Table 3.
Comparison of methods for handling missing data for ITT analysis of the FREE trial
| 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 |
EE, estimated effect; EQ5D, EuroQol 5-dimension; RMD, Roland-Morris Disability; SE, standard error; SF-36, short form 36 health survey; VAS, visual analogue scale