Relationships between some risk factors and breast cancer incidence are known to vary by tumor subtype. However, breast tumors can be classified according to a number of markers, which may be correlated, making it difficult to identify heterogeneity of risk factors with specific tumor markers when using standard competing-risk survival analysis. In this paper, we propose a constrained competing-risk survival model that allows for assessment of heterogeneity of risk factor associations according to specific tumor markers while controlling for other markers. These methods are applied to Nurses' Health Study data from 1980-2006, during which 3,398 incident invasive breast cancers occurred over 1.4 million person-years of follow-up. Results suggested that when estrogen receptor (ER) and progesterone receptor (PR) status are mutually considered, some risk factors thought to be characteristic of "estrogen-positive tumors," such as high body mass index during postmenopause and increased height, are actually significantly associated with PR-positive tumors but not ER-positive tumors, while other risk factors thought to be characteristic of "estrogen-negative tumors," such as late age at first birth, are actually significantly associated with PR-negative rather than ER-negative breast cancer. This approach provides a strategy for evaluating heterogeneity of risk factor associations by tumor marker levels while controlling for additional tumor markers.
Keywords: breast cancer; competing risks; proportional hazards model.