BAYESIAN SHRINKAGE METHODS FOR PARTIALLY OBSERVED DATA WITH MANY PREDICTORS.
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 outcomeYto a large number of covariatesX, eg measurements from current, state-of-the-art technology. For most of the samples, only the outcomeYand surrogate covariates,W, 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 tradeoff. 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 dataset, predicting survival time (Y) using qRT-PCR (X) and microarray (W) measurements.
University of Michigan.
Philip S
PS
Boonstra
University of Michigan.
Bhramar
B
Mukherjee
University of Michigan.
Jeremy Mg
JM
Taylor
High-dimensional data; Markov chain Monte Carlo; measurement error; missing data; shrinkage