Table 3.
Modifiers of dose response for various categories of 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 and smoking habit and quantity. Stomach dose is used for all cancer and stomach cancer, pancreatic dose is used for pancreatic cancer, (average of left and right lobe) lung dose is used for lung cancer, active bone marrow dose is used for leukemia, and stomach dose is used for all other cancers. Follow-up starts > 2 years after treatment for leukemia, and > 5 years after treatment for all other cancers. Unless otherwise stated, all p-values relate to the improvement in fit over the model immediately above.
| Model no. | Model/parameters | All cancer | Stomach | Pancreas | Lung | Leukemia excluding CLL | All other cancers | |
|---|---|---|---|---|---|---|---|---|
| 1 | Background[1+ α D] | α (Gy−1) | 0.024 (0.011, 0.039) | 0.042 (−0.002, 0.119) | 0.055 (−0.002, 0.157) | 0.559 (0.221, 1.021) | 1.087 (−0.018, 4.925) | 0.006 (−0.008, 0.024) |
| p-valuesa | <0.001 | 0.066 | 0.059 | <0.001 | 0.057 | 0.428 | ||
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| 2 | Background[1+αD+βD2] | α (Gy−1) | 0.045 (0.017, 0.075) | 0.064 (−0.048, 0.200) | 0.114c (−0.006b, 0.235b) | 0.353 (−0.466, 1.249) | −0.958 (−4.657b, 2.740b) | 0.031c (0.004b, 0.057b) |
| β (Gy−2) | −0.001 (−0.002, 0.000) | −0.001 (−0.007b, 0.006) | −0.004c (−0.007b, 0.002) | 0.142 (−0.336, 0.753) | 1.219 (−1.218b, 3.655b) | −0.001c (−0.002b, −0.000) | ||
| p-values | 0.099 | 0.680 | 0.113 | 0.590 | 0.547 | 0.020 | ||
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| 3 | Background[1+αDexp[γD]] | α (Gy−1) | 0.129 (0.027, 0.443) | 0.223 (−0.508b, 4.906) | 2.286 (0.143, 14.49) | 0.343(0.029, 1.723) | 0.831 (−2.136b, 13.49) | 0.243 (−3.900, 1.365) |
| γ (Gy−1) | −0.104 (−0.211, −0.011) | −0.110 (−0.539, 0.251) | −0.273 (−0.548, −0.062) | 0.324 (−0.893, 1.366) | 0.161 (−1.451b, 1.773b) | −0.193 (−0.418, −0.032) | ||
| p-valuesd | 0.026 | 0.491 | 0.012 | 0.527 | 0.827 | 0.024 | ||
| p-valuese | <0.001 | 0.146 | 0.007 | 0.001 | 0.160 | 0.058 | ||
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| 4 | Background[1+ α D exp[κ 1sex=female]] | α (Gy−1) | 0.021 (0.007, 0.037) | 0.033 (−0.023b, 0.115) | 0.036 (0.015, 0.134) | 0.547 (0.201, 1.026) | 2.047 (0.188, 11.37) | 0.001 (−0.014b, 0.020) |
| κ | 0.747 (−1.037, 2.000) | 0.960 (−107.6, 3.776b) | 1.688 (−10.89, 4.166b) | 0.276 (−55.86, 2.108) | −39.06 (NA, NA) | 3.169 (<−104, 14.54b) | ||
| p-valuesd | 0.280 | 0.528 | 0.245 | 0.828 | 0.132 | 0.188 | ||
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| 5 | Background[1+ α D exp[τ (age at exposure − 41.32)]] | α (Gy−1) | 0.030 (0.014, 0.048) | 0.046 (0.004, 0.135) | 0.043 (0.001, 0.170) | 0.598 (0.224, 1.110) | 1.067 (−0.987b, 5.091) | 0.009 (−0.011b, 0.030) |
| τ (y−1) | −0.052 (−0.105, −0.012) | −0.090 (−0.223, 0.014) | −0.136 (−0.356, −0.035) | −0.010 (−0.056, 0.036) | 0.003 (−0.092b, 0.098b) | −0.106 (−0.260b, 0.048b) | ||
