Fig 1.
Scheme of the mechanistic model.
A) Individual processes (adapted from [7]). Parameter α quantifies tumor growth while parameter μ quantifies metastatic dissemination. B) Population scheme, with S(t) the survival function of the random variable TTR. pdf = probability density function.
Fig 2.
Mean and 95% confidence interval of each estimated parameter.
The index h in Θh refers to the number of parameters that were jointly estimated. Red and blue lines are the estimations with the first and second objective functions respectively, corresponding to accounting for the initial proportion of metastatic patients (blue) or not (red). The dashed black lines corresponds to the true value of the parameter. The parameters that have also been estimated in each situation are displayed above the solid lines.
Fig 3.
Effect of a categorical covariate.
A) Scheme of model simulation with an effect of a categorical covariate in α or μ. The individual values αi and μi are sampled from different distributions depending on the group. In the right panel, differences in the survival curves are displayed for the two groups. B) Inference of the right effect from the data.
Fig 4.
Effect of a continuous covariate.
A) Individual values of αi or μi are taken from different distributions depending on the covariate value and the type of effect. B) Synthetic DMFS curves at different thresholds simulated with a constant and linear effect in the variable α. P-values at different thresholds are displayed in the center figure C) Scheme of inferring the right effect from the data. Number 1–3 refers to effects group, linear, constant and linear in the variable αpop and 4–6 in the variable μpop. D) Results from the minimization process with a gamma distribution for the covariate. Red box plots correspond to the real model used to generate the data with the model and Fval is the value of the objective function with the parameter estimated.
Table 1.
RSE for the parameters b and c True values were b* = 0.3 for group effect, b* = 0.7 for linear and constant and linear and c* = 0.5 for normal distribution, c* = 0.05 for gamma distribution and c* = 0.13 for log-normal distribution, except for linear effect, in which c* = 0.1 independently of the distribution.
Fig 5.
Results of the mathematical model applied to the clinical dataset.
A) Goodness-of-fit between the model without covariates and the Kaplan-Meier estimator of the clinical data. B) Goodness-of-fit between the model with the effect of FG in μ and the data separated by FG groups. Individual μi distributions according to values of C) Führman Grade, D) MMR, E) GPRC5a F) Goodness-of-fit for the model with a constant and linear effect in μ for the covariate MMR. The different subfigures are the fits obtained for different thresholds. Dashed lines correspond to the clinical data and solid lines correspond to simulations. Blue lines are the results for group 1 (MMRi < threshold) and red lines for group 2 (MMRi ≥ threshold). G) Goodness-of-fit of the fit between the model with a group effect in μ for the covariate GPRC5a.
Table 2.
The parameter difμ,c has been set to compensate for the unknown value of the parameter μpop when studying the covariate c (μpop,c = μpop + difμ,c). a.u. = arbitrary unit. RSE = relative standard error.