Cancer hazard rates reveal a hidden dimension of cancer

Despite detailed reports on the epidemiology of cancer published by registries they hardly ever mention hazard rates h(t). Which is unfortunate since hazard rates reveal more cancer biology than any survival curve S(t). Observe the next curve depicting breast cancer observed survival. It obviously declines, yet what is less obvious how it declines! From the third year and onward the slope of the curve continually declines. In other words, the magnitude of this decline declines with time. This cumbersome sentence means that breast cancer hazard rate h(t) declines. In other words, the longer a patient lives the better her chances to survive! Yet this optimistic message may be deduced solely from hazard rates,

Data source: Surveillance, Epidemiology, and End Results (SEER) Program (www.seer.cancer.gov) SEER*Stat Database: Incidence - SEER 9 Regs Public-Use, Nov 2004 Sub (1973-2002), National Cancer Institute, DCCPS, Surveillance Research Program, Cancer Statistics Branch, released April 2005, based on the November 2004 submission.
Selection: Caucasian females with breast cancer, all stages. Age= {20 - 85y}.
Number at diagnosis: 313303
Computation: h(t) = #died / (#live at start of the interval - #lost to follow up)
Interval: One month
End point: Death from any cause


Bi-modal hazard BMH

The survival curve smooths out variation and hides a pattern of great consequence. The hazard rate is bi-modal. Initially it rises then declines to rise again. This pattern is called here bi-modal hazard (BMH). It is unique to cancer and does not appear in other chronic diseases. It is an epidemiological hallmark of cancer. It is so typical of cancer that it distinguishes cancer from other chronic diseases.

Cancer proceeds through two phases, compensated, when the tumor does not cause any damage or distress, and de-compensated, when the patient suffers. BMH is more pronounced in compensated cancer. The earlier cancer is detected the more distinct is BMH. In breast cancer it is most pronounced and far less distinct in lung cancer since when detected it is decompensated.

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