How Many Etiological Subtypes of Breast Cancer
Our group has leveraged the application of biostatistical models to complement descriptive epidemiology. First, we used two-component mixture models to determine whether bimodal age distributions at diagnosis fitted the data better than a single density (Figure 2, A and B). Then, to confirm qualitative age interactions (eg, Figure 1A), we used age–period–cohort (APC) models to evaluate age-specific effects independent of calendar-period effects (that relate to screening, changing diagnostic and/or practice patterns) and/or birth-cohort effects (generational and/or exposure factors).
We initially identified three distinct age-specific incidence rate patterns that were closely associated with seven histopathological breast cancer subtypes. Incidence rates of infiltrating duct, tubular, and lobular carcinomas rose rapidly until age 50 years, then increased more slowly, similar to rates for breast cancer overall. Rates for medullary and inflammatory breast carcinomas increased rapidly until age 50 years, then flattened or fell, similar to ER-negative rates (Figure 1A). Finally, rates for papillary and mucinous carcinomas increased steadily with age, similar to ER-positive rates (Figure 1A) and much like cancers at many other organ sites such as colorectal cancer.
Notwithstanding the three distinct incidence rate patterns, two-component mixture models demonstrated that six of the histopathological subtypes had bimodal age distributions at diagnosis with early-onset and/or late-onset peak frequencies around the stereotypical ages of 50 and 70 years. The one notable exception was medullary carcinoma, which showed a unimodal age distribution with mode close to age 50 years. Medullary carcinomas are linked to the loss of BRCA1 function, which we propose may represent the closest known approximation to an etiologically pure early-onset subtype of breast cancer.
Similar to ER-positive and ER-negative breast cancers (Figure 2B), the bimodal peaks for different histopathological categories do not sharply divide cancers into pure groups, but rather reflect central tendencies of what we propose are two fundamental etiological classes. Breast cancers that develop at extreme ages are likely to be highly enriched for one etiological class, but both of these classes span the entire lifespan, with substantial mixing during the middle years, when many cancers occur. The mixing fraction or proportion of each etiological group varies within a class of breast cancers depending on its definition; however, the peak ages remain near ages 50 and 70 years.
A useful APC function is the fitted (or longitudinal) age-specific incidence rate curve (Figure 1A). The fitted curve stitches together the age-specific incidence rates from a collection of birth cohorts, each one observed over a limited and variable age span (ie, younger cohorts are observed at younger ages and older cohorts at older ages). The resulting curve estimates the age-specific rates of the middle or reference cohort over the entire age range. In contrast with the typical cross-sectional, age-specific incidence rate curve that may be confounded by period and cohort effects, the fitted curve is conditioned upon cohort and adjusted for period changes.
Clemmesen's menopausal hook for breast cancer overall was once dismissed as a birth-cohort artifact, where the progressive increase in breast cancer risk from one generation to the next gave the appearance of falling incidence rates among older persons. This view is refuted by APC models, which demonstrate that the Clemmesen's phenomenon is a true age-related event that persists in the fitted age-specific incidence rate curve (Figure 1A). Similar modeling approaches confirm that the qualitative age interaction remains for the fitted curves for ER-positive and ER-negative breast cancers, respectively.
Biostatistical Models
Our group has leveraged the application of biostatistical models to complement descriptive epidemiology. First, we used two-component mixture models to determine whether bimodal age distributions at diagnosis fitted the data better than a single density (Figure 2, A and B). Then, to confirm qualitative age interactions (eg, Figure 1A), we used age–period–cohort (APC) models to evaluate age-specific effects independent of calendar-period effects (that relate to screening, changing diagnostic and/or practice patterns) and/or birth-cohort effects (generational and/or exposure factors).
Two-component Mixture Models
We initially identified three distinct age-specific incidence rate patterns that were closely associated with seven histopathological breast cancer subtypes. Incidence rates of infiltrating duct, tubular, and lobular carcinomas rose rapidly until age 50 years, then increased more slowly, similar to rates for breast cancer overall. Rates for medullary and inflammatory breast carcinomas increased rapidly until age 50 years, then flattened or fell, similar to ER-negative rates (Figure 1A). Finally, rates for papillary and mucinous carcinomas increased steadily with age, similar to ER-positive rates (Figure 1A) and much like cancers at many other organ sites such as colorectal cancer.
Notwithstanding the three distinct incidence rate patterns, two-component mixture models demonstrated that six of the histopathological subtypes had bimodal age distributions at diagnosis with early-onset and/or late-onset peak frequencies around the stereotypical ages of 50 and 70 years. The one notable exception was medullary carcinoma, which showed a unimodal age distribution with mode close to age 50 years. Medullary carcinomas are linked to the loss of BRCA1 function, which we propose may represent the closest known approximation to an etiologically pure early-onset subtype of breast cancer.
Similar to ER-positive and ER-negative breast cancers (Figure 2B), the bimodal peaks for different histopathological categories do not sharply divide cancers into pure groups, but rather reflect central tendencies of what we propose are two fundamental etiological classes. Breast cancers that develop at extreme ages are likely to be highly enriched for one etiological class, but both of these classes span the entire lifespan, with substantial mixing during the middle years, when many cancers occur. The mixing fraction or proportion of each etiological group varies within a class of breast cancers depending on its definition; however, the peak ages remain near ages 50 and 70 years.
APC Models
A useful APC function is the fitted (or longitudinal) age-specific incidence rate curve (Figure 1A). The fitted curve stitches together the age-specific incidence rates from a collection of birth cohorts, each one observed over a limited and variable age span (ie, younger cohorts are observed at younger ages and older cohorts at older ages). The resulting curve estimates the age-specific rates of the middle or reference cohort over the entire age range. In contrast with the typical cross-sectional, age-specific incidence rate curve that may be confounded by period and cohort effects, the fitted curve is conditioned upon cohort and adjusted for period changes.
Clemmesen's menopausal hook for breast cancer overall was once dismissed as a birth-cohort artifact, where the progressive increase in breast cancer risk from one generation to the next gave the appearance of falling incidence rates among older persons. This view is refuted by APC models, which demonstrate that the Clemmesen's phenomenon is a true age-related event that persists in the fitted age-specific incidence rate curve (Figure 1A). Similar modeling approaches confirm that the qualitative age interaction remains for the fitted curves for ER-positive and ER-negative breast cancers, respectively.
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