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Table 3 Bias and imprecision of population means for the HADS depression subscale, and correlation with quality of life

From: Handling missing items in the Hospital Anxiety and Depression Scale (HADS): a simulation study

Method Bias Imprecision Correlation with QoLa
Random Demog Subscale Random Demog Subscale Random Demog Subscale
25 % missing item, rate = psub = 0.5 pitem = 0.5
 Subject mean 0.083 0.002 −0.061 0.037 0.033 0.047 −0.754 −0.759 −0.752
 Subscale mean 0.004 −0.011 −0.024 0.046 0.051 0.071 −0.722 −0.715 −0.701
 Subscale ½ mean 0.000 −0.357 −1.102 0.141 0.258 1.377 −0.756 −0.757 −0.729
 Item mean 0.001 −0.360 −1.110 0.062 0.189 1.277 −0.756 −0.721 −0.717
 Multiple imputation 0.016 −0.086 −0.324 0.038 0.053 0.175 −0.711 −0.744 −0.729
 Multiple imputation ½ 0.005 −0.382 −1.218 0.136 0.274 1.638 −0.742 −0.769 −0.732
 Complete case −0.016 −1.026 −3.168 0.348 1.347 10.162 −0.769 −0.769 −0.427
10 % missing item rate, psub = 0.5 pitem = 0.2
 Subject mean 0.028 0.002 −0.025 0.010 0.009 0.013 −0.768 −0.769 −0.768
 Subscale mean −0.003 0.001 −0.002 0.010 0.010 0.015 −0.760 −0.768 −0.754
 Subscale ½ mean −0.000 −0.025 −0.067 0.016 0.019 0.026 −0.769 −0.768 −0.743
 Item mean −0.002 −0.123 −0.372 0.014 0.030 0.154 −0.758 −0.755 −0.743
 Multiple imputation 0.005 −0.012 −0.075 0.011 0.012 0.023 −0.766 −0.765 −0.765
 Multiple imputation ½ 0.003 −0.033 −0.130 0.016 0.021 0.040 −0.770 −0.769 −0.746
 Complete case −0.000 −0.695 −2.122 0.201 0.699 4.720 −0.770 −0.770 −0.716
10 % missing item rate, psub = 0.2 pitem = 0.5
 Subject mean 0.034 0.003 −0.082 0.014 0.014 0.025 −0.764 −0.767 −0.765
 Subscale mean 0.000 −0.006 −0.010 0.018 0.020 0.028 −0.750 −0.747 −0.740
 Subscale ½ mean 0.002 −0.134 −0.701 0.041 0.064 0.575 −0.764 −0.766 −0.730
 Item mean −0.002 −0.132 −0.702 0.022 0.041 0.514 −0.745 −0.746 −0.731
 Multiple imputation −0.005 −0.027 −0.234 0.013 0.015 0.080 −0.761 −0.761 −0.758
 Multiple imputation ½ −0.000 −0.139 −0.774 0.040 0.064 0.672 −0.766 −0.769 −0.734
 Complete case −0.003 −0.285 −1.540 0.077 0.161 2.409 −0.768 −0.772 −0.666
2 % missing item rate, psub = 0.1 pitem = 0.2
 Subject mean 0.006 −0.000 −0.023 0.002 0.002 0.003 −0.769 −0.771 −0.771
 Subscale mean −0.000 −0.000 0.001 0.002 0.002 0.003 −0.767 −0.767 −0.767
 Subscale ½ mean 0.000 −0.009 −0.034 0.003 0.004 0.010 −0.768 −0.768 −0.766
 Item mean 0.000 −0.029 −0.166 0.003 0.004 0.033 −0.766 −0.766 −0.767
 Multiple imputation 0.001 −0.004 −0.038 0.002 0.002 0.005 −0.768 −0.769 −0.769
 Multiple imputation ½ 0.001 −0.01 −0.068 0.003 0.004 0.014 −0.769 −0.769 −0.768
 Complete case −0.000 −0.119 −0.679 0.026 0.043 0.500 −0.770 −0.770 −0.729
  1. N = 52 for random, demographic dependent and subscale dependent missingness mechanisms. 1000 simulated datasets
  2. aCorrelation = −0.767 for original data (n = 1444)