Background
Materials and methods
The Fracture Reduction Evaluation (FREE) trial
Statistical methods
Assumptions
Imputation model
Results
Missing response
Follow-up (time after randomisation) | |||||||
---|---|---|---|---|---|---|---|
Measure | Baseline | 1 month | 3 months | 6 months | 12 months | 24 months | Mean |
SF-36 PCS | 2.7 | 13.0 | 19.7 | 21.0 | 25.0 | 27.3 | 18.1 |
EQ-5D | 2.3 | 13.0 | 19.3 | 20.7 | 24.7 | 25.3 | 17.6 |
RMD score | 1.7 | 15.7 | 25.0 | 26.7 | 32.0 | 36.0 | 22.8 |
Back pain | 0.7 | 12.0 | 18.0 | 19.7 | 24.7 | 24.3 | 16.6 |
Restricted activity | 4.0 | 18.0 | 22.3 | 22.0 | 26.0 | 28.3 | 20.1 |
Days in bed | 3.3 | 15.3 | 20.7 | 20.7 | 24.7 | 27.0 | 18.6 |
Estimated fraction of missing information
Follow-up period | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
1 month | 3 months | 6 months | 12 months | 24 months | ||||||
Outcome | FMI | MD | FMI | MD | FMI | MD | FMI | MD | FMI | MD |
SF-36 PCS | 11.9 | 15.7 | 15.8 | 22.3 | 17.2 | 23.7 | 23.9 | 27.7 | 30.1 | 30.0 |
EQ-5D | 14.5 | 15.3 | 13.1 | 21.7 | 18.0 | 23.0 | 18.4 | 27.0 | 20.9 | 27.7 |
RMD | 9.9 | 17.3 | 19.8 | 26.7 | 18.2 | 28.3 | 21.0 | 33.7 | 19.9 | 37.7 |
Back pain | 12.3 | 12.7 | 15.7 | 18.7 | 19.0 | 20.3 | 17.3 | 25.3 | 29.6 | 25.0 |
Restricted activity | 9.6 | 22.0 | 14.0 | 26.3 | 19.6 | 26.0 | 19.3 | 30.0 | 20.0 | 32.3 |
Days in bed | 21.2 | 18.7 | 24.6 | 24.0 | 27.5 | 24.0 | 35.4 | 28.0 | 34.3 | 30.3 |
Comparison of analysis methods
Complete case analysis | Last observation carried forward | Mixed effects model | Multiple imputation | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Measure | EE | SE | 95% CI | P value | EE | SE | 95% CI | P value | EE | SE | 95% CI | P value | EE | SE | 95% CI | P value |
SF-36 PCS
| ||||||||||||||||
1 month follow-up |
8.00
| 1.3724 | [5.31,10.69] | 0.0000 |
5.24
| 1.0320 | [3.22,7.27] | 0.0000 |
5.32
| 1.1139 | [3.14,7.51] | 0.0000 |
5.09
| 1.1509 | [2.83,7.34] | 0.0000 |
3 months follow-up |
5.60
| 1.3724 | [2.91,8.29] | 0.0000 |
4.52
| 1.0320 | [2.50,6.54] | 0.0000 |
4.13
| 1.1453 | [1.89,6.38] | 0.0003 |
4.06
| 1.1778 | [1.75,6.37] | 0.0006 |
6 months follow-up |
4.16
| 1.3724 | [1.47,6.85] | 0.0025 |
4.06
| 1.0320 | [2.04,6.08] | 0.0001 |
3.39
| 1.1482 | [1.13,5.64] | 0.0032 |
3.39
| 1.1853 | [1.06,5.71] | 0.0043 |
12 months follow-up |
2.07
| 1.3724 | [-0.62,4.76] | 0.1315 |
2.92
| 1.0320 | [0.90,4.95] | 0.0046 |
1.70
| 1.1647 | [-0.59,3.98] | 0.1451 |
2.42
| 1.2333 | [0.00,4.84] | 0.0499 |
24 months follow-up |
2.49
| 1.3724 | [-0.20,5.18] | 0.0694 |
2.81
| 1.0320 | [0.78,4.83] | 0.0065 |
1.68
| 1.1757 | [-0.63,3.98] | 0.1538 |
2.40
| 1.2855 | [-0.12,4.92] | 0.0617 |
Overall treatment effect |
4.47
| 1.1027 | [2.30,6.63] | 0.0001 |
3.91
| 0.8497 | [2.24,5.58] | 0.0000 |
3.24
| 0.8979 | [1.48,5.00] | 0.0003 |
3.47
| 0.9264 | [1.66,5.29] | 0.0002 |
EQ5D
| ||||||||||||||||
