multivariate data for diagnosis of breast cancer. We study the performance of this rule using two well known databases and compare the results with the conventional k-NN rule. We observe that this rule performed remarkably well, and the computational complexity of the proposed k-RNN is much less than the conventional k-NN rule.

Statistical Analysis of Internet Traffic Data
Cheolwoo Park
University of Florida

It is important to characterize burstiness of Internet traffic and find the causes for building models that can mimic real traffic. To achieve this goal, exploratory analysis tools and statistical tests are needed, along with new models for aggregated traffic. This talk introduces statistical tools based on wavelets and SiZer (SIgnificance of ZERo crossings of the derivative). The intricate fluctuations of Internet traffic are explored in various respects and lessons from real data analyses are summarized.

Estimation of a Normal Dispersion Matrix Using Shrinkage Correlation L Estimators
Nabendu Pal
University of Louisiana at Lafayette

Estimation of a normal dispersion matrix in a decision theoretic set-up has received attention from many researchers over the past three decades. However, relatively less attention was paid to estimation of correlation coefficients (simple correlation coefficient, intra-class correlation coefficient, coefficient of multiple determination, etc.). In the recent past, we have shown that shrinkage correlation estimators perform better under risk as well as Pitman Nearness criterion. In this paper we have constructed improved dispersion matrix estimators by using shrinkage correlation estimators thereby bridging the gap between improved dispersion matrix estimation and improved correlation estimation.

On Selecting a Process with the Smallest Number of Unfortunate Events
Madhuri S. Mulekar
University of South Alabama

Managers often desire to assign resources to minimize balking in service systems. Discrete event simulations are often used to study alternative assignments. When the number of balking events in a business day is approximated by a Poisson distribution, the objective becomes that of selecting a population corresponding to the smallest mean number of unfortunate events. A procedure for selecting a Poisson population with the smallest mean is described in which the selection is carried out based on a random sample of size n from each population. Examples of a bank lobby and manufacturing process are used to illustrate this procedure.

Exact Properties of Five Tests for Multinomial Proportions
Yong Cai
University of Louisiana at Lafayette
[11/20/2004, 11:00 - 11:30]

Exact properties the chi-square test, likelihood ratio test (LRT), Hoel's test (1938, Annals of Mathematical Statistics, 9, 158-165), Nass' test (1959, Biometrika, 46, 365-385) and an exact test, for testing the multinomial proportions are investigated numerically. Based on our numerical investigation, we have some interesting findings to discuss about the commonly used the $\chi^2$-test. Some recommendations regarding the choice of a test for practical applications are given, and the tests are illustrated using a biological example.

Visual Analysis For Cultivar Evaluation On Soybean Data Using GGE Biplot
Meiqin Zhang
Louisiana State University

Multi-environment trials (MET) are conducted every year for major crops throughout the world to evaluate cultivars and make recommendations. This has been an important issue in plant breeding and agricultural research. Superior crop cultivars must be identified through MET. Typically, there are two types of data, genotype by environment data and genotype by trait data, in multi-environment trials. GGE biplot software is a powerful and ideal tool to visually analyze these two types of MET data. The methodology has numerous merits. It can draw conclusions visually and reveal patterns more easily and elegantly. In this study, we used GGE biplot software to analyze a two year and two location soybean data from the Agricultural Research Station of Virginia State University. The results have provided insightfully graphic views on yield and multiple trait performance, as well as the correlations among traits for soybean maturity groups.

An Exact Method for Testing Equality of Several Binomial Proportions to a Specified Standard
Jessica Thomson
Louisiana State University Health Sciences Center

The problem of testing equality of several binomial proportions to a specified standard is considered. An exact method of testing based on the test statistic considered in Kulkarni and Shah (1995, Statistics and Probability Letters, 25, 213-219) is proposed. Exact properties of the exact test and the approximate test due to Kulkarni and Shah are evaluated numerically. Numerical studies show that the sizes of the approximate test due to Kulkarni and Shah often exceed the nominal level by a considerable amount, while the exact test never exceeds the nominal level. A procedure for constructing simultaneous confidence intervals is also given. The methods are illustrated by application to data involving epilepsy and mental health disorders.

Modified Nel and Van der Merwe test for the multivariate Behrens-Fisher problem
Jianqi Yu
University of Louisiana at Lafayette

A new test for the multivariate Behrens-Fisher problem is obtained by modifying Nel and Van der Merwe's (1986) test. The new test is affine invariant and it simplifies to the Welch's approximate solution to the univariate case. The merits of the new test and two existing invariant tests are evaluated using Monte Carlo method. Monte Carlo comparison shows that the new test is as powerful as other two methods while controlling the sizes satisfactorily.

The Joint Distribution of Surplus Immediately Before Ruin And The Deficit at Ruin Under Interest Force
Kumer Das
Auburn University

Consider an insurance portfolio. Suppose the number of claims occurring in the portfolio in a time interval is a homogeneous Poisson process. The premium that the insurance company receives for this portfolio is paid continuously with a constant rate . The company also receives interest on its reserves with an interest force. It is assumed that the premiums received per unit time exceed the expected claim payments per unit time. The surplus of the insurance company at a given time is treated as a continuous-time stochastic process. Ruin is said to occur at the first instant the surplus becomes negative, if it ever happens. The purpose of this study is to show how a Laplace Transformation technique can be used to derive results concerning the probabilities of ruin, given that ruin occurs. Two special cases are treated in more detail: the case with exponential claim sizes and gamma claim sizes.

Dynamic SAS Programming
Annapurna Ravi
Sam Houston State University

This paper shows how to implement various procedures in SAS without actually knowing the syntax (i.e., dynamic SAS programming). It particularly makes life easy for non-SAS users who actually know which procedure to use but don't have complete knowledge of the procedure. It shows various screens (A/F frames) which have Click and Go capability for different procedures. It helps Non-SAS users to use numerous procedures in SAS more efficiently as they can select the procedure, select the required data set and then implement the procedure on the selected data set without actually typing in source code. For SAS users, it's a time saver if the required number of options is large.