BMC Medical Research Methodology

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

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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