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Table 2 Simulation results for the estimation of attributable risk A(.) under proportional hazards, decreasing baseline hazard (γ=3/4) with regression parameter β= ln(2) and probability of exposure q=0.5

From: Comparison of methods for estimating the attributable risk in the context of survival analysis

Estimation method    n=1, 000 n=10, 000
  Time A(t) Bias SEE SSD CP Bias SEE SSD CP
KM τ/4 0.269 0.001799 0.044659 0.045486 0.940 0.000129 0.014162 0.014200 0.946
  τ/2 0.231 0.001217 0.036054 0.036037 0.943 0.000351 0.011437 0.011547 0.946
  3 τ/4 0.200 0.001164 0.034218 0.034637 0.948 −0.000204 0.010895 0.010746 0.956
  τ 0.176 0.003532 0.041550 0.047835 0.915 0.000299 0.016351 0.019086 0.948
WKM τ/4 0.269 0.001832 0.044713 0.045359 0.942 0.000131 0.014153 0.014197 0.946
  τ/2 0.231 0.001283 0.035999 0.035858 0.947 0.000368 0.011408 0.011509 0.947
  3 τ/4 0.200 0.001132 0.034004 0.034272 0.950 −0.000193 0.010838 0.010716 0.956
  τ 0.176 0.002628 0.039647 0.045615 0.906 0.000116 0.015851 0.017720 0.947
COX τ/4 0.269 0.000957 0.036029 0.035611 0.955 0.000107 0.011401 0.011229 0.955
  τ/2 0.231 0.001067 0.031741 0.031499 0.954 0.000129 0.010031 0.009949 0.953
  3 τ/4 0.200 0.000972 0.028300 0.028071 0.962 0.000060 0.008937 0.008899 0.949
  τ 0.176 0.002177 0.026818 0.027274 0.955 0.000168 0.008790 0.008771 0.956
PCH τ/4 0.269 0.003717 0.035027 0.035896 0.940 0.002630 0.011076 0.011300 0.939
  τ/2 0.231 0.002926 0.030819 0.031734 0.945 0.001853 0.009736 0.009995 0.936
  3 τ/4 0.200 0.002124 0.027440 0.028260 0.949 0.001247 0.008666 0.008949 0.940
  τ 0.176 0.001883 0.025457 0.025679 0.958 0.000621 0.008014 0.008240 0.946
Simpler 0.333 0.000814 0.041900 0.041749 0.952 0.000050 0.013257 0.013257 0.947
  1. KM nonparametric approach based on Kaplan-Meier estimation for S(t), WKM nonparametric approach based on weighted Kaplan-Meier estimation for S(t), COX semiparametric approach, PCH parametric approach using a piecewise constant hazards model, Simpler simpler approach based on proportion of exposed subjects, Bias sampling mean of the difference between \(\hat {A}(t)\) and A(t), SEE sampling mean of standard error estimate of A(t), SSD sampling standard deviation of \(\hat {A}(t)\), CP coverage probability of the 95% Wald confidence interval