Bayesian shrinkage methods for partially observed data with many predictors
arXiv:1401.2324 · doi:10.1214/13-AOAS668
Abstract
Motivated by the increasing use of and rapid changes in array technologies, we consider the prediction problem of fitting a linear regression relating a continuous outcome to a large number of covariates , for example, measurements from current, state-of-the-art technology. For most of the samples, only the outcome and surrogate covariates, , are available. These surrogates may be data from prior studies using older technologies. Owing to the dimension of the problem and the large fraction of missing information, a critical issue is appropriate shrinkage of model parameters for an optimal bias-variance trade-off. We discuss a variety of fully Bayesian and Empirical Bayes algorithms which account for uncertainty in the missing data and adaptively shrink parameter estimates for superior prediction. These methods are evaluated via a comprehensive simulation study. In addition, we apply our methods to a lung cancer data set, predicting survival time () using qRT-PCR () and microarray () measurements.
Published in at http://dx.doi.org/10.1214/13-AOAS668 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)