The fitting result and Probabilistic distributions of the estimated parameters using approximate Bayesian computation schemes involving the simulated likelihood density for the pathway with <i>APC</i>^+/− → <i>TP</i>53^+/− → <i>APC</i>^−/− → <i>KRAS</i>⁺ → <i>TP</i>53^−/− or <i>TP</i>53^+/− → <i>APC</i>^+/− → <i>APC</i>^−/− → <i>KRAS</i>⁺ → <i>TP</i>53^−/−.

(a) or (NμN of model), (b) or ( of model), (c) ( of model), (d) ( of model), (e) ( of model), (f) The colorectal cancer incidence rate per 100,000 patients from SEER registry and rates predicted by the model.</p

Comparison of the approximate hazard function given by (6) with the exact numerical solution of hazard function given by (9).

All parameters of the model are set as follows: N = 107, , λi = 0.1 + (i − 1) * 0.05.</p

Estimate values of parameters in the pathway with <i>APC</i>^+/− → <i>TP</i>53^+/− → <i>APC</i>^−/− → <i>KRAS</i>⁺ → <i>TP</i>53^−/− or <i>TP</i>53^+/− → <i>APC</i>^+/− → <i>APC</i>^−/− → <i>KRAS</i>⁺ → <i>TP</i>53^−/−.

Estimate values of parameters in the pathway with APC+/− → TP53+/− → APC−/− → KRAS+ → TP53−/− or TP53+/− → APC+/− → APC−/− → KRAS+ → TP53−/−.</p

Estimate values of parameters in the pathway with <i>APC</i>^+/− → <i>APC</i>^−/− → <i>TP</i>53^+/− → <i>TP</i>53^−/− → <i>KRAS</i>⁺.

Estimate values of parameters in the pathway with APC+/− → APC−/− → TP53+/− → TP53−/− → KRAS+.</p

The logarithm of expected number of mutated cells with the combination of different genetic mutations for the pathways involving <i>KRAS</i>⁺ → <i>APC</i>^+/− → <i>APC</i>^−/− → <i>TP</i>53^+/− → <i>TP</i>53^−/−, <i>APC</i>^+/− → <i>APC</i>^−/− → <i>TP</i>53^+/− → <i>TP</i>53^−/− → <i>KRAS</i>⁺ and <i>APC</i>^+/− → <i>APC</i>^−/− → <i>KRAS</i>⁺ → <i>TP</i>53^+/− → <i>TP</i>53^−/−.

The values of parameters are decided by Tables 1–8.</p

The fitting result and Probabilistic distributions of the estimated parameters using approximate Bayesian computation schemes involving the simulated likelihood density for the pathway with <i>APC</i>^+/− → <i>APC</i>^−/− → <i>KRAS</i>⁺ → <i>TP</i>53^+/− → <i>TP</i>53^−/−.

(a) (NμN of model), (b) ( of model), (c) ( of model), (d) ( of model), (e) ( of model), (f) The colorectal cancer incidence rate per 100,000 patients from SEER registry and rates predicted by the model.</p

All pathways are accepted to explain the development of colorectal cancer at different ages.

All pathways are accepted to explain the development of colorectal cancer at different ages.</p

Estimate values of parameters in the pathway with <i>APC</i>^+/− → <i>APC</i>^−/− → <i>KRAS</i>⁺ → <i>TP</i>53^+/− → <i>TP</i>53^−/−.

Estimate values of parameters in the pathway with APC+/− → APC−/− → KRAS+ → TP53+/− → TP53−/−.</p

Estimate values of parameters in the pathway with <i>APC</i>^+/− → <i>APC</i>^−/− → <i>TP</i>53^+/− → <i>KRAS</i>⁺ → <i>TP</i>53^−/−.

Estimate values of parameters in the pathway with APC+/− → APC−/− → TP53+/− → KRAS+ → TP53−/−.</p

The fitting result and Probabilistic distributions of the estimated parameters using approximate Bayesian computation schemes involving the simulated likelihood density for the pathway with <i>APC</i>^+/− → <i>KRAS</i>⁺ → <i>APC</i>^−/− → <i>TP</i>53^+/− → <i>TP</i>53^−/−.

(a) (NμN of model), (b) ( of model), (c) ( of model), (d) ( of model), (e) ( of model), (f) The colorectal cancer incidence rate per 100,000 patients from SEER registry and rates predicted by the model.</p