From: Evaluating risk factor assumptions: a simulation-based approach
Model component | |
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Adenoma incidence: non-homogeneous Poisson process | |
Log-risk for the i th individual at time t, ℓn(Ψ_{ i }(t)) = | |
${\alpha}_{0i}+{\alpha}_{1}se{x}_{i}+\sum _{k=1}^{4}\delta \left({A}_{k}<ag{e}_{i}\left(t\right)\le {A}_{k+1}\right)\left\{ag{e}_{i}\left(t\right){\alpha}_{2k}+\sum _{j=2}^{k}{A}_{j}\left({\alpha}_{2,j-1}-{\alpha}_{2j}\right)\right\}$ | |
• Baseline log-risk, α_{0i}, is Normally distributed, mean Λ, standard deviation σ • δ(.) is an indicator function with δ(x) = 1 when the condition x is true and δ(x) = 0 otherwise • age _{ i }(t) is the i th individual's age at time t • A_{1} = 20, A_{2} = 50, A_{3} = 60, A_{4} = 70, A_{5}=∞ (effectively 100 years old) | |
Adenoma location probabilities: cecum: 0.08; ascending colon: 0.23; transverse colon: 24; descending colon: 0.12; sigmoid colon: 0.24; rectum: 0.09. | |
Adenoma growth: Janoshek growth curve | |
_{ dij }(t) = d _{∞} - (d _{∞} - d _{0}) exp (-λ _{ ij } t) • d _{ij}(t) is the maximum diameter of the j th adenoma in the i th individual at time t after initiation. • d _{0} = 1 mm, minimal detectable adenoma size • d _{∞} = 50 mm, maximum adenoma size • time to reach 10 mm: -In((d _{∞} - 10)/(d _{∞} - d _{0}))/λ. | |
Time to reach 10 mm: type 2 extreme value distribution | |
Adenomas in the colon: distribution parameterized by β_{1c} and β_{2c} | |
Adenomas in the rectum: distribution parameterized by β_{1r} and β_{2r} | |
Transition to preclinical cancer: normal cumulative distribution | |
Probability of transition, male colon | Ф({In (γ _{ 1 cm } size) + γ _{ 2 cm } (a-50)}/γ _{3} |
Probability of transition, male rectum | Ф({In (γ _{ 1 rm } size) + γ _{ 2 rm } (a-50)}/γ _{3} |
Probability of transition, female colon | Ф({In (γ _{ 1 cf } size) + γ _{ 2 cf } (a-50)}/γ _{3} |
Probability of transition, female rectum | Ф({In (γ _{ 1 rf } size) + γ _{ 2 rf } (a-50)}/γ _{3} |
Where Ф(.) is the standard Normal cumulative distribution function, size is adenoma size in mm, and a is age at adenoma initiation. | |
Sojourn time: lognormal distribution | |
Preclinical colon cancer, lognormal with mean μ_{c}, standard deviation τ_{c}μ_{c} | |
Preclinical rectal cancer, lognormal with mean μ_{r}, standard deviation τ_{r}μ_{r} |