Tree-structured supervised learning and the genetics of hypertension

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Abstract
This paper is about an algorithm, FlexTree, for general supervised learning. It extends the binary tree-structured approach (Classification and Regression Trees, CART) although it differs greatly in its selection and combination of predictors. It is particularly applicable to assessing interactions: gene by gene and gene by environment as they bear on complex disease. One model for predisposition to complex disease involves many genes. Of them, most are pure noise; each of the values that is not the prevalent genotype for the minority of genes that contribute to the signal carries a “score.” Scores add. Individuals with scores above an unknown threshold are predisposed to the disease. For the additive score problem and simulated data, FlexTree has cross-validated risk better than many cutting-edge technologies to which it was compared when small fractions of candidate genes carry the signal. For the model where only a precise list of aberrant genotypes is predisposing, there is not a systematic pattern of absolute superiority; however, overall, FlexTree seems better than the other technologies. We tried the algorithm on data from 563 Chinese women, 206 hypotensive, 357 hypertensive, with information on ethnicity, menopausal status, insulin-resistant status, and 21 loci. FlexTree and Logic Regression appear better than the others in terms of Bayes risk. However, the differences are not significant in the usual statistical sense.