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Schwartz et al. suggest that our observation (1) of the well-reported black–white crossover in age-specific breast cancer incidence disappearing after stratification by molecular subtype is an example of a Simpson’s Paradox. A Simpson’s Paradox can lead observers to incorrectly conclude that effects seen within subgroups reflect the true effect in the overall group. In such a situation, the observer must then carefully consider causality, confounding, and other knowledge about the subject matter to decide whether the subgroup or the overall population provides better information for answering the question under study (2).
We approached our analysis from a different perspective—namely, to ask whether the black–white crossover in overall breast cancer rates is also observed for breast cancer subtypes that are based on well-studied molecular subtypes defined jointly by hormone receptor and HER2 status. We concluded that the joint distributions of race/ethnicity and molecular subtype are more useful than race/ethnicity alone in understanding racial and ethnic differences in breast cancer occurrence. We further identified triple-negative (ie, hormone receptor–negative and HER2-negative) breast cancer as having very different age-specific incidence patterns compared with other subtypes, inferring etiologic heterogeneity. Schwartz and colleagues provide a graph of age-specific incidence rate ratios for estrogen receptor (ER)–positive vs ER-negative breast cancer among whites and blacks, which shows that the ratios are relatively consistent among races and suggests “similar effects within similar populations.” Using our own data, we extended that analysis by stratifying ratios further by HER2 status (Figure 1). The rate ratios for black and white women with HER2-positive cancers are similar across age groups, but for HER2-negative cancers the rate ratios increase slightly with age among black women and increase markedly with age among white women. This additional stratification by HER2 status shows that HER2-negative cancers may have differential occurrence among white women, especially at older ages.
We see a clear and continuing trend toward more division of cancers (not just breast cancers) into subtypes defined by factors beyond the anatomical site at which they were diagnosed so as to enable targeted therapeutics, to better unravel etiology, or simply to improve upon traditional taxonomy and nomenclature. The comments of Schwartz and colleagues serve as a reminder that those efforts to subdivide tumors can create the statistical conditions for seemingly paradoxical, but by no means insurmountable, subgroup vs overall effects.
This study was supported by the National Cancer Institute’s Surveillance, Epidemiology and End Results (SEER) program under contract HHSN261201000040C awarded to the Cancer Prevention Institute of California (CPIC).The collection of cancer incidence data used in this study was supported by the California Department of Public Health as part of the statewide cancer reporting program mandated by California Health and Safety Code Section 103885; the SEER Program under contract HHSN261201000040C awarded to CPIC (formerly the Northern California Cancer Center), contract HHSN261201000035C awarded to the University of Southern California, and contract HHSN261201000034C awarded to the Public Health Institute; the Centers for Disease Control and Prevention’s National Program of Cancer Registries, under agreement 1U58DP00807-01 awarded to the Public Health Institute.
The ideas and opinions expressed herein are those of the authors, and endorsement by the State of California, Department of Public Health the National Cancer Institute, and the Centers for Disease Control and Prevention or their Contractors and Subcontractors is not intended nor should be inferred. No authors report any financial conflict of interest. The study sponsors did not have any role in the design of the study, the analysis or interpretation of the data, the writing of the article, or the decision to submit the article for publication.