Fig 1.
Multistage clonal expansion (MSCE) model for ESCC.
Model parameters are: ν the rate of an ESCC predisposing field-defect, μ1 the mutation rate (per field) for the initiation of premalignant (dysplastic) clones, α the cell division rate, β the cell death rate, and μ2 the rate of malignant transformations. A lag-time of 5 years is assumed for a viable malignant cell to progress to clinical cancer.
Fig 2.
Functional regularization of period (year) trends on the field-defect rate νFD.
The parameters s0, y0, w1, w2 and ν0 are estimated from the data. Note, νFD approaches the background rate ν0 smoothly at the reference point y0 and is assumed to remain constant for y > y0. Here s refers to age, B to birth year, y to period. For illustration, we also show some randomly generated νFD trajectories with the attenuating term log(s/s0) included (solid lines) and with this term omitted (dotted lines).
Fig 3.
A) Two-hit process for the initiation of dysplastic clones; B) Sporadic formation of field-defect followed by single hit process for the initiation of dysplastic clones. Note, only the product is identifiable and represents the rate at which dysplastic clones are initiated in the defective field.
Table 1.
Parameter estimates are based on posterior samples obtained via Markov Chain Monte Carlo (MCMC) using random uniform prior distributions with boundaries that were well outside the obtained 95% confidence regions.
For sampling, we used a multivariate Metropolis-Hastings algorithm with >100, 000 samples for Males and >200, 000 samples for Females. The marginal medians listed in this table agreed well with the obtained maximum likelihood estimates and led to very similar incidence predictions (S3 Fig).
Fig 4.
ESCC incidence (data, black shapes; model fits, black lines) by sex, race and age group as indicated from 1975-2016.
For comparison, non-parametric fits using 4th-order smoothing splines are shown in red.
Fig 5.
Period profiles of the field-defect rate νFD(s;B) by birth cohort as indicated.
Fig 6.
Predicted field-defect rates νFD (panel A) and corresponding field-defect prevalences as functions of age (1920 birth cohort) by race and sex.