title: Incorporating auxiliary information for improved prediction in high-dimensional datasets: an ensemble of shrinkage approaches.
abstract: With advancement in genomic technologies, it is common that two high-dimensional datasets are available, both measuring the same underlying biological phenomenon with different techniques. We consider predicting a continuous outcome Y using X, a set of p markers which is the best available measure of the underlying biological process. This same biological process may also be measured by W, coming from a prior technology but correlated with X. On a moderately sized sample, we have (Y,X,W), and on a larger sample we have (Y,W). We utilize the data on W to boost the prediction of Y by X. When p is large and the subsample containing X is small, this is a p>n situation. When p is small, this is akin to the classical measurement error problem; however, ours is not the typical goal of calibrating W for use in future studies. We propose to shrink the regression coefficients β of Y on X toward different targets that use information derived from W in the larger dataset. We compare these proposals with the classical ridge regression of Y on X, which does not use W. We also unify all of these methods as targeted ridge estimators. Finally, we propose a hybrid estimator which is a linear combination of multiple estimators of β. With an optimal choice of weights, the hybrid estimator balances efficiency and robustness in a data-adaptive way to theoretically yield a smaller prediction error than any of its constituents. The methods, including a fully Bayesian alternative, are evaluated via simulation studies. We also apply them to a gene-expression dataset. mRNA expression measured via quantitative real-time polymerase chain reaction is used to predict survival time in lung cancer patients, with auxiliary information from microarray technology available on a larger sample.
authors.affiliation: Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109, USA. philb@umich.edu
authors.forename: Philip S
authors.initials: PS
authors.lastname: Boonstra
authors.forename: Jeremy M G
authors.initials: JM
authors.lastname: Taylor
authors.forename: Bhramar
authors.initials: B
authors.lastname: Mukherjee
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D056808:Biostatistics; D003198:Computer Simulation; D030541:Databases, Genetic / Q000706:statistics & numerical data*; D020869:Gene Expression Profiling / Q000706:statistics & numerical data; D023281:Genomics / Q000706:statistics & numerical data; D006801:Humans; D016018:Least-Squares Analysis; D016014:Linear Models; D008175:Lung Neoplasms / Q000235:genetics / Q000401:mortality; D012044:Regression Analysis; D016019:Survival Analysis