#### Abstract

We propose a new approach to studying the relationship between a very high dimensional random variable and an outcome. Our method is based on a novel concept, the supervised distance matrix, which quantifies pairwise similarity between variables based on their association with the outcome. A supervised distance matrix is derived in two stages. The first stage involves a transformation based on a particular model for association. In particular, one might regress the outcome on each variable and then use the residuals or the influence curve from each regression as a data transformation. In the second stage, a choice of distance measure is used to compute all pairwise distances between variables in this transformed data. When the outcome is right-censored, we show that the supervised distance matrix can be consistently estimated using inverse probability of censoring weighted (IPCW) estimators based on the mean and covariance of the transformed data. The proposed methodology is illustrated with examples of gene expression data analysis with a survival outcome. This approach is widely applicable in genomics and other fields where high-dimensional data is collected on each subject.

#### Disciplines

Biostatistics | Statistical Methodology | Statistical Models | Statistical Theory

#### Suggested Citation

POLLARD, Katherine S. and van der Laan, Mark J., "Supervised Distance Matrices: Theory and Applications to Genomics" (June 2008). *U.C. Berkeley Division of Biostatistics Working Paper Series.* Working Paper 238.

http://biostats.bepress.com/ucbbiostat/paper238

#### Included in

Biostatistics Commons, Statistical Methodology Commons, Statistical Models Commons, Statistical Theory Commons