The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers
Background It is widely believed that cancers develop upon acquiring a particular number of (epi) mutations in driver genes, but the law governing the kinetics of this process is not known. We have previously shown that the age distribution of incidence for the 20 most prevalent cancers of old age i...
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| Format: | Article |
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PeerJ Inc.
2021-08-01
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| Series: | PeerJ |
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| Online Access: | https://peerj.com/articles/11976.pdf |
| _version_ | 1827607314072338432 |
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| author | Aleksey V. Belikov Alexey Vyatkin Sergey V. Leonov |
| author_facet | Aleksey V. Belikov Alexey Vyatkin Sergey V. Leonov |
| author_sort | Aleksey V. Belikov |
| collection | DOAJ |
| description | Background It is widely believed that cancers develop upon acquiring a particular number of (epi) mutations in driver genes, but the law governing the kinetics of this process is not known. We have previously shown that the age distribution of incidence for the 20 most prevalent cancers of old age is best approximated by the Erlang probability distribution. The Erlang distribution describes the probability of several successive random events occurring by the given time according to the Poisson process, which allows an estimate for the number of critical driver events. Methods Here we employ a computational grid search method to find global parameter optima for five probability distributions on the CDC WONDER dataset of the age distribution of childhood and young adulthood cancer incidence. Results We show that the Erlang distribution is the only classical probability distribution we found that can adequately model the age distribution of incidence for all studied childhood and young adulthood cancers, in addition to cancers of old age. Conclusions This suggests that the Poisson process governs driver accumulation at any age and that the Erlang distribution can be used to determine the number of driver events for any cancer type. The Poisson process implies the fundamentally random timing of driver events and their constant average rate. As waiting times for the occurrence of the required number of driver events are counted in decades, and most cells do not live this long, it suggests that driver mutations accumulate silently in the longest-living dividing cells in the body—the stem cells. |
| first_indexed | 2024-03-09T06:51:40Z |
| format | Article |
| id | doaj.art-ef4a82c0d4bb460aaaec831eeae97c4e |
| institution | Directory Open Access Journal |
| issn | 2167-8359 |
| language | English |
| last_indexed | 2024-03-09T06:51:40Z |
| publishDate | 2021-08-01 |
| publisher | PeerJ Inc. |
| record_format | Article |
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| spelling | doaj.art-ef4a82c0d4bb460aaaec831eeae97c4e2023-12-03T10:25:48ZengPeerJ Inc.PeerJ2167-83592021-08-019e1197610.7717/peerj.11976The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancersAleksey V. Belikov0Alexey Vyatkin1Sergey V. Leonov2Laboratory of Innovative Medicine, School of Biological and Medical Physics, Moscow Institute of Physics and Technology, Moscow, RussiaLaboratory of Innovative Medicine, School of Biological and Medical Physics, Moscow Institute of Physics and Technology, Moscow, RussiaLaboratory of Innovative Medicine, School of Biological and Medical Physics, Moscow Institute of Physics and Technology, Moscow, RussiaBackground It is widely believed that cancers develop upon acquiring a particular number of (epi) mutations in driver genes, but the law governing the kinetics of this process is not known. We have previously shown that the age distribution of incidence for the 20 most prevalent cancers of old age is best approximated by the Erlang probability distribution. The Erlang distribution describes the probability of several successive random events occurring by the given time according to the Poisson process, which allows an estimate for the number of critical driver events. Methods Here we employ a computational grid search method to find global parameter optima for five probability distributions on the CDC WONDER dataset of the age distribution of childhood and young adulthood cancer incidence. Results We show that the Erlang distribution is the only classical probability distribution we found that can adequately model the age distribution of incidence for all studied childhood and young adulthood cancers, in addition to cancers of old age. Conclusions This suggests that the Poisson process governs driver accumulation at any age and that the Erlang distribution can be used to determine the number of driver events for any cancer type. The Poisson process implies the fundamentally random timing of driver events and their constant average rate. As waiting times for the occurrence of the required number of driver events are counted in decades, and most cells do not live this long, it suggests that driver mutations accumulate silently in the longest-living dividing cells in the body—the stem cells.https://peerj.com/articles/11976.pdfProbability distributionDriver mutationsGrid searchPoisson processGamma distributionStem cells |
| spellingShingle | Aleksey V. Belikov Alexey Vyatkin Sergey V. Leonov The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers PeerJ Probability distribution Driver mutations Grid search Poisson process Gamma distribution Stem cells |
| title | The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers |
| title_full | The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers |
| title_fullStr | The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers |
| title_full_unstemmed | The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers |
| title_short | The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers |
| title_sort | erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers |
| topic | Probability distribution Driver mutations Grid search Poisson process Gamma distribution Stem cells |
| url | https://peerj.com/articles/11976.pdf |
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