The study of racial/ethnic inequalities in health is important to reduce the uneven burden of disease. In the case of colorectal cancer (CRC), disparities in survival among non-Hispanic Whites and Blacks are well documented, and mechanisms leading to these disparities need to be studied formally. It has also been established that body mass index (BMI) is a risk factor for developing CRC, and recent literature shows BMI at diagnosis of CRC is associated with survival. Since BMI varies by racial/ethnic group, a question that arises is whether differences in BMI are partially responsible for observed racial/ethnic disparities in survival for CRC patients. This article presents new methodology to quantify the impact of the hypothetical intervention that matches the BMI distribution in the Black population to a potentially complex distributional form observed in the White population on racial/ethnic disparities in survival. Our density mediation approach can be utilized to estimate natural direct and indirect effects in the general causal mediation setting under stronger assumptions. We perform a simulation study that shows our proposed Bayesian density regression approach performs as well as or better than current methodology allowing for a shift in the mean of the distribution only, and that standard practice of categorizing BMI leads to large biases when BMI is a mediator variable. When applied to motivating data from the Cancer Care Outcomes Research and Surveillance (CanCORS) Consortium, our approach suggests the proposed intervention is potentially beneficial for elderly and low-income Black patients, yet harmful for young or high-income Black populations.

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