A Simple 3-Parameter Model for Cancer Incidences

Abstract

Abstract We propose a simple 3-parameter model that provides very good fits for incidence curves of 18 common solid cancers even when variations due to different locations, races, or periods are taken into account. From a data perspective, we use model selection (Akaike information criterion) to show that this model, which is based on the Weibull distribution, outperforms other simple models like the Gamma distribution. From a modeling perspective, the Weibull distribution can be justified as modeling the accumulation of driver events, which establishes a link to stem cell division based cancer development models and a connection to a recursion formula for intrinsic cancer risk published by Wu et al. For the recursion formula a closed form solution is given, which will help to simplify future analyses. Additionally, we perform a sensitivity analysis for the parameters, showing that two of the three parameters can vary over several orders of magnitude. However, the shape parameter of the Weibull distribution, which corresponds to the number of driver mutations required for cancer onset, can be robustly estimated from epidemiological data.