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Table 6 Results when linked attainment score MNAR with 20% missing linked data (correlation between linked attainment score and IQ = 0.7); different values of difference in Pr(KS4 observed) for one SD increase in KS4 (diff Pr(KS4obs)) (factor 5 in scenarios)

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

Scenario [in each case: IQ MNAR (diff Pr(IQ obs) = 0.10), correlation(IQ:KS4) = 0.7, Complete recordsa MI including linked attainment score (KS4)
linked attainment = 20% missing] Estimate (empirical SE) % bias MSE Estimate (empirical SE) % bias MSE Gain in precision (%) FMI (%)
IQ 20% missing 0.08 (0.034) − 17 0.001 0.09 (0.033) − 7 0.001 8 17
Diff Pr(KS4obs) = − 0.10 0.17 (0.030) − 14 0.002 0.19 (0.030) − 7 0.001 6 14
  0.26 (0.025) − 12 0.002 0.28 (0.026) − 6 0.001 7 15
IQ 20% missing As above 0.09 (0.033) − 12 0.001 7 18
Diff Pr(KS4obs) = + 0.10 0.18 (0.030) − 11 0.001 7 15
  0.27 (0.025) − 9 0.001 9 15
IQ 40% missing, 0.07 (0.041) − 29 0.003 0.09 (0.037) − 15 0.002 16 34
Diff Pr(KS4obs) = − 0.10 0.16 (0.035) −20 0.003 0.18 (0.034) − 10 0.002 16 31
  0.26 (0.029) − 15 0.003 0.28 (0.027) − 8 0.001 17 32
IQ 40% missing As above 0.08 (0.037) − 20 0.002 22 35
Diff Pr(KS4obs) = + 0.10 0.17 (0.034) − 15 0.002 15 32
  0.27 (0.028) − 11 0.002 13 32
IQ 60% missing 0.03 (0.049) − 74 0.008 0.06 (0.043) − 43 0.004 32 55
Diff Pr(KS4obs) = − 0.10 0.10 (0.043) − 49 0.01 0.14 (0.039) − 30 0.005 24 52
  0.19 (0.037) − 36 0.01 0.24 (0.032) − 21 0.005 29 52
IQ 60% missing As above 0.05 (0.042) − 50 0.004 24 55
Diff Pr(KS4obs) = + 0.10 0.13 (0.037) − 35 0.006 35 52
  0.23 (0.031) − 25 0.006 33 52
IQ 80% missing − 0.14 (0.068) − 237 0.06 − 0.06 (0.060) − 162 0.03 28 81
Diff Pr(KS4obs) = − 0.10 − 0.13 (0.062) − 165 0.11 − 0.02 (0.054) − 111 0.05 30 78
  − 0.05 (0.052) − 116 0.12 0.07 (0.047) − 78 0.06 25 80
IQ 80% missing As above − 0.06 (0.060) − 156 0.03 37 80
Diff Pr(KS4obs) = + 0.10 − 0.01 (0.053) − 108 0.05 36 77
  0.07 (0.045) − 76 0.05 30 79
  1. aThe results for the complete records analysis presented here are the same as those presented in Table 5 but are included here for comparison