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Table 1 Basic structure of the CRC-SPIN Model

From: Evaluating risk factor assumptions: a simulation-based approach

Model component
Adenoma incidence: non-homogeneous Poisson process
   Log-risk for the i th individual at time t, ℓn(Ψ i (t)) =
    α 0 i + α 1 s e x i + k = 1 4 δ ( A k < a g e i ( t ) A k + 1 ) a g e i ( t ) α 2 k + j = 2 k A j ( α 2 , j - 1 - α 2 j )
• Baseline log-risk, α0i, 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 • A1 = 20, A2 = 50, A3 = 60, A4 = 70, A5=∞ (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 β1c and β2c
   Adenomas in the rectum: distribution parameterized by β1r and β2r
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 μc, standard deviation τcμc
   Preclinical rectal cancer, lognormal with mean μr, standard deviation τrμr