Abstract
The widely accepted multiple-hit hypothesis of carcinogenesis states that cancers arise after several successive events. However, no consensus has been reached on the quantity and nature of these events, although “driver” mutations or epimutations are considered the most probable candidates. By using the largest publicly available cancer incidence statistics (20 million cases), I show that incidence of 20 most prevalent cancer types in relation to patients’ age closely follows the Erlang probability distribution (R2 = 0.9734–0.9999). The Erlang distribution describes the probability y of k independent random events occurring by the time x, but not earlier or later, with events 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 the maximal populational susceptibility to a given type of cancer. These parameters are estimated for 20 most common cancer types and provide numerical reference points for experimental research on cancer development.
Highlights
The value of cancer incidence and mortality curves for inferring information about the underlying carcinogenic processes has long been recognized[1]
The probability to be diagnosed with a particular cancer type at a particular age is the product of the maximal probability to be diagnosed with this cancer type at all during lifetime and the mortality-independent probability of the age at the cancer diagnosis falling within this age group
I have shown that cancer incidence by age is best approximated by the Erlang distribution
Summary
The value of cancer incidence and mortality curves for inferring information about the underlying carcinogenic processes has long been recognized[1]. Current data unequivocally show that cancer incidence ceases to increase with age but, for at least some cancers, decreases[8,9] This behaviour cannot be explained by growth equations and has been puzzling biologists and clinicians for considerable time. Of 16 tested continuous distributions, the best fit is observed for the gamma distribution and its special case – the Erlang distribution These two distributions describe the probability of several independent random events occurring precisely by the given time. This takes the multiple-hit hypothesis to a new level and allows to estimate the number of key carcinogenic events and the average time interval between them, for each cancer type. The estimated parameters suggest high heterogeneity in the carcinogenesis process and populational susceptibility amongst cancer types and provide reference points for experimental research
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