Multi-stage models for the failure of complex systems, cascading disasters, and the onset of disease

Webster, Anthony J

doi:10.1371/journal.pone.0216422

Cited by 16 publications

(20 citation statements)

References 50 publications

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“…Thus, it appears that the gamma/Erlang distribution is the only classical probability distribution that fits universally well to cancers of childhood, young adulthood and old age. The Weibull distribution can also approximate cancer incidence ( Webster, 2019 ), but would only be exactly correct for cancers with k = 1, when it becomes the exponential distribution.…”

Section: Discussionmentioning

confidence: 99%

The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers

Belikov

Vyatkin

Leonov

2021

PeerJ

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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.

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Section: Discussionmentioning

confidence: 99%

The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers

Belikov

Vyatkin

Leonov

2021

PeerJ

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“…More generally, trade-offs between longevity and reproductive success are common in nature (see Flatt and Partridge (2018) for a review; Sudyka et al (2019) for a study showing that reproductive success increases telomere attrition rate in birds). Cancer is merely one way for a body to fail over time, and our model, being suitable to be modified for different failures resulting from insufficient somatic maintenance (Kirkwood, 2015; Webster, 2019), could also shed light on other aspects of senescence.…”

Section: Discussionmentioning

confidence: 99%

Bird size with dinosaur-level cancer defences: can evolutionary lags during miniaturisation explain cancer robustness in birds?

Erten

Tollis

2020

Preprint

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An increased appreciation of the ubiquity of cancer risk across the tree of life means we also need to understand the more robust cancer defences some species seem to have. Peto's paradox, the finding that large-bodied species do not suffer from more cancer even if their lives require far more cell divisions than those of small species, can be explained if large size selects for better cancer defences. Since birds live longer than non-flying mammals of an equivalent body size, and birds are descendants of moderate-sized dinosaurs, we ask whether ancestral cancer defence innovations are retained if body size shrinks in an evolutionary lineage. Our model derives selection coefficients and fixation events for gains and losses of cancer defence innovations over macroevolutionary time, based on known relationships between body size, intrinsic cancer risk, extrinsic mortality (modulated by flight ability) and effective population size. We show that evolutionary lags can, under certain assumptions, explain why birds, descendants of relatively large bodied dinosaurs, retain low cancer risk. Counterintuitively, it is possible for a bird to be 'too robust' for its own good: excessive cancer suppression can take away from reproductive success. On the other hand, an evolutionary history of good cancer defences may also enable birds to reap the lifespan-increasing benefits of other innovations such as flight.

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“…Firstly consider m diseases in a composite endpoint that may be influenced by the same factors or processes, but are otherwise independent of each other. The survival probability is determined from the probability of an individual surviving all m diseases until time t. If S j (t) is the probability of surviving disease j to time t, and S(t) is the probability of surviving all m independent diseases, then [15],…”

Section: Composite Endpoints In Proportional Hazards Studiesmentioning

confidence: 99%

“…This will produce different baseline hazards for individuals with the genetic change. Importantly however, such changes will qualitatively modify the incident rate to a different power of time [15][16][17][18][19][20][21], and cannot be adjusted for in a proportional hazards model. Instead, the variant should be used to stratify the data, so that different strata have differing baseline hazards.…”

Section: Multi-stage Disease Processesmentioning

confidence: 99%

“…(Although as will be discussed in the context of clinical trials, insufficient cases of a disease that prevent tests of heterogeneity, should only be included if there are strong prior reasons to expect the same risk-factor associations as for the other diseases in the endpoint.) The conceptual multi-stage model of diseases [15] such as cancer [16][17][18] and motor neuron disease [19][20][21], is used to highlight some additional implicit assumptions that are needed when the proportional hazards methodology is used.…”

Section: Introductionmentioning

confidence: 99%

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Statistical tests for heterogeneity of clusters and composite endpoints

Webster

2021

Preprint

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Clinical trials and epidemiological cohort studies often group similar diseases together into a composite endpoint, to increase statistical power. A common example is to use a 3-digit code from the International Classification of Diseases (ICD), to represent a collection of several 4-digit coded diseases. More recently, data-driven studies are using associations with risk factors to cluster diseases, leading this article to reconsider the assumptions needed to study a composite endpoint of several potentially distinct diseases. An important assumption is that the (possibly multivariate) associations are the same for all diseases in a composite endpoint (not heterogeneous). Therefore, multivariate measures of heterogeneity from meta analysis are considered, including multi-variate versions of the I2 statistic and Cochran's Q statistic. Whereas meta-analysis offers tools to test heterogeneity of clustering studies, clustering models suggest an alternative heterogeneity test, of whether data are better described by one, or more, clusters of elements with the same mean. The assumptions needed to model composite endpoints with a proportional hazards model are also considered. It is found that the model can fail if one or more diseases in the composite endpoint have different associations. Tests of the proportional hazards assumption can help identify when this occurs. It is emphasised that in multi-stage diseases such as cancer, some germline genetic variants can strongly modify the baseline hazard function and cannot be adjusted for, but must instead be used to stratify the data.

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Multi-stage models for the failure of complex systems, cascading disasters, and the onset of disease

Cited by 16 publications

References 50 publications

The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers

The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers

Bird size with dinosaur-level cancer defences: can evolutionary lags during miniaturisation explain cancer robustness in birds?

Statistical tests for heterogeneity of clusters and composite endpoints

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