Abstract A01: Prism regression: A new statistical tool for understanding determinants of cancer health disparities
Authors: Messinger Shari , Kobetz Erin , Rao J Sunil 
Published: October 2015

Abstract
As part of our ongoing collaboration with community stakeholders throughout the Miami metropolitan area, we have become increasingly aware of the limitations imposed by current measurements of race. Our stakeholders uphold that the categorical variable (black vs. white) most commonly used to approximate this social construct lacks necessary dimension for understanding its significance and contribution to persistent health disparity.
In response to this input, we introduce a class of generalized regression models for cancer outcomes, which allow the coefficient of race to vary as a function of other variables. These other variables involve factors that typically interact with the race focus variable. Existing varying coefficient models (VCMs) have been limited in a number of ways: they do not easily extend to allow multiple effect modifiers at once, and they do not allow interactions between the effect modifier variables. We developed “prism regression” to overcome these limitations in a data-adaptive, non-parametric manner. Joint modeling of the effect modifiers can be viewed as a prism through which the overall race coefficient is “refracted” in different directions (the variables defining the prism are what we term prism variables). This allows one to delineate patterns of racial differences in cancer outcomes that were previously hidden or masked. Our particular implementation of prism regression uses a rule-based decision tree structure, which is extremely intuitive to understand. Importantly, these tree-like structures can be extended in elegant ways to allow for much more complex effect modification. One such example, which we term hierarchical prism regression, allows the effect of race to vary as a function of layered, directional effect modifiers (i.e. prism variables and hierarchical variables together). This cannot be accomplished by existing methods such as multiway interactions, mediation or moderation. We detail the prism regression methodology and demonstrate some optimality properties based on a new constrained parameter estimation algorithm called “prism fusion” that provides not only more accurate predictions due to shrinkage, but also evidence for or against the presence of effect modification. We compare prism regression to existing methods using a series of simulation studies and show significant gains in predictive accuracy. In addition, we analyzed data from the cancer registry of Florida to search for complex effect modification of racial disparity.
The Florida Cancer Data System is Florida's legislatively mandated, population-based, statewide cancer registry. It is the second largest population based, cancer incidence registry in the nation processing over 180,000 new cases are from patient medical records annually, corresponding to 1155,000 newly diagnosed tumors since 1981. Cancer cases are submitted by hospitals, freestanding ambulatory surgical facilities, radiation therapy facilities, private physicians and death certificates. Information includes routine personal and demographic data, includes diagnosis, stage of disease, tissue pathology, and first course of medical treatment as well as passive death certificate linkage information. We illustrate the usefulness of prism regression focusing on breast cancer patients from the FCDS registry to investigate the individual and contextual level factors that lead to differential effects of race in relation to stage of disease at diagnosis. Individual level variables obtained from the FCDS registry are linked by geocode to obtain contextual variables from census data. We consider the individual level information as prism variables, and the geocode linked contextual level variables as hierarchical variables.
Citation Format: Shari Messinger, Erin Kobetz, J Sunil Rao. Prism regression: A new statistical tool for understanding determinants of cancer health disparities. [abstract]. In: Proceedings of the Seventh AACR Conference on The Science of Health Disparities in Racial/Ethnic Minorities and the Medically Underserved; Nov 9-12, 2014; San Antonio, TX. Philadelphia (PA): AACR; Cancer Epidemiol Biomarkers Prev 2015;24(10 Suppl):Abstract nr A01.