Cancer onset prediction by applying extreme value theory
Colorectal cancer (CRC) is increasingly diagnosed at younger ages, with early-onset CRC (EO-CRC) rising despite declining incidence among older adults. These early diagnoses form the lower tail of the age-at-diagnosis distribution, where observations are sparse and may be difficult to predict accurately using models fitted to the full distribution. Extreme value theory (EVT) provides a framework for directly modelling this tail behaviour.
Using SEER data, a Weibull accelerated failure time (AFT) model fitted to the full distribution was compared with a generalized Pareto distribution (GPD) fitted to threshold exceedances below age 50. The Weibull systematically underestimated early-diagnosis quantiles by one to two years, whereas the GPD closely tracked empirical quantiles across the tail, supporting the use of EVT for direct modelling of the lower tail.
The GPD framework was then applied to the GECCO consortium to investigate whether genetic burden contributes to earlier diagnosis. Eleven genetic variants were forward-selected by AIC as covariates on the scale parameter, and were summarized into a genetic scale score. This score was used to compute theoretical endpoint and expected age at diagnosis across representative percentiles of its distribution. Genetic burden was associated with progressively earlier EO-CRC diagnosis: individuals in the 90th percentile of the genetic scale score had a theoretical endpoint age 8.8 years younger (95% CI: 6.6, 11.0) and an expected age 3.3 years younger (95% CI: 2.5, 4.4) than those in the 10th percentile.
Applied to an external test cohort, the model retained good calibration, and the genetic
scale score discriminated early-onset from late-onset CRC (AUC = 0.618, 95% CI: 0.549, 0.688). Separately, an interaction test confirmed that the genetic effect was specific to CRC cases rather than age in general.
These findings demonstrate that EVT offers a more accurate characterization of the lower tail of the CRC age-at-diagnosis distribution than conventional bulk models, and that genetic burden measurably alters the timing of diagnosis within the early-onset range, with potential relevance for personalized screening.
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