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Table 1 Results for the Gompertz distribution

From: Limitations of the incidence density ratio as approximation of the hazard ratio

BLR True HR CP MPE MSE SE
IDR HR IDR HR IDR HR IDR HR
0.01 0.4 0.976 0.978 −22.678 −9.860 0.595 0.580 0.026 0.027
0.7 0.964 0.978 −45.271 −5.351 0.612 0.634 0.023 0.024
0.9 0.983 0.989 − 128.131 1.149 0.466 0.461 0.021 0.022
1 0.977 0.976 NA 0.458 0.455 0.020 0.021
0.02 0.4 0.956 0.970 −7.247 7.156 0.369 0.404 0.018 0.019
0.7 0.952 0.956 −34.036 1.679 0.280 0.285 0.015 0.016
0.9 0.943 0.953 − 118.042 4.062 0.240 0.243 0.014 0.015
1 0.956 0.973 NA NA 0.209 0.214 0.014 0.014
0.05 0.4 0.930 0.948 −11.000 3.343 0.145 0.149 0.011 0.012
0.7 0.928 0.964 −35.534 1.250 0.098 0.091 0.009 0.010
0.9 0.936 0.966 − 133.290 −13.655 0.095 0.083 0.009 0.009
1 0.929 0.946 NA NA 0.087 0.077 0.009 0.009
0.075 0.4 0.931 0.970 −12.835 2.092 0.086 0.082 0.009 0.009
0.7 0.921 0.958 − 37.182 −1.180 0.070 0.059 0.008 0.008
0.9 0.914 0.954 − 125.979 −6.983 0.069 0.055 0.007 0.007
1 0.916 0.945 0.065 0.053 0.007 0.007
0.1 0.4 0.914 0.943 −11.975 2.503 0.076 0.072 0.008 0.008
0.7 0.907 0.941 −33.896 2.140 0.061 0.052 0.007 0.007
0.9 0.927 0.968 −102.743 13.059 0.047 0.038 0.006 0.006
1 0.902 0.959 NA NA 0.053 0.038 0.006 0.006
0.15 0.4 0.885 0.942 −14.697 0.333 0.058 0.046 0.006 0.006
0.7 0.875 0.943 −35.599 0.407 0.045 0.033 0.005 0.006
0.9 0.888 0.953 − 115.852 0.054 0.039 0.027 0.005 0.005
1 0.884 0.958 NA NA 0.037 0.024 0.005 0.005
0.2 0.4 0.851 0.949 −15.946 −1.037 0.049 0.031 0.005 0.006
0.7 0.852 0.945 −36.576 −1.049 0.037 0.023 0.005 0.005
0.9 0.869 0.955 − 111.602 0.545 0.031 0.019 0.004 0.004
1 0.862 0.951 NA NA 0.031 0.019 0.004 0.004
0.25 0.4 0.835 0.957 −15.713 −0.142 0.043 0.025 0.005 0.005
0.7 0.830 0.951 −36.719 −0.629 0.033 0.019 0.004 0.004
0.9 0.854 0.950 −115.785 −5.196 0.028 0.015 0.004 0.004
1 0.872 0.956 NA NA 0.024 0.015 0.004 0.004
0.3 0.4 0.829 0.950 −16.209 0.014 0.038 0.019 0.004 0.004
0.7 0.818 0.956 −36.302 − 0.295 0.029 0.014 0.004 0.004
0.9 0.862 0.946 − 103.272 6.879 0.023 0.013 0.004 0.004
1 0.857 0.948 NA NA 0.021 0.013 0.003 0.004
  1. Gompertz distribution with shape parameter α = 1, sample size N = 1000, and a relative average follow-up duration of 90% in the control group
  2. If the true HR is 1 the MPE cannot be calculated
  3. BLR baseline risk, CP coverage probability, HR hazard ratio, IDR incidence density ratio, MPE mean percent error, MSE mean square error, SE standard error
  4. Numbers in boldface indicate a CP below 90%