Table 4.
Modifiers of dose response for various auxiliary cancer categories (colon cancer, female breast cancer, prostate cancer). Parameter estimates (all Gy−1) with 95% profile likelihood CI, unless otherwise indicated. Background model is cubic model in age, with adjustment for gender (for colon) and smoking habit and quantity. Average of minimum and maximum colon dose is used for colon cancer, average of left and right breast dose is used for breast cancer, and prostate dose is used for prostate cancer. Follow-up starts > 5 years after treatment. Unless otherwise stated, all p-values relate to the improvement in fit over the model immediately above.
| Model no. | Model/parameters | Colon | Female breast | Prostate | |
|---|---|---|---|---|---|
| 1 | Background[1+ α D] | α (Gy−1) | 0.025 (−0.044, 0.140) | 8.024 (−1.414, 30.38) | −3.697 (−7.167b, 1.670) |
| p-valuesa | 0.549 | 0.124 | 0.145 | ||
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| |||||
| 2 | Background [1+αD+βD2] | α (Gy−1) | 0.082 (−0.172, 0.231b) | 11.70 (−29.58, 43.49b) | −2.286 (NA, NA) |
| β (Gy−2) | −0.007 (−0.015b, 0.028) | −29.34 (−236.3b, 370.5) | −8.964 (−8.965b, −8.964b) | ||
| p-values | 0.530 | 0.830 | 0.617 | ||
|
| |||||
| 3 | Background[1+αDexp[γD]] | α (Gy−1) | 0.049 (−1.702, 50.54) | 10.64 (−3571, >104) | −2.601 (<−104, >104) |
| γ (Gy−1) | −0.082 (−1.234b, 1.069b) | −2.276 (<−104, 30.17b) | 2.234 (−69.78, 12.02b) | ||
| p-valuesc | 0.791 | 0.872 | 0.648 | ||
| p-valuesd | 0.807 | 0.302 | 0.312 | ||
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| |||||
| 4 | Background[1+ α D exp[κ 1sex=female]] | α (Gy−1) | 0.019 (−0.049, 0.144) | - | - |
| κ | 1.131 (−127.7, 7.754b) | - | - | ||
| p-valuesc | 0.763 | - | - | ||
|
| |||||
| 5 | Background[1+ α D exp[τ (age at exposure − 41.32)]] | α (Gy−1) | 0.049 (−0.072b, 0.187) | 7.107 (−1.802, 31.86) | −2.662e (−6.451b, 1.127b) |
| τ (y−1) | −0.082 (−0.265b, 0.100b) | 0.015 (−0.108b, 0.137b) | 0.023e (−0.027b, 0.073b) | ||
| p-valuesc | 0.221 | 0.818 | 0.284 | ||
|
| |||||
| 6 | Background[1+ α D exp[γD+τ (age at exposure − 41.32)]] | α (Gy−1) | 0.034 (−0.162b, 0.231b) | 10.71 (−38.69b, >104) | −2.368e (−8.214b, 3.478b) |
| γ (Gy−1) | 0.047 (−4.943, 0.671b) | −3.623 (<−104, 32.16b) | 0.555e (−7.535b, 8.645b) | ||
| τ (Gy−1) | −0.089 (−0.289b, 0.112b) | 0.019 (−0.104b, 0.141b) | 0.023e (−0.024b, 0.071b) | ||
| p- valuesf | 0.226 | 0.775 | 0.331 | ||
|
| |||||
| 7 | Background[1+ α D exp[δ (time since exposure − 20.78)] | α (Gy−1) | 0.027 (−0.068b, 0.136) | 8.106 (−6.683b, 30.83) | −3.209e (−7.035b, 0.616b) |
| δ (y−1) | 0.047 (−0.121b, 0.215b) | −0.035 (−0.173b, 0.104b) | −0.019e (−0.120b, 0.081b) | ||
| p-valuesc | 0.451 | 0.542 | 0.527 | ||
|
| |||||
| 8 | Background[1+ α D exp[τ(age at exposure − 41.32) + δ (time since exposure − 20.78)]] | α (Gy−1) | 0.057 (−0.090b, 0.242) | 9.692 (−10.46b, 49.80) | −2.649 (−6.769b, 1.471b) |
| τ (y−1) | −0.109 (−0.329b, 0.111b) | −0.020 (−0.183b, 0.142b) | 0.023 (−0.040b, 0.086b) | ||
| δ (y−1) | −0.030 (−0.189, 0.130) | −0.045 (−0.222b, 0.132b) | −0.000 (−0.079b, 0.078b) | ||
| p-valuesg | 0.685 | 0.539 | 0.899 | ||
| p-values | 0.295 | 0.806 | 0.383 | ||
|
| |||||
| 9 | Background[1+ α D exp[τ (age at exposure − 41.32) + ψ (age at exposure − 41.32)2]] | α (Gy−1) | 0.178 (−0.275b, 0.743) | 6.936 (−8.666b, 32.52) | −1.542e (−7.632b, 4.549b) |
| τ (y−1) | .1.409 (−4.792b, −0.589) | 0.023 (−0.203b, 0.249b) | 0.062e (−0.252b, 0.377b) | ||
| ψ (y−2) | −0.486 (−2.055, 0.607b) | −0.000 (−0.009b, 0.009b) | −0.001e (−0.007b, 0.006b) | ||
| p-valuesg | 0.028 | 0.944 | 0.652 | ||
p-value for improvement of fit over null model without linear term in dose.
Wald-based confidence limit.
p-value for improvement of fit over model with (unadjusted) linear term in dose.
p-value for improvement of fit (2 df) over null model without linear term in dose.
indications of lack of convergence.
p-value for improvement of fit over model with linear-exponential term in dose.
p-value for improvement of fit over model with adjustment for age at exposure.