Apr 12

1:45 pm

## Pacific Northwest Statistics Meeting 1996

### P Gustafson & R Olshen

Seminar

**Paul Gustafson, Department of Statistics, University of British Columbia**

*Hierarchical Bayesian Modelling for Survival Data*

Hierarchical Bayes models can be flexible tools for the analysis of failure time data. This will be illustrated by two examples. The first example is in a clinical trials context, when there are several response times for each patient, and many patients at each clinical centre. Frailties are used to model both across-patient variability and across-centre variability. The second example involves a hierarchical model which relaxes some of the common modelling assumptions for survival data. In particular, hazards are not assumed to be proportional, and covariate effects are not assumed to be additive on the log-hazard scale. The hierarchical structure is useful in that it parsimoniously penalizes violations of the two assumptions, with the strength of the penalty being determined by the data. The hybrid Monte Carlo algorithm is the computational tool used in both examples. This algorithm may have some advantages over better-known Markov Chain Monte Carlo algorithms.

**Richard Olshen, Departments of Health Research and Policy, Electrical Engineering, & Statistics, Stanford University**

*Tree-Structured Clustering with Applications to Imaging and HIV Genetics*

The talk will begin with a review of statistical problems in classification and clustering, with an emphasis on binary tree-structured methods. The clustering is of k-means type and is used for "lossy" coding of images. We sometimes wish to "compress" an image by coding its pixel blocks and also to classify the blocks as to whether they contain something of special interest such as a tumor in the case of a medical image. I will present algorithms that enable both goals to be achieved. The clustering also applies to understanding "quasi-species" in the context of HIV genetics, in particular the V3 loop region. Examples will be given to illustrate the applications. If time permits, I will describe some asymptotic properties of the algorithms. These results come from collaborations with many individuals over the past six years.