1 month follow-up |
0.20
| 0.0429 | [0.12,0.28] | 0.0000 |
0.18
| 0.0378 | [0.10,0.25] | 0.0000 |
0.17
| 0.0377 | [0.10,0.24] | 0.0000 |
0.16
| 0.0397 | [0.09,0.24] | 0.0000 |
3 months follow-up |
0.10
| 0.0429 | [0.02,0.18] | 0.0195 |
0.15
| 0.0378 | [0.07,0.22] | 0.0001 |
0.11
| 0.0387 | [0.03,0.18] | 0.0054 |
0.10
| 0.0394 | [0.03,0.18] | 0.0090 |
6 months follow-up |
0.11
| 0.0429 | [0.02,0.19] | 0.0130 |
0.17
| 0.0378 | [0.09,0.24] | 0.0000 |
0.12
| 0.0389 | [0.04,0.20] | 0.0019 |
0.11
| 0.0405 | [0.03,0.19] | 0.0065 |
12 months follow-up |
0.11
| 0.0429 | [0.02,0.19] | 0.0125 |
0.15
| 0.0378 | [0.08,0.23] | 0.0000 |
0.10
| 0.0394 | [0.02,0.18] | 0.0097 |
0.10
| 0.0406 | [0.02,0.18] | 0.0131 |
24 months follow-up |
0.09
| 0.0429 | [0.00,0.17] | 0.0451 |
0.13
| 0.0378 | [0.05,0.20] | 0.0007 |
0.08
| 0.0395 | [0.00,0.16] | 0.0497 |
0.07
| 0.0411 | [-0.01,0.15] | 0.0909 |
Overall treatment effect |
0.12
| 0.0339 | [0.05,0.19] | 0.0004 |
0.15
| 0.0319 | [0.09,0.22] | 0.0000 |
0.12
| 0.0302 | [0.06,0.18] | 0.0001 |
0.11
| 0.0302 | [0.05,0.17] | 0.0003 |
RMD score
| ||||||||||||||||
1 month follow-up | -4.45
| 0.8743 | [-6.16, -2.74] | 0.0000 |
-3.52
| 0.6573 | [-4.81,-2.23] | 0.0000 |
-4.22
| 0.6793 | [-5.55,-2.89] | 0.0000 |
-3.86
| 0.6845 | [-5.20, -2.52] | 0.0000 |
3 months follow-up | -2.86
| 0.8743 | [-4.58,-1.15] | 0.0011 |
-3.48
| 0.6573 | [-4.77,-2.19] | 0.0000 |
-3.64
| 0.7034 | [-5.01,-2.26] | 0.0000 |
-3.30
| 0.7319 | [-4.74, -1.87] | 0.0000 |
6 months follow-up | -2.04
| 0.8743 | [-3.75,-0.32] | 0.0198 |
-3.07
| 0.6573 | [-4.36,-1.78] | 0.0000 |
-2.96
| 0.7072 | [-4.35,-1.58] | 0.0000 |
-2.76
| 0.7258 | [-4.19, -1.34] | 0.0001 |
12 months follow-up | -1.95
| 0.8743 | [-3.66,-0.24] | 0.0258 |
-2.99
| 0.6573 | [-4.28,-1.70] | 0.0000 |
-2.81
| 0.7207 | [-4.22,-1.40] | 0.0001 |
-2.50
| 0.7409 | [-3.95, -1.05] | 0.0007 |
24 months follow-up | -0.60
| 0.8743 | [-2.31,1.12] | 0.4945 |
-2.34
| 0.6573 | [-3.62,-1.05] | 0.0004 |
-1.43
| 0.7327 | [-2.87,0.00] | 0.0506 |
-1.65
| 0.7431 | [-3.10, -0.19] | 0.0267 |
Overall treatment effect | -2.38
| 0.7355 | [-3.82,-0.94] | 0.0012 |
-3.08
| 0.5667 | [-4.19,-1.97] | 0.0000 |
-3.01
| 0.5716 | [-4.13,-1.89] | 0.0000 |
-2.81
| 0.5737 | [-3.94, -1.69] | 0.0000 |
VAS score
| ||||||||||||||||
1 month follow-up |
-1.92
| 0.3329 | [-2.57,-1.27] | 0.0000 |
-1.87
| 0.2807 | [-2.42,-1.32] | 0.0000 |
-1.89
| 0.2872 | [-2.46,-1.33] | 0.0000 |
-1.76
| 0.3064 | [-2.36,-1.16] | 0.0000 |
3 months follow-up |
-1.51
| 0.3329 | [-2.16,-0.86] | 0.0000 |
-1.71
| 0.2807 | [-2.26,-1.16] | 0.0000 |
-1.53
| 0.2958 | [-2.11,-0.95] | 0.0000 |
-1.35
| 0.3120 | [-1.96,-0.74] | 0.0000 |
6 months follow-up |
-1.53
| 0.3329 | [-2.18,-0.88] | 0.0000 |
-1.76
| 0.2807 | [-2.31,-1.21] | 0.0000 |
-1.56
| 0.2980 | [-2.15,-0.98] | 0.0000 |
-1.43
| 0.3181 | [-2.05,-0.80] | 0.0000 |
12 months follow-up |
-0.77
