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Table 5 Simulation Performance Measures for Multiple Imputation (MI) without and with an Auxiliary Variable (MI-Aux)

From: Impact of missing data on bias and precision when estimating change in patient-reported outcomes from a clinical registry

Missing Mechanism Model Parameter Performance Measure 10% Missing 25% Missing 50% Missing
MI MI-Aux MI MI-Aux MI MI-Aux
  ρ = 0.2 ρ = 0.5 ρ = 0.8   ρ = 0.2 ρ = 0.5 ρ = 0.8   ρ = 0.2 ρ = 0.5 ρ = 0.8
MCAR β 0 Bias 4.48 3.75 3.70 3.29 2.31 3.05 3.25 0.74 3.89 4.81 5.05 4.36
RMSE 1.78 1.78 1.77 1.74 1.88 1.89 1.85 1.77 2.19 2.18 2.11 1.94
CI Width 8.11 8.09 8.03 7.92 8.58 8.53 8.39 8.09 9.50 9.42 9.10 8.46
β T Bias −2.16 −2.06 −0.54 2.18 −19.72 −21.47 −21.49 −12.81 −36.70 − 37.14 −31.22 −16.90
RMSE 0.46 0.46 0.46 0.45 0.47 0.46 0.46 0.44 0.52 0.53 0.52 0.47
CI Width 2.16 2.16 2.15 2.12 2.32 2.31 2.29 2.21 2.65 2.64 2.57 2.38
β TS Bias 4.18 3.84 2.61 −1.39 29.38 32.62 33.04 21.74 61.45 62.28 52.82 29.08
RMSE 0.56 0.56 0.56 0.56 0.57 0.57 0.57 0.56 0.60 0.60 0.60 0.58
CI Width 2.82 2.82 2.81 2.77 3.00 3.00 2.96 2.88 3.34 3.31 3.25 3.05
MAR β 0 Bias −1.29 −0.56 0.67 3.06 −11.52 −10.87 − 10.59 −8.20 −26.62 − 19.67 − 10.71 4.93
RMSE 1.77 1.76 1.76 1.74 1.87 1.88 1.84 1.76 2.26 2.24 2.13 1.95
CI Width 8.05 8.04 8.01 7.93 8.44 8.45 8.32 8.10 9.34 9.31 9.03 8.44
β T Bias 9.13 6.53 4.63 3.17 −4.55 −11.15 −18.72 −18.78 −14.41 −14.83 − 10.96 −2.48
RMSE 0.46 0.46 0.46 0.46 0.45 0.46 0.46 0.45 0.52 0.51 0.50 0.47
CI Width 2.15 2.15 2.14 2.12 2.31 2.30 2.28 2.21 2.62 2.60 2.54 2.35
β TS Bias −8.19 −6.72 −6.81 −5.64 15.21 20.60 24.92 21.05 31.05 30.19 22.37 6.38
RMSE 0.57 0.57 0.57 0.57 0.54 0.55 0.56 0.56 0.55 0.54 0.55 0.57
CI Width 2.83 2.82 2.81 2.77 3.02 3.02 2.99 2.89 3.34 3.32 3.25 3.05
MNAR β 0 Bias −42.75 −40.05 −31.76 −13.71 −86.54 −84.55 −73.35 − 42.67 −102.96 − 99.42 −89.10 −53.11
RMSE 1.89 1.87 1.81 1.73 2.49 2.44 2.26 1.90 3.17 3.10 2.80 2.20
CI Width 7.97 7.97 7.90 7.84 8.33 8.32 8.20 7.97 9.37 9.27 8.95 8.35
β T Bias 7.95 6.41 3.46 1.73 −31.14 −34.74 −35.36 −25.04 − 101.73 − 99.73 −80.58 − 41.96
RMSE 0.45 0.45 0.45 0.45 0.48 0.48 0.48 0.45 0.74 0.73 0.65 0.51
CI Width 2.17 2.16 2.16 2.12 2.34 2.35 2.31 2.22 2.74 2.71 2.63 2.40
β TS Bias −16.91 −14.34 −8.65 −3.75 −5.30 1.39 11.72 16.71 16.66 18.66 15.27 8.17
RMSE 0.55 0.55 0.55 0.56 0.53 0.54 0.55 0.55 0.54 0.54 0.55 0.57
CI Width 2.82 2.82 2.80 2.77 3.01 3.02 2.98 2.88 3.41 3.39 3.30 3.07
  1. CI Width Average width of the 95% confidence interval, Bias Standardized bias, RMSE Root mean squared error