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Table 1 Simulation results for the estimation of attributable risk A(.) under proportional hazards, constant baseline hazard (γ=1) 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 0.284 0.001584 0.052440 0.052591 0.949 −0.000011 0.016622 0.016349 0.944
  τ/2 0.240 0.001496 0.039210 0.039099 0.948 0.000235 0.012434 0.012420 0.944
  3 τ/4 0.200 0.001100 0.035666 0.035948 0.946 −0.000333 0.011353 0.011354 0.949
  τ 0.166 0.004047 0.043238 0.053015 0.912 0.001025 0.017251 0.019598 0.943
WKM τ/4 0.284 0.001594 0.052516 0.052483 0.949 0.000003 0.016613 0.016357 0.946
  τ/2 0.240 0.001541 0.039144 0.038926 0.950 0.000285 0.012401 0.012398 0.946
  3 τ/4 0.200 0.001093 0.035402 0.035479 0.953 −0.000286 0.011283 0.011297 0.952
  τ 0.166 0.002922 0.040635 0.048602 0.902 0.000497 0.016646 0.018245 0.942
COX τ/4 0.284 0.000977 0.038843 0.038208 0.958 −0.000136 0.012292 0.012206 0.956
  τ/2 0.240 0.001108 0.033847 0.033524 0.951 0.000006 0.010700 0.010616 0.958
  3 τ/4 0.200 0.001031 0.029264 0.028893 0.958 −0.000081 0.009237 0.009253 0.954
  τ 0.166 0.002577 0.027146 0.027753 0.946 0.000148 0.008965 0.009087 0.950
PCH τ/4 0.284 0.001356 0.038338 0.038248 0.952 −0.000086 0.012120 0.012209 0.953
  τ/2 0.240 0.001372 0.033380 0.033529 0.948 0.000034 0.010543 0.010608 0.952
  3 τ/4 0.200 0.001113 0.028804 0.028870 0.957 −0.000081 0.009088 0.009263 0.952
  τ 0.166 0.001564 0.025811 0.025420 0.961 −0.000154 0.008105 0.008153 0.952
Simpler 0.333 0.000826 0.043356 0.043147 0.952 −0.000209 0.013715 0.013776 0.955
  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