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Table 1 Mean of the log hazard ratio estimates (Est), mean of the standard error estimates SE , standard error of the estimates (SE) and mean of the mean square error (MSE). Results of 1,000 simulations.

From: Multiple imputation for estimating hazard ratios and predictive abilities in case-cohort surveys

   Full cohort     Multiple imputation a    Weighted estimator  
  Est SE SE MSE Est SE SE MSE Est SE SE MSE
Z2 normally distributed           
β 1 = β 2 = β 3 = 0            
β 1 -0.003 0.107 0.100 0.010 -0.003 0.107 0.110 0.010 -0.001 0.133 0.128 0.016
β 2 -0.001 0.054 0.058 0.003 -0.001 0.060 0.062 0.004 0.001 0.065 0.068 0.005
β3 -0.004 0.053 0.056 0.003 -0.004 0.054 0.057 0.003 -0.003 0.058 0.060 0.004
β 1 = β 2 = β 3 = log(2)           
β 1 0.689 0.118 0.113 0.013 0.676 0.119 0.112 0.013 0.696 0.168 0.165 0.027
β 2 0.687 0.058 0.057 0.003 0.679 0.070 0.068 0.005 0.701 0.088 0.097 0.009
β 3 0.683 0.057 0.057 0.003 0.679 0.058 0.058 0.004 0.689 0.080 0.090 0.007
Z2 log normally distributed          
β 1 = β 2 = β 3 = 0            
β 1 -0.003 0.107 0.100 0.010 -0.003 0.107 0.100 0.010 -0.004 0.133 0.128 0.016
β2 -0.001 0.027 0.034 0.001 0.015 0.031 0.032 0.001 0.002 0.034 0.038 0.001
β 3 -0.004 0.053 0.056 0.003 -0.004 0.054 0.058 0.004 -0.005 0.059 0.062 0.004
β 1 = β 2 = β 3 = log(2)           
β 1 0.686 0.058 0.056 0.003 0.621 0.061 0.055 0.008 0.686 0.112 0.117 0.014
β 2 0.692 0.013 0.015 2e0-4 0.602 0.015 0.014 0.008 0.695 0.020 0.023 0.001
β 3 0.685 0.029 0.031 0.001 0.686 0.032 0.031 0.001 0.687 0.049 0.053 0.003
Z2 uniformly distributed           
β 1 = β 2 = β 3 = 0            
β 1 0.007 0.181 0.175 0.031 0.007 0.181 0.175 0.031 0.007 0.197 0.188 0.035
β 2 -0.001 0.092 0.087 0.008 0.004 0.094 0.088 0.008 -0.002 0.098 0.095 0.009
β 3 0.003 0.090 0.090 0.008 0.002 0.090 0.090 0.008 0.004 0.093 0.093 0.009
β 1 = β 2 = β 3 = log(2)           
β 1 0.690 0.120 0.116 0.013 0.680 0.121 0.115 0.013 0.694 0.166 0.169 0.028
β 2 0.695 0.069 0.063 0.004 0.656 0.075 0.066 0.006 0.698 0.087 0.082 0.007
β 3 0.690 0.058 0.054 0.003 0.689 0.059 0.055 0.003 0.698 0.081 0.081 0.007
  1. a MI estimates with imputation model: Z 2 = α 0 + α 1 Ind case + α 2 Strata + ε, ε ~ N(0, σ)