The left graph below depicts age adjusted incidence rate of breast cancer in white females. The data were derived from the SEER data base. The age adjusted rate stands for the chance of a woman to get breast cancer at a given age. Up to the age of 45y the curve becomes steeper and steeper and then takes a turn and   climbs    somewhat slower. At the age of 75y it reaches a peak and then declines. The right graph depicts the rate of change of the left graph, known also as incidence rate acceleration IA = Incidence[age] - Incidence[age+1].

Thet change in the slope at the age of 45y is known as Clemmessen’s hook (Clemmesen J: Carcinoma of the breast. Br J Radiol 21(252): 583–590, 1948). It is attributed to menopause.  Yet there is more to it. The curve indicates the  capability of the organism to resist cancer.   Two processes determine the outcome of cancer. 1. From birth and onward cancer is driven by an independent carcinogenic process. 2. Tumor growth which is controlled by the organism.  The age adjusted incidence depicts the probability of tumor surfacing at a given age.

This probability is determined by the tumor growth rate. The faster tumor growth the steeper the curve.  Tumor growth rate depends further on   host resistance.    Initially host resistance is low and  the rate of tumor surfacing rises. At the age of 45y the curve takes a turn and rises slower.   Beyond the age of 80y tumor surfacing stops.

The downward trend of the curve in old age has yet another explanation. Since at this age death from myocardial infarction or stroke predominates, some of these patients may carry into their grave a hidden cancer
and contribute to the downward incidence rate. However phenomena like Clemmessen's hook indicate that the decline of the tumor surfacing rate starts relatively early in life when strokes are not so common like in old age.

Since tumor surfacing depends on   host resistance  the curve indicates that with age the organism resists cancer better and better attaining its greatest potency in advanced age. Menopause is a manifestation of rising  host resistance. Since some tumors are estrogen dependent, menopause slows down tumor growth.  This also is the rationale of the adjuvant chemotherapy of an estrogen antagonist called tamoxifen.

Since a similar curve flattening appears in most chronic cancers, like lung and bronchus (see below). Host resistance is mediated also by factors other than hormones.

Further reading: Late life mortality

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