BMC Medical Research Methodology

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

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

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