The number of key carcinogenic events can be predicted from cancer incidence

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.

Context-dependent selection as the keystone in the somatic evolution of cancer

“…Total and age-specific incidence: The pooled incidence of all cancer types lies well below 30%, while age-specific and cumulative incidence patterns show more variations between cancer types 24 . Interestingly, recent analyses have shown for several cancers that the age-specific incidence rates decline late in life in humans as well as in rodents [25][26][27] , in contrast with a previous belief of a monotonic power law increase in incidence with age 1,28 . Some theoretical explanations for this decline have been suggested 29,30 , but biologically interpretable and translationally useful insights are yet to be obtained.…”

Anthropogenic risk factors as the major cause of cancer driver events

“…It allows to estimate this number for any cancer type, upon fitting the Erlang distribution to the actual age distribution of incidence. I have shown that these numbers vary considerably, from 1 in retinoblastoma [2] to 41 in prostate cancer [1]. Next, it is important to show that these predictions correspond to experimentally observed variables, such as the number of driver mutations per tumor predicted from sequencing data.…”

“…I have recently proposed that the age distribution of cancer incidence can be interpreted as the statistical distribution of probability to accumulate the required number of driver events by the given age [1]. I have shown that, of all standard probability distributions, the gamma distribution (and its special case -the Erlang distribution) fits the actual age distribution of incidence for 20 most prevalent cancers the best [1].…”

“…I have recently proposed that the age distribution of cancer incidence can be interpreted as the statistical distribution of probability to accumulate the required number of driver events by the given age [1]. I have shown that, of all standard probability distributions, the gamma distribution (and its special case -the Erlang distribution) fits the actual age distribution of incidence for 20 most prevalent cancers the best [1]. I have then shown that the gamma/Erlang distribution is the only standard distribution that, in addition, converges for all studied childhood and young adulthood cancers, thus validating it as the universal equation describing cancer incidence [2].…”

“…Next, it is important to show that these predictions correspond to experimentally observed variables, such as the number of driver mutations per tumor predicted from sequencing data. However, the variability of DNA alterations that can contribute to cancer progression, some of which are not yet routinely assessed, and the imperfection of algorithms for separating driver and passenger mutations severely complicate this task, as discussed in [1]. Thus, a simpler correlate is required to prove the meaningfulness of the predictions, before engaging in a full-scale confirmation effort.…”