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Table 5 Results for IQ MNAR: difference in Pr(IQ observed) = 0.10 for 1 SD increase in IQ (factor 3)

From: Multiple imputation using linked proxy outcome data resulted in important bias reduction and efficiency gains: a simulation study

Scenario (factors 1 and 2) Complete records MI including linked attainment score (KS4)
Estimate (empirical SE) % bias MSE Estimate (empirical SE) % bias MSE Gain in precision (%) FMI (%)
IQ 20% missing 0.08 (0.034) − 17 0.001 0.08 (0.034) − 16 0.001 − 0.1 24
Correlation(IQ:KS4) = 0.1 0.17 (0.030) − 14 0.002 0.17 (0.030) − 14 0.002 1 21
  0.26 (0.025) − 12 0.002 0.26 (0.025) − 12 0.002 0.2 21
IQ 20% missing As above 0.08 (0.034) − 15 0.001 2 23
Correlation(IQ:KS4) = 0.3 0.18 (0.030) − 13 0.001 4 20
  0.27 (0.025) − 11 0.002 1 20
IQ 20% missing As above 0.09 (0.033) − 13 0.001 6 20
Correlation(IQ:KS4) = 0.5 0.18 (0.029) − 11 0.001 8 18
  0.27 (0.025) − 9 0.001 4 18
IQ 20% missing As above 0.09 (0.032) − 9 0.001 14 16
Correlation(IQ:KS4) = 0.7 0.19 (0.028) − 7 0.001 14 13
  0.28 (0.024) − 6 0.001 9 13
IQ 20% missing As above 0.10 (0.031) − 4 0.0009 27 7
Correlation(IQ:KS4) = 0.9 0.19 (0.027) − 3 0.0008 21 6
  0.29 (0.023) − 2 0.0006 18 6
IQ 40% missing 0.07 (0.041) − 29 0.003 0.07 (0.041) − 28 0.002 − 0.2 45
Correlation(IQ: KS4) = 0.1 0.16 (0.035) − 20 0.003 0.16 (0.035) − 20 0.003 − 0.5 41
  0.26 (0.029) − 15 0.003 0.26 (0.029) − 14 0.003 0.5 42
IQ 40% missing As above 0.07 (0.040) − 26 0.002 4 43
Correlation(IQ: KS4) = 0.3 0.16 (0.035) − 19 0.003 2 40
  0.26 (0.029) − 14 0.002 3 40
IQ 40% missing As above 0.08 (0.039) − 23 0.002 12 39
Correlation(IQ: KS4) = 0.5 0.17 (0.034) − 16 0.002 8 36
  0.27 (0.028) − 12 0.002 9 37
IQ 40% missing As above 0.08 (0.037) − 17 0.002 27 32
Correlation(IQ:KS4) = 0.7 0.18 (0.032) − 11 0.002 20 28
  0.28 (0.027) − 8 0.001 22 29
IQ 40% missing As above 0.09 (0.032) − 7 0.001 56 16
Correlation(IQ:KS4) = 0.9 0.19 (0.029) − 5 0.0009 44 14
  0.29 (0.025) − 3 0.0007 50 14
IQ 60% missing 0.03 (0.049) − 74 0.008 0.03 (0.050) − 73 0.008 − 1 65
Correlation(IQ:KS4) = 0.1 0.10 (0.043) − 49 0.011 0.10 (0.043) − 49 0.011 − 1 62
  0.19 (0.037) − 36 0.013 0.19 (0.037) − 35 0.013 − 1 63
IQ 60% missing As above 0.03 (0.049) − 68 0.007 0.6 64
Correlation(IQ:KS4) = 0.3 0.11 (0.042) − 46 0.01 1 61
  0.20 (0.037) − 33 0.011 2 61
IQ 60% missing As above 0.04 (0.047) − 58 0.006 8 60
Correlation(IQ:KS4) = 0.5 0.12 (0.041) − 39 0.008 11 57
  0.22 (0.035) − 28 0.008 12 57
IQ 60% missing As above 0.06 (0.044) − 42 0.004 28 52
Correlation(IQ: KS4) = 0.7 0.14 (0.037) − 28 0.004 31 48
  0.24 (0.032) − 20 0.005 32 48
IQ 60% missing As above 0.08 (0.036) − 17 0.002 84 30
Correlation(IQ:KS4) = 0.9 0.18 (0.032) − 11 0.001 83 27
  0.28 (0.027) − 8 0.001 86 28
IQ 80% missing − 0.14 (0.068) − 237 0.06 − 0.14 (0.069) − 236 0.06 − 3 86
Correlation(IQ: KS4) = 0.1 − 0.13 (0.062) − 165 0.11 − 0.13 (0.062) − 164 0.11 − 0.5 85
  − 0.05 (0.052) − 116 0.12 − 0.05 (0.053) − 115 0.12 − 1 85
IQ 80% missing As above − 0.12 (0.068) − 223 0.05 − 0.3 85
Correlation(IQ: KS4) = 0.3 − 0.11 (0.060) − 155 0.1 6 84
  − 0.03 (0.051) − 109 0.11 5 84
IQ 80% missing As above − 0.09 (0.065) − 194 0.04 9 84
Correlation(IQ: KS4) = 0.5 − 0.07 (0.056) − 134 0.08 21 81
  0.02 (0.048) − 94 0.08 19 82
IQ 80% missing As above − 0.04 (0.059) − 143 0.02 36 79
Correlation(IQ:KS4) = 0.7 0.002 (0.050) − 99 0.04 56 76
  0.09 (0.043) − 70 0.05 50 77
IQ 80% missing As above 0.04 (0.044) − 58 0.006 140 59
Correlation(IQ:KS4) = 0.9 0.12 (0.038) − 41 0.008 170 55
  0.21 (0.033) − 29 0.009 156 57