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Table 4 Simulation results: estimations of bias and mean squared error for the log-logistic model

From: Estimating time-to-onset of adverse drug reactions from spontaneous reporting databases

       Naive estimator   TBE
      λ ̂   β ̂   λ ̂   β ̂  
λ β p n BIAS MSE BIAS MSE BIAS MSE BIAS MSE NPM
0.05 0.5 0.25 100 6.45 44 0.384 0.16 0.258 0.25 0.041 0.008 217
    500 6.33 40 0.372 0.14 0.043 0.01 0.005 0.001 52
0.05 0.5 0.50 100 1.05 1.2 0.319 0.108 0.045 0.012 0.020 0.006 22
    500 1.02 1.1 0.308 0.096 0.009 0.001 0.003 0.001 0
0.05 0.5 0.80 100 0.165 0.031 0.195 0.041 0.008 0.001 0.008 0.004 0
    500 0.158 0.026 0.189 0.036 0.001 <0.001 0.001 <0.001 0
1 0.5 0.25 100 129 17533 0.383 0.15 5.06 87 0.042 0.008 207
    500 127 16217 0.374 0.14 1.01 6 0.008 0.001 41
1 0.5 0.50 100 21.0 467 0.317 0.106 0.93 5.0 0.019 0.006 43
    500 20.5 426 0.308 0.096 0.20 0.6 0.004 0.001 0
1 0.5 0.80 100 3.31 12 0.201 0.044 0.209 0.55 0.016 0.005 0
    500 3.17 10 0.190 0.037 0.037 0.09 0.002 <0.001 0
0.05 2 0.25 100 0.150 0.022 1.06 1.2 <0.001 0.001 0.08 0.085 4
    500 0.149 0.022 1.04 1.1 -0.001 <0.001 0.01 0.018 0
0.05 2 0.50 100 0.079 0.006 0.932 0.94 <0.001 <0.001 0.06 0.094 5
    500 0.078 0.006 0.903 0.83 <0.001 <0.001 0.01 0.017 0
0.05 2 0.80 100 0.035 0.001 0.665 0.50 <0.001 <0.001 0.03 0.078 0
    500 0.035 0.001 0.649 0.43 <0.001 <0.001 0.01 0.013 0
1 2 0.25 100 2.99 9.0 1.07 1.2 0.024 0.57 0.08 0.089 0
    500 2.98 8.9 1.04 1.1 -0.028 0.20 0.01 0.020 0
1 2 0.50 100 1.57 2.49 0.943 0.96 0.007 0.19 0.063 0.095 1
    500 1.56 2.45 0.896 0.82 -0.013 0.04 0.004 0.018 0
1 2 0.80 100 0.702 0.50 0.668 0.50 0.004 0.042 0.045 0.072 0
    500 0.693 0.48 0.648 0.43 0.004 0.007 0.015 0.013 0
  1. The mean squared error formula is MSE( λ ̂ )=Var( λ ̂ )+ ( BIAS ( λ ̂ ) ) 2 . Calculations were made on the replications where there was no problem of maximization. In the last column appear the number of problems of maximization for the truncation-based approach. There was no problem of maximization for the naive approach. Abbreviations : TBE truncation-based estimator, MSE mean squared error, NPM number of maximization problems.