Hormonal Regulation of Breast Cancer Incidence Dynamics: A Mathematical Analysis Explaining the Clemmesen's Hook.

Clemmesen's hook refers to a commonly observed slowdown and rebound in breast cancer incidence around the age at menopause. It suggests a shift in the underlying carcinogenic dynamics, but the mechanistic basis remains poorly understood. Building on our previously developed Extended Multistage Clonal Expansion Tumor (MSCE-T) model, we perform a theoretical analysis to determine the conditions under which Clemmesen's hook would occur. Our results show that Clemmesen's hook can be quantitatively explained by time-specific changes in the proliferative and apoptotic balance of early-stage mutated cell populations, corresponding to the decline in progesterone levels and progesterone-driven proliferation due to reduced menstrual cycles preceding menopause, and changing dominant carcinogenic impact from alternative growth pathways post-menopause (e.g., adipose-derived growth signals). In contrast, variation in last-stage clonal dynamics cannot effectively reproduce the observed non-monotonic incidence pattern. Analytical results further demonstrate that midlife incidence dynamics corresponding to the hook are governed primarily by intrinsic proliferative processes rather than detection effects. Overall, this study provides a mechanistic and mathematical explanation for Clemmesen's hook and establishes a quantitative framework linking hormonal transitions during menopause to age-specific breast cancer incidence curve.