Online Supplementary Material

Online Appendix

The relationship between probability and hazard functions were then used to calculate the 10-year probability or fracture for a combination of the risk factors. Let h(t) denote the fracture hazard function, d(t) the death hazard function and g(t) the hazard function of the combined event hip fracture or death. Though the functions in typical applications contain several variables, only a time variable is given in order to simplify the notations. The hazard function g of having the first event of death or hip fracture is well approximated by d + h. From the general and well-known relationship between survival and hazard functions it is known that the probability of being free from any of the two types of events at the end of the period (0,t) is

exp(.

The probability p of a hip fracture event before t is therefore given by

p = .

When taking account of the hazard function of death in the calculation of 10 year probability, as showed above, the risk of death is taken account of twice, i.e. as a hazard function and also as a censoring factor when looking at the time to fracture when applying the Poisson model.

Online Table 1 Hazard function for osteoporotic fracture without TBS

Variable / β-coefficient / variance / Two-sided p-value
Constant / -7.488 / 0.0386
Current age / 0.0289 / 0.0000079 / <0.001
Current time since baseline / 0.0212 / 0.000184 / 0.12
Prior fracture / 2.104 / 0.125 / <0.001
Glucocorticoids / 0.228 / 0.00678 / 0.0056
RA / 0.303 / 0.0117 / 0.0051
Secondary osteoporosis / 0.291 / 0.00501 / <0.001
Alcohol / 0.563 / 0.0139 / <0.001
Femoral neck BMD T-score < -1.20b / -0.499 / 0.00136 / <0.001
Femoral neck BMD T-score > -1.20b / -0.247 / 0.00314 / <0.001
Prior fracture x current age / -0.0135 / 0.0000239 / 0.0060
Prior fracture x time since baseline / -0.145 / 0.000723 / <0.001

b piecewise linear function with knot at the mean

Online Table 2 Hazard function for osteoporotic fracture with TBS

Variable / β-coefficient / variance / Two-sided p-value
Constant / -5.898 / 0.174
Current age / 0.0245 / 0.0000084 / <0.001
Current time since baseline / 0.0251 / 0.000184 / 0.065
Prior fracture / 1.985 / 0.127 / <0.001
Glucocorticoids / 0.201 / 0.00680 / 0.015
RA / 0.297 / 0.0117 / 0.0060
Secondary osteoporosis / 0.242 / 0.00507 / <0.001
Alcohol / 0.514 / 0.0140 / <0.001
Femoral neck BMD T-score < -1.20b / -0.455 / 0.00140 / <0.001
Femoral neck BMD T-score > -1.20b / -0.205 / 0.00315 / <0.001
Prior fracture x current age / -0.0122 / 0.0000243 / 0.013
Prior fracture x time since baseline / -0.146 / 0.000723 / <0.001
TBS < 1.3b / -0.912 / 0.0704 / <0.001
TBS > 1.3b / -2.136 / 0.127 / <0.001

b piecewise linear function with knot at the mean

Online Table 3 Hazard function for death without TBS

Variable / β-coefficient / variance / Two-sided p-value
Constant / -11.484 / 0.0566
Current age / 0.0850 / 0.0000098 / <0.001
Current time since baseline / 0.0346 / 0.000478 / 0.11
Smoking / 0.755 / 0.00385 / <0.001
Glucocorticoids / 3.503 / 0.173 / <0.001
Glucocorticoids x current age / -0.0365 / 0.0000316 / <0.001
Secondary osteoporosis / 1.784 / 0.213 / <0.001
Secondary osteoporosis x current age / -0.0165 / 0.0000379 / 0.0073
Alcohol / 4.178 / 0.477 / <0.001
Alcohol x current age / -0.0505 / 0.000109 / <0.001
Femoral neck BMD T-score -1.20b / -0.216 / 0.00270 / <0.001
Femoral neck BMD T-score -1.20b / 0.117 / 0.00337 / 0.044
Femoral neckBMD x current time / -0.0245 / 0.000103 / 0.016

b piecewise linear function with knot at the mean

Online Table 4 Hazard function for death with TBS

Variable / β-coefficient / variance / Two-sided p-value
Constant / -19.373 / 0.153
Current age / 0.0818 / 0.0000102 / <0.001
Current time since baseline / 0.0357 / 0.000478 / 0.10
Smoking / 0.697 / 0.00393 / <0.001
Glucocorticoids / 3.426 / 0.174 / <0.001
Glucocorticoids x current age / -0.0357 / 0.0000318 / <0.001
Secondary osteoporosis / 1.604 / 0.216 / <0.001
Secondary osteoporosis x current age / -0.0147 / 0.0000385 / 0.018
Alcohol / 4.161 / 0.485 / <0.001
Alcohol x current age / -0.0507 / 0.000111 / <0.001
Femoral neck BMD T-score -1.20b / -0.168 / 0.00274 / 0.0013
Femoral neck BMD T-score -1.20b / 0.154 / 0.00338 / 0.0081
Femoral neckBMD x current time / -0.0247 / 0.000103 / 0.015
TBS / -1.397 / 0.0423 / <0.001

b piecewise linear function with knot at the mean

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Lumbar Spine Texture and Fractures

Online Table 5 Ten year probability of a major osteoporotic fracture in women according to age and the T-score for femoral neck BMD in the absence of clinical risk factors using the models both incorporating TBS and not incorporating TBS. TBS values are set at the 10th percentile (TBS=1.16) and the 90th percentile (TBS=1.47) termed high and low TBS, respectively. Average is when TBS is not incorporated in the model for calculating fracture probability.

Age 50 / Age 60 / Age 70 / Age 80
T-score / Average / Low TBS / High TBS / Average / Low TBS / High TBS / Average / Low TBS / High TBS / Average / Low TBS / High TBS
-2 / 7.9 / 9.7 / 6.1 / 10.3 / 12.0 / 7.6 / 13.1 / 14.5 / 9.4 / 16.0 / 16.6 / 11.2
-1 / 5.1 / 6.6 / 4.1 / 6.7 / 8.3 / 5.2 / 8.7 / 10.1 / 6.4 / 10.8 / 11.8 / 7.8
0 / 4.0 / 5.4 / 3.4 / 5.3 / 6.8 / 4.2 / 6.8 / 8.3 / 5.3 / 8.4 / 9.7 / 6.4
1 / 3.2 / 4.4 / 2.8 / 4.1 / 5.5 / 3.5 / 5.3 / 6.8 / 4.3 / 6.5 / 7.9 / 5.2

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Lumbar Spine Texture and Fractures