Abstract
Regression analysis is a mature body of knowledge, but there might be room for one more strategy with advantages regarding a class of problems common in modern medical research. Specifically, modern lines of investigation often involve several tens or a few hundred subjects but several hundred assays of cryptically related markers (e.g. blood plasma proteins for ~100 patients vs the same for ~100 unaffected persons). The class arises because research is expensive and sometimes carries a degree of risk to subjects. Also, reliable interpretation of results may employ not just a set of individually distinguished markers, but networks of related markers that are collectively—but not so much individually—informative. This article explores a linear regression strategy that chooses markers parsimoniously but also calculates weights robustly in the sense that both marker choices and weights are generally invariant with respect to small changes in input data. Furthermore, the method allows integration of markers of very different types, thereby improving classification performance and suggesting etiologies and treatments.
