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MILC: A microsimulation model of the natural history of lung cancer

  1. Stavroula A Chrysanthopoulou  Is a corresponding author
  1. Brown University School of Public Health, United States
Research article
Volume 10(3) Winter 2017
Cite this article as: S. A Chrysanthopoulou; 2017; MILC: A microsimulation model of the natural history of lung cancer; International Journal of Microsimulation; 10(3); 5-26. doi: 10.34196/ijm.00164
7 figures and 3 tables

Figures

Figure 1
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Markov state diagram of the MILC model.
Figure 2
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Structure of the MILC model.
Figure 3
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Predicted versus observed lung cancer incidence rates by age-group and sex.
Figure 4
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Predicted individual risk of lung cancer for people, 50 years old, smoking on average 10 cigarettes per day, by sex.
Figure 5
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Predicted individual risk of lung cancer for people, 50 years old, smoking on average 30 cigarettes per day, by sex.
Figure 6
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Predicted individual risk of lung cancer for people, 50 years old, smoking on average 50 cigarettes per day, by sex.
Figure A.1
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Examples of individual trajectories generated by the MILC model.

Tables

Table 1
MILC model parameterization.
Model components
Initiation of the local stage: Two-Stage Clonal Expansion (TSCE) carcinogenesis model
Risk for the onset of the first malignant cell: h(t)=νμX[ exp(γ+2B)⋅t−1 ]γ+B[ exp(γ+2B)⋅t+1 ]
where γ = α − β − µ and B=12(−γ+γ2+4αμ)
X: total number of normal stem cells
ν: normal cell initiation rate
α: division rate of initiated cells
β: apoptosis rate of initiated cells
µ: malignant conversion rate of initiated cells
Effect of smoking on α and γ parameters: <disp-formula id="equu1"> αs=αns⋅[ 1+α1⋅q(t)α2 ]  and  γs⋅[ 1+α1⋅q(t)α2 ]</disp-formula>
where
q(t): average number of cigarettes smoked per day at age t
(αs, γs) and (αns, γns): parameters for smokers and non-smokers respectively.
Tumor growth: Gompertz function <disp-formula id="equu2"> V(t)V0=exp[ sm(1−exp(mt)) ] </disp-formula>
where
V(t): tumor volume at age t
V0: minimum tumor volume (one malignant cell)
Assuming spherical tumor growth: <disp-formula id="equu3"> V(t)=π6d(t)3 </disp-formula> d(t): diameter at age t
d0 = 0.01mm, diameter of one malignant cell
dmax = 13cm, maximum tumor diameter
Disease progression: Transition to regional and distant stages and tumor diagnosis
Tumor volume at:
— the beginning of the regional stage: Vreg ~ log-normal (µreg, sdreg)
— the beginning of the distant stage: Vdist ~ log-normal (µdist, sddist)
— diagnosis: Vdiagn ~ log-normal(µdiagn, sddiagn)
where <disp-formula id="equu4"> V0<Vreg<Vdist<VmaxV0<Vdiagn<Vmax </disp-formula>
Table 2
Values and calculations for the fixed and calibrated parameters of the MILC model.
Parameter Sex Description
Male Female
Onset of the first malignant cella
All
X IOe+7 Total number of normal stem cells
Non-Smokers
vns 7.16e-8 1.07e-7 Normal cell initiation rate
αns 7.7 15.82 Division rate of initiated cells
γns 0.09 0.071
µns vns Malignant conversion rate of initiated cells
βns αns − µns γns Apoptosis rate of initiated cells
Smokers
νs νns 0.98xνns Normal cell initiation rate
α1 0.6 0.5
α2 0.22 0.32
αs αns×(I+α1 × [q(t)]α2) Power law relationships between γ, α and
γs γns×(I+α1 × [q(t)]α2) smoking intensity q(t) at age t
µs µns Malignant conversion rate of initiated cells
βs αs − µs − γs Apoptosis rate of initiated cells
Tumor growthb
d0 0.01mm Minimum tumor diameter (one tumor cell)
dmax 130mm Maximum tumor diameter
m 3.4e-4 Scale parameter of the Gompertz distribution
[3.2e-4, 3.6e-4]
s 31× m Shape parameter of the Gompertz distribution
Disease progression
µreg = sdreg 2.16 [1.37, 3.06] Mean and sd of the logNormal distribution for
µdist = sddist 5.62 [3.59, 8.02] the tumor volume at the beginning of the regional,
µdiagn = sddiagn 2.65 [1.52, 3.94] distant stage, and diagnosis

  1. Notes: Values for the calibrated MILC parameters are presented as Q2 [Q1, Q3], where Q2 is the median, and Q1, Q3 are the 1st and 3rd quartiles respectively. The values and distributions of MILC parameters are the same for males and females, unless otherwise indicated.

  2. Sources:

  3. a

    Ad hoc values from Hazelton et al. (2005).

  4. b

    Ad hoc values from Koscielny et al. (1985).

Table A.1
Simulation algorithm to predict the lung cancer trajectory of an individual using the MILC model.
Steps
1. “Feed” the model with the individual baseline characteristics X=(age, sex, smoking history a).
2. Simulate age of death (Td_other) from a cause other than lung cancer given age, sex, and smoking status.
3. Simulate age at the onset of the first malignant cell (Tmal), given sex, and smoking history.
4. Simulate ages at the beginning of regional (Treg), and distant stage (Tdist) given Tmal, and tumor growth rate.
5. Simulate age (Tdiagn) at diagnosis given Tmal, and tumor diameter (ddiagn).
6. Find tumor stage at diagnosis comparing Tdiagn with Treg and Tdist.
7. Simulate age of death from lung cancer (Td_lung) given the simulated individual’s characteristics at diagnosis (Tdiagn, and tumor stage).
8. Predict one trajectory, that is, combine the simulated characteristics to “tell” a story for the specific individual with covariates X.
  1. a

    Smoking history comprises: smoking status (never, former or current smoker), smoking intensity (average number of cigarettes smoked per day), as well as start and quit smoking ages where relevant.

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