Cancer death statistics: analogy between epidemiology and critical systems in physics

The determination of risk factors in carcinogenesis is said to be an essential step towards the understanding of this disease. Most mathematical models describing the evolution of mortality figures use the concept of death probability (or "force of mortality" or "hazard of death"). When summarizing the death statistics through this unique parameter, one implicitly makes the assumption that the death events are independent from one individual to another. In this paper, we show that this hypothesis has profound consequences as it implies a "gaussian" behavior of the death statistics fluctuations. In order to verify the validity of this assumption, French cancer death statistics between the years 1978-1996 are examined. Their fluctuations, for every age bracket, are computed and then compared to the expected gaussian fluctuations that should emerge from a model of death probability. We show that the observed fluctuations are in close agreement with a gaussian model up to 35-40 years. After 40 years, the fluctuations are much higher and cannot be explained by a model where every individual would have a given "probability of death". These observations may produce a new insight into old-age cancer mortality. It suggests that there could exist a major difference between cancers in young or older organisms: cancer developed in young organisms are the consequence of a specific attack against an organ (essentially originated from a single cause, like a virus or a genetic deficiency). On the other hand, older organism are closer to a "critical state" and, as such, the outcome of a cancer in a given organ could be the consequence of a chain of "malfunctions" (analogous to an avalanche in physical systems) in the entire organism.