A Simple 3-Parameter Model for Cancer Incidences.

Area of Science:

• Epidemiology
• Biostatistics
• Cancer Research

Background:

• Cancer incidence curves often exhibit complex patterns influenced by various factors.
• Existing models may not fully capture the underlying biological processes of carcinogenesis.
• Understanding cancer risk requires robust statistical modeling linked to biological mechanisms.

Purpose of the Study:

• To propose and validate a simple, robust 3-parameter model for cancer incidence curves.
• To compare the proposed model's performance against other statistical distributions.
• To establish a theoretical link between the model and cancer development mechanisms.

Main Methods:

• Utilized a 3-parameter model based on the Weibull distribution.
• Employed model selection criteria (Akaike information criterion) for comparison.
• Performed sensitivity analysis on model parameters.
• Derived a closed-form solution for a related cancer risk recursion formula.

Main Results:

• The proposed Weibull model demonstrated excellent fits for incidence curves of 18 common solid cancers.
• The Weibull model outperformed simpler models like the Gamma distribution.
• The model's shape parameter, representing driver mutations, was robustly estimated.
• Two parameters showed high variability, while the shape parameter was consistently identifiable.

Conclusions:

• The 3-parameter Weibull model offers a powerful tool for analyzing cancer incidence data.
• The model provides a mechanistic link to the accumulation of driver events in carcinogenesis.
• Robust estimation of the shape parameter offers insights into the number of mutations required for cancer onset.