Multiple third-variable analysis for competing risk data-With an application to explore racial disparity in breast cancer recurrence.

There are many racial and ethnic disparities in cancer outcomes. Through special studies supported by CDC, we found that compared with Caucasians, African-American women with breast cancer were more likely to have cancer recurrences. We are interested in exploring this racial disparity by identifying risk factors that contribute to the disparity and quantify their effects. Cancer may recur after a disease-free (cancer cannot be detected) period. In exploring cancer recurrences, it is important to take into account competing events, for example, a patient died of cancer but never had a disease-free period. We propose the use of the Fine-Gray model in the multiple third-variable analysis to explore the racial disparity. The challenges were that we have to deal with left-truncated and right-censored data and use different weights in the third-variable analysis when exploring different distributions of risk factors among different racial populations. We propose an algorithm for the analysis and apply the method to explore the racial disparity in cancer recurrence on breast cancer patients diagnosed in 2011 in Louisiana. The racial disparity in breast cancer recurrence was partially explained by the tumour characteristics at the time of diagnosis, cancer subtypes and treatment, and the patients' residential environmental conditions. We are able to explain 50% of the disparity. The method is implemented in the R package .