Abstract:
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High-throughput technologies generate a large number of biomarkers and the biomarkers involved in the same underlying etiological mechanism are often connected through some biological networks. Moreover, the effects of biomarkers on the disease onset time may vary with a particular disease marker representative of a subject's disease stage. We propose a varying-coefficient proportional hazards model to incorporate high-dimensional and network-structured biomarkers or covariates to predict time to disease onset subject to right censoring. For estimation, we propose a doubly regularized local partial likelihood function, where a weighted $L_1$-penalty is used to retrieve sparsity and a Laplacian regularization is used to incorporate the network information among the covariates. We describe an efficient algorithm to estimate the regression coefficients, establish theoretical properties of the effect estimators, and derive weak oracle properties. Numeric simulations demonstrate these advantages and significant improvements over existing methods. Finally, the methods are applied to a newly completed comprehensive epidemiological study on Huntington's disease (HD).
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