Table 1.

Unknown Parameters of CRC-AIM Natural History Model

Unknown Parameter	Plausible Range	Best Parameter Value Selected by Calibration
Adenoma generation
Baseline log risk, ${\beta }_0$	${\beta }_0~T{N}_{[-7,-5]}(-6.3,0.4)$	−5.661
Standard deviation of baseline log-risk, ${\sigma }_0$	${\sigma }_0~T{N}_{[1,2]}(1.1,0.2)$	1.270
Sex effect, ${\beta }_1$	${\beta }_1~T{N}_{[-0.5,-0.1]}(-0.5,0.1)$	−0.384
Age effect (ages 20–<50), ${\beta }_2$	${\beta }_2~T{N}_{[0.03,0.07]}(0.045,0.007)$	0.039
Age effect (ages 50–<60), ${\beta }_3$	${\beta }_3~T{N}_{[0.01,0.05]}(0.03,0.01)$	0.023
Age effect (ages 60–<70), ${\beta }_4$	${\beta }_4~T{N}_{[-0.01,0.05]}(0.03,0.01)$	0.020
Age effect (ages ≥70), ${\beta }_5$	${\beta }_5~T{N}_{[-0.02,0.03]}(0.03,0.03)$	−0.018
Adenoma growth (time to 10 mm)
Scale (colon), $s_c$	$s_c~U(10.7,40)$	24.364
Shape (colon), ${\alpha }_c$	${\alpha }_c~U(0.5,4)$	1.388
Scale (rectum), $s_r$	$s_r~U(5,20)$	6.734
Shape (rectrum), ${\alpha }_r$	${\alpha }_r~U(2,5)$	3.601
Adenoma growth (Richard’s growth model)
Shape parameter, $p$	$p~T{N}_{[0.5,3.2]}(1.0,0.5)$	0.710
Transition from adenoma to cancer
Size (male, colon), ${\gamma }_{1\mathrm{cm}}$	${\gamma }_{1\mathrm{cm}}~U(0.02,0.06)$	0.040
Age at initiation (male, colon), ${\gamma }_{2\mathrm{cm}}$	${\gamma }_{2\mathrm{cm}}~U(0.0,0.02)$	0.016
Size (male, rectum), ${\gamma }_{1\mathrm{rm}}$	${\gamma }_{1\mathrm{rm}}~U(0.02,0.07)$	0.039
Age at initiation (male, rectum), ${\gamma }_{2\mathrm{rm}}$	${\gamma }_{2\mathrm{rm}}~U(0.0,0.02)$	0.004
Size (female, colon), ${\gamma }_{1\mathrm{cf}}$	${\gamma }_{1\mathrm{cf}}~U(0.02,0.05)$	0.043
Age at initiation (female, colon), ${\gamma }_{2\mathrm{cf}}$	${\gamma }_{2\mathrm{cf}}~U(0.0,0.02)$	0.014
Size (female, rectum), ${\gamma }_{1\mathrm{rf}}$	${\gamma }_{1\mathrm{rf}}~U(0.02,0.055)$	0.035
Age at initiation (female, rectum), ${\gamma }_{2\mathrm{rf}}$	${\gamma }_{2\mathrm{rf}}~U(0.0,0.02)$	0.010
Sojourn time
Scale (colon), ${\lambda }_c$	${\lambda }_c~U(3.0,5.0)$	4.683
Shape (colon and rectum), $k$	$k~U(2.0,5.0)$	3.620
Log-hazard ratio, $\alpha$	$\alpha ~U(-1.0,1.0)$	−0.018

$T{N}_{[a,b]}(\mu ,\sigma )$ represents a truncated normal distribution with mean µ and standard deviation σ over the domain [a,b]. U(a,b) represents a uniform distribution with domain (a,b). CRC-AIM, Colorectal Cancer-Adenoma Incidence and Mortality Model.