| p-valuesd | 0.012 | 0.080 | 0.006 | 0.639 | 0.944 | 0.103 | ||
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| 6 | Background[1+ α D exp[γD+τ (age at exposure − 41.32)]] | α (Gy−1) | 0.080 (0.015, 0.315) | 0.079 (−0.180b, 2.500) | 0.510 (−0.777b, 9.335) | 0.342 (0.024, 1.678) | 0.838 (−2.155b, 13.64) | 0.229 (−0.346b, 1.504) |
| γ (Gy−1) | −0.061 (−0.172, 0.028) | −0.038 (−0.353, 0.159) | .0.144 (−0.446, 0.136) | 0.387 (−0.822, 1.580) | 0.155 (−1.512b, 1.822b) | −0.186 (−0.456, 0.062) | ||
| τ (y−1) | −0.036 (−0.090, 0.004) | −0.087 (−0.220, 0.021) | −0.072 (−0.314, 0.025) | −0.014 (−0.069, 0.034) | 0.001 (−0.097b, 0.098b) | −0.003 (−0.237, 0.097) | ||
| p-valuesf | 0.081 | 0.100 | 0.155 | 0.545 | 1.000 | 0.929 | ||
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| 7 | Background[1+ α D exp[δ (time since exposure − 20.78)]] | α (Gy−1) | 0.023 (0.010, 0.038) | 0.043 (0.002, 0.120) | 0.032 (0.002, 0.122) | 0.558 (0.216, 1.023) | 0.984 (−0.946b, 4.826) | 0.006 (−0.009, 0.024) |
| δ (y−1) | 0.024 (−0.009, 0.057) | 0.037 (−0.047, 0.132) | 0.094 (0.026, 0.192) | 0.001 (−0.052, 0.045) | −0.034 (−0.147b, 0.177) | 0.027 (−0.113b, 0.168b) | ||
| p-values | 0.142 | 0.269 | 0.008 | 0.964 | 0.597 | 0.583 | ||
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| 8 | Background[1+ α D exp[τ (age at exposure − 41.32) + δ (time since exposure − 20.78)]] | α (Gy−1) | 0.033 (0.015, 0.055) | 0.047 (0.001, 0.153) | 0.034 (−0.035b, 0.159) | 0.682 (0.215, 1.394) | 0.030c (−0.243b, 0.303b) | 0.009 (−0.013b, 0.036) |
| τ (y−1) | −0.072 (−0.146, −0.009) | −0.147 (−0.447, 0.157) | −0.091 (−0.330, 0.086) | −0.024 (−0.092, 0.049) | −0.296c (−0.804b, 0.213b) | −0.160 (−0.675, 0.004) | ||
| δ (y−1) | −0.019 (−0.065, 0.027) | −0.049 (−0.278, 0.115) | 0.044 (−0.087, 0.180) | −0.017 (−0.091, 0.054) | −0.519c (−1.223b, −0.037) | −0.046 (−0.245, 0.048) | ||
| p-valuesg | 0.389 | 0.397 | 0.470 | 0.604 | 0.036 | 0.235 | ||
| p-values | 0.027 | 0.109 | 0.289 | 0.485 | 0.042 | 0.052 | ||
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| 9 | Background[1+ αD exp[τ (age at exposure − 41.32) + ψ (age at exposure − 41.32)2]] | α (Gy−1) | 0.029 (0.013, 0.049) | 0.013 (−0.043b, 0.119) | 0.049 (−0.026b, 0.166) | 0.725 (0.269, 1.390) | 1.300 (−1.203b, 7.656) | 0.007 (−0.001, 0.037) |
| τ (y−1) | −0.050 (−0.087b, −0.012) | −0.537 (−1.486b, −0.044) | −0.100 (−1.027, −0.033) | 0.002 (−0.069b, 0.083) | 0.027 (−0.148b, 0.201b) | −0.609 (−1.942b, −0.027) | ||
| ψ (y−2) | 0.000 (−0.002b, 0.003) | −0.026 (−0.078b, 0.027b) | 0.002 (−0.004b, 0.006) | −0.002 (−0.007b, 0.001) | −0.002 (−0.012b, 0.005) | −0.046 (−0.149b, 0.058b) | ||
| p-valuesg | 0.772 | 0.065 | 0.611 | 0.294 | 0.597 | 0.136 | ||
p-value for improvement of fit over null model without linear term in dose.
Wald-based confidence limit.
indications of lack of convergence.
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.
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.