Auxiliary Marker-Assisted Classification in the Absence of Class Identifiers

Constructing classification rules for accurate diagnosis of a disorder is an important goal in medical practice. In many clinical applications, there is no clinically significant anatomical or physiological deviation that exists to identify the gold standard disease status to inform development of classification algorithms. Despite the absence of perfect disease class identifiers, there are usually one or more disease-informative auxiliary markers along with feature variables that comprise known symptoms. Existing statistical learning approaches do not effectively draw information from auxiliary prognostic markers. We propose a large margin classification method, with particular emphasis on the support vector machine, assisted by available informative markers to classify disease without knowing a subject's true disease status. We view this task as statistical learning in the presence of missing data, and introduce a pseudo-Expectation-Maximization (EM) algorithm to the classification. A major difference between a regular EM algorithm and the algorithm proposed here is that we do not model the distribution of missing data given the observed feature variables either parametrically or semiparametrically. We also propose a sparse variable selection method embedded in the pseudo-EM algorithm. Theoretical examination shows that the proposed classification rule is Fisher consistent, and that under a linear rule, the proposed selection has an oracle variable selection property and the estimated coefficients are asymptotically normal. We apply the methods to build decision rules for including subjects in clinical trials of a new psychiatric disorder and present four applications to data available at the University of California, Irvine Machine Learning Repository.