Peto's paradox

Peto's Paradox is the observation, due to Richard Peto, that at the species level, the incidence of cancer does not appear to correlate with the number of cells in an organism. For example, the incidence of cancer in humans is much higher than the incidence of cancer in whales. This is despite the fact that a whale has many more cells than a human. If the probability of carcinogenesis were constant across cells, one would expect whales to have a higher incidence of cancer than humans.

Peto, a statistical epidemiologist at the University of Oxford, first formulated the paradox in 1977. Writing an overview of the multistage model of cancer, Peto noted that, on a cell-for-cell basis, humans were much less susceptible to cancer than mice:

A man has 1000 times as many cells as a mouse... and we usually live at least 30 times as long as mice. Exposure of two similar organisms to risk of carcinoma, one for 30 times as long as the other, would give perhaps 30⁴ or 30⁶ (i.e., a million or a billion) times the risk of carcinoma induction per epithelial cell. However, it seems that, in the wild, the probabilities of carcinoma induction in mice and in men are not vastly different. Are our stem cells really, then, a billion or a trillion times more "cancerproof" than murine stem cells? This is biologically pretty implausible; if human DNA is no more resistant to mutagenesis in vitro than mouse DNA, why don't we all die of multiple carcinomas at an early age?

Peto went on to suggest that evolutionary considerations were likely responsible for varying per-cell carcinogenesis rates across species.

Within members of the same species, cancer risk and body size appear to be positively correlated, even once other risk factors are controlled for. A 25-year longitudinal study of 17,738 male British civil servants, published in 1998, showed a positive correlation between height and cancer incidence with a high degree of statistical confidence, even after risk factors like smoking were controlled for. A similar 2011 study of more than one million British women found strong statistical evidence of a relationship between cancer and height, even after controlling for a number of socioeconomic and behavioral risk factors. A 2011 analysis of the causes of death of 74,556 domesticated North American dogs found that cancer incidence was lowest in the smaller breeds, confirming the results of earlier studies.

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