A Generalized Integration Approach to Association Analysis with Multi-category Outcome: An Application to a Tumor Sequencing Study of Colorectal Cancer and Smoking.

Cancer is a heterogeneous disease, and rapid progress in sequencing and -omics technologies has enabled researchers to characterize tumors comprehensively. This has stimulated an intensive interest in studying how risk factors are associated with various tumor heterogeneous features. The Cancer Prevention Study-II (CPS-II) cohort is one of the largest prospective studies, particularly valuable for elucidating associations between cancer and risk factors. In this paper, we investigate the association of smoking with novel colorectal tumor markers obtained from targeted sequencing. However, due to cost and logistic difficulties, only a limited number of tumors can be assayed, which limits our capability for studying these associations. Meanwhile, there are extensive studies for assessing the association of smoking with overall cancer risk and established colorectal tumor markers. Importantly, such summary information is readily available from the literature. By linking this summary information to parameters of interest with proper constraints, we develop a generalized integration approach for polytomous logistic regression model with outcome characterized by tumor features. The proposed approach gains the efficiency through maximizing the joint likelihood of individual-level tumor data and external summary information under the constraints that narrow the parameter searching space. We apply the proposed method to the CPS-II data and identify the association of smoking with colorectal cancer risk differing by the mutational status of APC and RNF43 genes, neither of which is identified by the conventional analysis of CPS-II individual data only. These results help better understand the role of smoking in the etiology of colorectal cancer.