The bimodal hazard (BMH) is implied in a study published by Demicheli et al. (3). In their publication the  authors  concluded that surgical resection of primary breast tumor accelerates metastatic development. They  wrote : "The hazard functions for local-regional recurrences and distant metastases for breast cancer patients undergoing mastectomy alone proved to be double-peaked, with an early peak at about 18 months after surgery, a second peak at about 60 months, and a plateau-like tail extending out to 15 years”. They hypothesized that that “the early peak of the hazard function for recurrence is generated by the sudden acceleration of the metastatic process due to surgery”.

Demicheli et al. (3) studied recurrence hazard in pre-  and post-menopausal women.  1173 patients were treated solely with mastectomy and did not receive   neither chemotherapy nor x-irradiation.  The figure below was copied from their paper where it was labeled as Figure 2. It depicts  hazard rate for breast cancer recurrence (local-regional plus distant) after mastectomy alone as primary treatment in 1173 patients: (a) pre-menopausal patients; (b) post-menopausal patients

It is striking that the same pattern is observed in the SEER data.

The hazard rate actually indicates how fast cancer progresses.  In the young female the disease proceeds faster than in the old, and her hazard rate is higher, which is illustrated in  the figures below. They depict hazard rates of women with localized and regional breast cancer,  aged respectively  20-29y and 50-59y.

Following treatment the hazard rate of the young female is 0.004. It climbs to about 0.006, declines again and for the coming years remains at the 0.004 level which is higher than that of the older female (0.0025). In the older female the hazard following treatment is 0.0005, and it climbs to about 0.004. Altogether it climbs higher than in the younger one, yet returns to a lower level so that her disease progresses slower.

The next figures depict hazard rates during the first three years after treatment has begun.

In the young female the hazard rate rises immediately after treatment has begun and then drops to 0.004 whereupon it rises again. These women were particularly dependent upon their tumors since it was detected too early, before seeding metastasis. The older women were less tumor dependent. Note the similarity with Figure 2 above (3).

The next figures depict the relationship between  age at diagnosis and the change of the hazard rate during the first three years. The older the female at diagnosis the higher her hazard rate.  The distance between the two curves indicates how harmful  the treatment was. It is depicted in the right figure. The  higher the curve the more had the patient to depend upon her tumor.

Mammography paradox

These studies explain a mammography paradox described by Retsky et al. (2)  In the first years following screening the mortality of women aged 40–49 is somewhat higher than  in controls. This phenomenon was discovered by Cox (3)  Figure  1 (Retsky et al (2)) is reproduced  here. (The text in the graph was added by me)

Figure 1. Meta-analysis data for six screening trials for younger women from Cox showing the cumulative breast cancer specific mortality per screened individual and the equivalent mortality per unscreened control. The significant disadvantage ntage first appears 3 years into the trial where it is maximum. Modified from Cox (2)(3)


1.R.Demicheli ,G.Bonadonna,  WJM Hrushesky,  MW Retsky, P. Valagussa
Menopausal status dependence of the timing of breast cancer recurrence after surgical removal of the primary tumour
Breast Cancer Res 2004, 6:R689-R696  
. M. Retsky, R. Demicheli and W. J.M. Hrushesky
Does surgery induce angiogenesis in breast cancer? Indirect evidence from relapse pattern and mammography paradox  International Journal of Surgery  Volume 3, Issue 3
, 2005, Pages 179-187
3. B. Cox, Variation in the effectiveness of breast screening by year of follow-up, J Natl Cancer Inst Monogr 22 (1997), pp. 69–72

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