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Table 4 Simulation results for the estimation of attributable risk A(.) under nonproportional hazards 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 0.181 0.001124 0.045053 0.045787 0.954 0.000289 0.014277 0.014126 0.949
  τ/2 0.133 0.001330 0.037581 0.037647 0.953 −0.000029 0.011915 0.012154 0.935
  3 τ/4 0.109 0.001211 0.036543 0.036593 0.953 −0.000301 0.011618 0.011608 0.952
  τ 0.093 0.002743 0.043713 0.051764 0.933 −0.000888 0.016362 0.019957 0.950
WKM τ/4 0.181 0.001138 0.045090 0.045739 0.954 0.000291 0.014274 0.014130 0.949
  τ/2 0.133 0.001347 0.037587 0.037593 0.956 −0.000024 0.011911 0.012151 0.938
  3 τ/4 0.109 0.001165 0.036511 0.036518 0.952 −0.000293 0.011612 0.011607 0.956
  τ 0.093 0.001685 0.042617 0.049261 0.920 −0.000708 0.016157 0.019107 0.946
COX τ/4 0.181 −0.018761 0.037521 0.037543 0.933 −0.019843 0.011869 0.011939 0.621
  τ/2 0.133 0.010548 0.033500 0.033580 0.941 0.009504 0.010588 0.010676 0.847
  3 τ/4 0.109 0.023376 0.030960 0.031017 0.879 0.022314 0.009775 0.009879 0.368
  τ 0.093 0.030360 0.029427 0.029588 0.830 0.029168 0.009323 0.009456 0.127
PCH τ/4 0.181 0.026479 0.048525 0.049191 0.908 −0.017516 0.011688 0.012080 0.672
  τ/2 0.133 0.057418 0.044915 0.045594 0.738 0.011082 0.010391 0.010768 0.806
  3 τ/4 0.109 0.070045 0.042342 0.043042 0.607 0.023478 0.009571 0.009936 0.313
  τ 0.093 0.075924 0.040403 0.041050 0.525 0.029848 0.009011 0.009360 0.098
  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, 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