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bioRxiv · 10.1101/060970

Fitting the Erlang distribution to cancer incidence by age may predict key carcinogenic events

Aleksey V. Belikov
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Abstract

Cancer is the second-leading cause of death worldwide, after cardiovascular diseases. Cancers arise from various cells and organs at different ages and develop at different rates. However, the reasons for this variation in the cancer progression rate and the age of onset are poorly understood. Especially puzzling is the late-life decrease in cancer incidence, which cannot be explained by previously proposed power law or exponential growth equations. By using the latest publicly available USA cancer incidence statistics, comprised of 20 million cancer cases documented over 14 years, I show that cancer incidence by age closely follows the Erlang probability distribution (R2=0.9543-0.9999), which is a special case of the gamma distribution. The Erlang distribution describes the probability y of k independent random events occurring by the time x, but not earlier or later, with each event happening on average every b time intervals. This fits well with the multiple-hit hypothesis, and potentially allows to predict the number k of key carcinogenic events and the average time interval b between them, for each cancer type. Moreover, the amplitude parameter A likely predicts maximal populational susceptibility to a given type of cancer. These parameters are estimated for 20 most common cancer types, and provide clues for further research on cancer development.

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Aleksey V. Belikov. 2016-06-27. Fitting the Erlang distribution to cancer incidence by age may predict key carcinogenic events. https://doi.org/10.1101/060970

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