A Simple 3-Parameter Model for Cancer Incidences

Xiaoxiao Zhang, Holger Fröhlich, Dima Grigoriev, Sergey Vakulenko, Jörg Zimmermann und Andreas Weber
In: Scientific Reports (Feb. 2018), 8:3388
 

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.

Stichwörter: Cancer epidemiology, Cancer stem cells, Computational models

Bibtex

@ARTICLE{ZhangFroehlichGrigorievVakulenkoZimmermannWeber2018a,
    author = {Zhang, Xiaoxiao and Fr{\"o}hlich, Holger and Grigoriev, Dima and Vakulenko, Sergey and Zimmermann,
              J{\"o}rg and Weber, Andreas},
     title = {A Simple 3-Parameter Model for Cancer Incidences},
   journal = {Scientific Reports},
    volume = {8},
    number = {3388},
      year = {2018},
     month = feb,
  keywords = {Cancer epidemiology, Cancer stem cells, Computational models},
  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.},
       url = {https://www.nature.com/articles/s41598-018-21734-x},
       doi = {10.1038/s41598-018-21734-x}
}