Table 3.

Conventional Model Description: Basic Structure of the CRC-SPIN Natural History Model (19).

Adenoma Risk: Non-homogeneous Poisson process

Log-risk for the ith individual = ${\alpha }_{0i}+{\alpha }_{1}se{x}_i+{\sum }_{k=1}^4\delta (A_k<ag{e}_i\left(t\right)\le A_{k+1})\left\{ag{e}_i\left(t\right){\alpha }_{2k}+{\sum }_{j=2}^k{A}_j({\alpha }_{2,j-1}-{\alpha }_{2j})\right\}$

Baseline log-risk, α0i, is Normally distributed, mean Λ, standard deviation σ  δ(·) is an indicator function with δ(x)=1 when x is true and δ(x)=0 otherwise  agei(t) is the ith individual's age at time t  A1=20, A2=50, A3=60, A4=70, A5=∞ (effectively 100 years old)

Calibrated parameters: Λ, σ, α1, α21, α22, α23, and α24

Adenoma Growth: Janoshek Growth Curve

dij (t) = d∞ − (d∞ − d0)exp(−λijt)

dij(t) is the maximum diameter of the jth adenoma in the ith individual at time t after initiation.  d0=1mm, minimal detectable adenoma size  d∞=50mm, maximum adenoma size  time to reach 10mm: − ln((d∞ −10)/(d∞ − d0))/λ .

Time to Reach 10mm: Type 2 extreme value distribution

Adenomas in the colon: distribution parameterised by β1c and β2c

Adenomas in the rectum: distribution parameterised by β1r and β2r

Calibrated parameters: β1c, β2c, β1r, and β2r

Transition to Preclinical Cancer: Normal cumulative distribution

Probability of transition, male colon  ϕ({ln(γ1cmsize + γ2cm(a − 50)}/γ3)

Probability of transition, male rectum  ϕ({ln(γ1rmsize + γ2rm(a − 50)}/γ3)

Probability of transition, female colon  ϕ({ln(γ1cfsize + γ2cf(a − 50)}/γ3)

Probability of transition, female rectum  ϕ({ln(γ1rfsize + γ2rf(a − 50)}/γ3)

Where ϕ(·) is the standard Normal cumulative distribution function, size is adenoma size in mm, and a is age at adenoma initiation.

Calibrated parameters: γ1cm, γ2cm, γ1rm, γ2rm, γ1cf, γ2cf, γ1rf, γ2rf, and γ3

Sojourn Time: Lognormal distribution

Preclinical colon cancer, lognormal with mean μc, standard deviation τcμc

Preclinical rectal cancer, lognormal with mean μr, standard deviation τrμr

Calibrated parameters: μc, τc, μr, and τr