Abstract
Carcinogenesis is commonly described as a multistage process, in which stem cells are transformed into cancer cells via a series of mutations. In this article, we consider extensions of the multistage carcinogenesis model by mixture modeling. This approach allows us to describe population heterogeneity in a biologically meaningful way. We focus on finite mixture models, for which we prove identifiability. These models are applied to human lung cancer data from several birth cohorts. Maximum likelihood estimation does not perform well in this application due to the heavy censoring in our data. We thus use analytic graduation instead. Very good fits are achieved for models that combine a small high risk group with a large group that is quasi immune.
Highlights
Cancers can arise in virtually any part of the body, and there are many tissue specific properties, a general multistage framework for carcinogenesis holds for most cancer types
We have studied an extension of the multistage carcinogenesis model by mixture
It is natural to introduce the notion of frailty in a biologically meaningful way
Summary
Cancers can arise in virtually any part of the body, and there are many tissue specific properties, a general multistage framework for carcinogenesis holds for most cancer types. A biological mechanism generating heterogeneity at this stage are germ line mutations of the genes involved, leading to individuals starting life with all cells in an intermediate stage This means that the population survivor function is t. The MLE fails completely to catch the behavior of the observed incidence at old ages; only the first few data points are well fitted Convergence to this model seems even more astonishing when we consider the initial model. In all cases where enough data at old ages is available (i.e. all but the 1920s cohort), the estimated proportion of the population at high risk, πu , is not sensitive to changes in the fixed parameter values. Note that we used the parametrization (logit(πl), log(γu - γl), log ν, log μ) in the fitting process
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