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A Systematic Approach to Determining the Identifiability of Multistage Carcinogenesis Models
Author(s) -
Brouwer Andrew F.,
Meza Rafael,
Eisenberg Marisa C.
Publication year - 2017
Publication title -
risk analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.972
H-Index - 130
eISSN - 1539-6924
pISSN - 0272-4332
DOI - 10.1111/risa.12684
Subject(s) - identifiability , ordinary differential equation , mathematics , ode , markov chain , markov model , markov process , mathematical optimization , differential equation , statistics , mathematical analysis
Multistage clonal expansion (MSCE) models of carcinogenesis are continuous‐time Markov process models often used to relate cancer incidence to biological mechanism. Identifiability analysis determines what model parameter combinations can, theoretically, be estimated from given data. We use a systematic approach, based on differential algebra methods traditionally used for deterministic ordinary differential equation (ODE) models, to determine identifiable combinations for a generalized subclass of MSCE models with any number of preinitation stages and one clonal expansion. Additionally, we determine the identifiable combinations of the generalized MSCE model with up to four clonal expansion stages, and conjecture the results for any number of clonal expansion stages. The results improve upon previous work in a number of ways and provide a framework to find the identifiable combinations for further variations on the MSCE models. Finally, our approach, which takes advantage of the Kolmogorov backward equations for the probability generating functions of the Markov process, demonstrates that identifiability methods used in engineering and mathematics for systems of ODEs can be applied to continuous‐time Markov processes.