| 0.3329 | [-1.42,-0.11] | 0.0214 |
-1.31
| 0.2807 | [-1.86,-0.76] | 0.0000 |
-0.93
| 0.3055 | [-1.53,-0.33] | 0.0023 |
-0.85
| 0.3153 | [-1.47,-0.23] | 0.0071 |
24 months follow-up |
-0.77
| 0.3329 | [-1.42,-0.12] | 0.0203 |
-1.14
| 0.2807 | [-1.69,-0.59] | 0.0000 |
-0.80
| 0.3043 | [-1.39,-0.20] | 0.0089 |
-0.61
| 0.3408 | [-1.28,0.06] | 0.0725 |
Overall treatment effect |
-1.42
| 0.2316 | [-1.87,-0.96] | 0.0000 |
-1.65
| 0.2123 | [-2.07,-1.23] | 0.0000 |
-1.49
| 0.2000 | [-1.88,-1.10] | 0.0000 |
-1.20
| 0.2248 | [-1.64,-0.76] | 0.0000 |
Resticted activity
| ||||||||||||||||
1 month follow-up |
-4.44
| 0.9193 | [-6.24,-2.63] | 0.0000 |
-2.95
| 0.6979 | [-4.31,-1.58] | 0.0000 |
-3.46
| 0.7466 | [-4.93,-2.00] | 0.0000 |
-3.13
| 0.7356 | [-4.57,-1.69] | 0.0000 |
3 months follow-up |
-3.79
| 0.9193 | [-5.59,-1.98] | 0.0000 |
-3.82
| 0.6979 | [-5.19,-2.45] | 0.0000 |
-3.94
| 0.7649 | [-5.44,-2.44] | 0.0000 |
-3.59
| 0.7542 | [-5.07,-2.11] | 0.0000 |
6 months follow-up |
-3.00
| 0.9193 | [-4.80,-1.19] | 0.0011 |
-2.96
| 0.6979 | [-4.32,-1.59] | 0.0000 |
-2.43
| 0.7647 | [-3.93,-0.93] | 0.0015 |
-2.64
| 0.7804 | [-4.17,-1.11] | 0.0007 |
12 months follow-up |
-1.48
| 0.9193 | [-3.28,0.32] | 0.1067 |
-2.64
| 0.6979 | [-4.00,-1.27] | 0.0002 |
-2.04
| 0.7788 | [-3.56,-0.51] | 0.0089 |
-1.86
| 0.7766 | [-3.38,-0.34] | 0.0167 |
24 months follow-up |
-1.56
| 0.9193 | [-3.36,0.24] | 0.0896 |
-2.17
| 0.6979 | [-3.54,-0.80] | 0.0019 |
-1.24
| 0.7905 | [-2.79,0.31] | 0.1156 |
-1.62
| 0.7800 | [-3.15,-0.09] | 0.0378 |
Overall treatment effect |
-2.85
| 0.6589 | [-4.14,-1.56] | 0.0000 |
-2.90
| 0.5328 | [-3.95,-1.86] | 0.0000 |
-2.62
| 0.5357 | [-3.67,-1.57] | 0.0000 |
-2.57
| 0.5189 | [-3.59,-1.55] | 0.0000 |
Days in bed
| ||||||||||||||||
1 month follow-up |
-2.71
| 0.4710 | [-3.63,-1.78] | 0.0000 |
-2.53
| 0.4897 | [-3.49,-1.57] | 0.0000 |
-2.55
| 0.4418 | [-3.42,-1.69] | 0.0000 |
-2.45
| 0.5682 | [-3.56,-1.34] | 0.0000 |
3 months follow-up |
-0.86
| 0.4710 | [-1.78,0.07] | 0.0693 |
-1.39
| 0.4897 | [-2.35,-0.43] | 0.0044 |
-0.96
| 0.4557 | [-1.86,-0.07] | 0.0342 |
-1.48
| 0.5809 | [-2.62,-0.34] | 0.0109 |
6 months follow-up |
-0.31
| 0.4710 | [-1.23,0.62] | 0.5155 |
-0.87
| 0.4897 | [-1.83,0.09] | 0.0757 |
-0.30
| 0.4565 | [-1.19,0.60] | 0.5143 |
-0.83
| 0.5929 | [-1.99,0.33] | 0.1606 |
12 months follow-up |
-0.08
| 0.4710 | [-1.00,0.85] | 0.8701 |
-0.67
| 0.4897 | [-1.63,0.29] | 0.1741 |
0.17
| 0.4672 | [-0.74,1.09] | 0.7113 |
-0.35
| 0.6261 | [-1.57,0.88] | 0.5800 |
24 months follow-up |
-0.64
| 0.4710 | [-1.57,0.28] | 0.1718 |
-0.83
| 0.4897 | [-1.79,0.13] | 0.0899 |
-0.70
| 0.4739 | [-1.63,0.23] | 0.1393 |
-1.21
| 0.6211 | [-2.42,0.01] | 0.0521 |
Overall treatment effect |
-0.92
| 0.3002 | [-1.51,-0.33] | 0.0022 |
-1.26
| 0.3894 | [-2.02,-0.49] | 0.0012 |
-0.87
| 0.2908 | [-1.44,-0.30] | 0.0028 |
-1.26
| 0.3629 | [-1.97,-0.55] | 0.0005 |