Table 5 Posterior means and 95% credible intervals of model parameters from original calibration to targets y, and from the model that is recalibrated to \(\{y,z\}\) using a start from scratch approach as well as a sequential calibration approach
Parameter | Original posterior | New targets (start from scratch) | New targets (sequential) |
|---|---|---|---|
Adenoma risk | |||
A | − 6.56 (− 6.89, − 6.11) | − 6.49 (− 6.76, − 6.10) | − 6.47 (− 6.72, − 6.11) |
\(\alpha _1\) | − 0.62 (− 0.70, − 0.49) | − 0.65 (− 0.70, − 0.56) | − 0.66 (− 0.70, − 0.60) |
\(\sigma _{\alpha }\) | 1.62 (1.43, 1.74) | 1.69 (1.59, 1.75) | 1.69 (1.57, 1.75) |
\(\alpha _{20}\) | 0.04 (0.03, 0.05) | 0.04 (0.04, 0.05) | 0.04 (0.04, 0.05) |
\(\alpha _{50}\) | 0.04 (0.02, 0.05) | 0.03 (0.02, 0.05) | 0.03 (0.01, 0.05) |
\(\alpha _{60}\) | 0.02 (− 0.01, 0.05) | 0.01 (− 0.01, 0.04) | 0.01 (− 0.01, 0.04) |
\(\alpha _{70}\) | 0.00 (− 0.02, 0.02) | 0.00 (− 0.02, 0.03) | 0.00 (− 0.02, 0.03) |
Adenoma growth | |||
\(\beta _{2c}\) | 37.67 (34.02, 39.86) | 35.34 (31.96, 38.79) | 35.42 (32.26, 38.75) |
\(\beta _{1c}\) | 1.43 (1.162, 1.701) | 1.59 (1.31, 1.83) | 1.58 (1.31, 1.81) |
\(\beta _{2r}\) | 15.28 (11.81, 19.53) | 14.17 (11.29, 18.14) | 14.14 (11.30, 17.82) |
\(\beta _{1r}\) | 3.39 (1.97, 4.76) | 3.24 (1.80, 4.82) | 3.39 (1.85, 4.83) |
p | 0.69 (0.56, 0.83) | 0.79 (0.65, 0.92) | 0.79 (0.66, 0.92) |
Transition to preclinical CRC | |||
\(\gamma _0\) | 3.16 (3.03, 3.35) | 3.17 (3.08, 3.26) | 3.17 (3.10, 3.26) |
\(\gamma _1\) | − 0.13 (− 0.19, − 0.07) | − 0.13 (− 0.18, − 0.08) | − 0.13 (− 0.18, − 0.09) |
\(\gamma _2\) | − 0.05 (− 0.24, 0.13) | − 0.04 (− 0.25, 0.14) | − 0.04 (− 0.23, 0.13) |
\(\gamma _3\) | 0.07 (− 0.03, 0.17) | 0.11 (0.01, 0.20) | 0.10 (0.01, 0.19) |
\(\gamma _4\) | − 1.11 (− 1.42, − 0.79) | − 0.74 (− 1.08, − 0.37) | − 0.75 (− 1.07, − 0.41) |
\(\gamma _5\) | 0.12 (0.01, 0.23) | 0.10 (0, 0.23) | 0.10 (− 0.001, 0.23) |
\(\sigma _{\gamma }\) | 0.56 (0.50, 0.65) | 0.52 (0.50, 0.55) | 0.52 (0.50, 0.56) |
Sojourn time | |||
\(\lambda _2\) | 3.72 (2.20, 4.92) | 2.38 (2.02, 3.07) | 2.42 (2.02, 3.23) |
\(\lambda _1\) | 2.57 (2.27, 3.06) | 3.77 (3.35, 4.16) | 3.80 (3.36, 4.18) |
\(\lambda _3\) | − 0.35 (− 0.96, 0.67) | 0.87 (0.65, 0.99) | 0.86 (0.61, 0.99) |