The Faculty of the Division of Biostatistics has an active program in methodological research. The areas of interest are broad and most of the research is devoted to the development of new statistical procedures that can be applied to the division’s collaborative research program.
- Survival Analysis
The Division is developing an international reputation as a locale for statistical research in the area of survival analysis and longitudinal data analysis. This area is anchored by the collaborative work of Professors Klein and Zhang with the researchers at Department of Biostatistics at the University of Copenhagen, which has resulted in 12 years of funding from the National Cancer Institute. Professor Laud is well known for his work in Bayesian methods for survival analysis. Professor Logan has also made contributions to this area.
- Clinical Trials
Professor Logan, working in the area of multiple comparisons, has interests in clinical trials with multiple end points and multiple decisions. He has proposed designs for randomized phase II clinical trials in which one is interested in evaluating several new treatments prior to a comparative phase III clinical trial. Professor Logan provides biostatistical support to a multicenter clinical trials network for blood and marrow transplant research.
- Bayesian Methodology
Bayesian methodology is finding increasing number of applications in Biostatistics. This is reflected in the work of the faculty in the Division. Professor Laud has been conducting methodological research in Bayesian nonparametric and semiparametric techniques, especially as applicable to survival data. He has also published papers in parametric Bayesian methodology, in linear and generalized linear models with an emphasis on model selection. Professor Logan also has an interest in Bayesian methods, in particular in the areas of clinical applications and in the analysis of fMRI (functional magnetic resonance imaging) data.
- Image Analysis
The Medical College of Wisconsin is a leading institution in the area of functional magnetic resonance imaging (fMRI) research with interdisciplinary research involving several departments such as Neurology, Psychiatry, Radiology and Biophysics. From the Division of Biostatistics, Professor Logan, Rowe and Zhang are conducting collaborative and methodological work in this area. Professor Zhang has analyzed fMRI data using covariate adjusted ROC curves, working with Professor Lee of the Biophysics Department. Professor Logan has compared individual voxel thresholding methods for identifying active voxels in single-subject fMRI datasets. Professors Rowe and Logan have proposed a way to directly model the complex valued fMRI data, rather than just the magnitude data as is typically done in fMRI analysis.
- Multiple Comparisons
The problem of multiple comparisons arises when performing many hypothesis tests, in which case the “familywise error rate” or chance of one or more incorrect significant findings among all these tests increases with the number of tests being performed. Professor Logan has a keen interest in this area in which he continues to publish new methods and applications. Working with Professor Rowe, Professor Logan has investigated multiple comparison thresholding techniques in single-subject fMRI analysis. Professor Logan's work with Professor Tamhane at Northwestern University includes the problem of comparing two treatments at multiple endpoints and multiple comparison procedures to identify the minimum effective dose and/or maximum safe dose in the dose-response setting. In collaboration with Professor Zhang, Professor Logan has investigated methods for controlling the familywise error rate when performing pairwise comparisons among several groups when the outcome is the time to an event of interest.
- Statistical Genetics
The Division's research in statistical genetics is led by Professor Wang. His recent work includes various genetic data analyses, linkage and association mapping of disease genes, modeling and methodology development for association mapping of quantitative trait loci, and haplotype association analysis of single nucleotide polymorphisms (SNPs).
Specifically, Professor Wang explored the definitions and properties of additive, dominance and epistatic effects of QTL and partition of genetic variance in an equilibrium as well as in a disequilibrium population. In joint work with Professors Weir and Zeng he developed a population-based multipoint LD method for fine mapping of quantitative trait loci. A mixture model was applied to describe the relationship between phenotype and QTL genotypes. An EM algorithm was developed to estimate the genetic effects of QTL and joint haplotype frequencies of QTL and markers.
- Model Selection
Model selection is one of the central issues in the application of statistical methods. It includes comparison of two models, variable selection in linear and generalized linear models, and model checking via goodness of fit tests as well as diagnostic statistics and plots.