Table 1.

Bias in estimating log causal hazard ratio parameter (ρ_a = 0, ρ_c = 0.5, ρ_r = 0.8, ${\theta }_c^1=3.33$, ${\theta }_c^0=1.67$)

α	δ	${\mathrm{Bias}}_{2\mathrm{sps}}^{\mathrm{analytic}}$	${\mathrm{Bias}}_{2\mathrm{sps}}^{\mathrm{AFT}}$	${\mathrm{Bias}}_{2\mathrm{sps}}^{\mathrm{Cox}}$	${\mathrm{Bias}}_{2\mathrm{sri}}^{\mathrm{analytic}}$	${\mathrm{Bias}}_{2\mathrm{sri}}^{\mathrm{AFT}}$	${\mathrm{Bias}}_{2\mathrm{sri}}^{\mathrm{Cox}}$
0.5	2	-0.094	-0.093	-0.091	-0.477	-0.476	-0.476
	1.5	-0.067	-0.068	-0.064	-0.238	-0.239	-0.235
	1	-0.039	-0.040	-0.039	-0.086	-0.087	-0.086
	0.5	-0.013	-0.016	-0.012	-0.015	-0.018	-0.014
	0	0.007	0.009	0.007	0.000	0.002	0.000
	-0.5	0.023	0.020	0.026	0.000	-0.003	-0.001
	-1	0.038	0.037	0.051	0.029	0.028	0.029
	-1.5	0.055	0.053	0.075	0.114	0.112	0.108
	-2	0.073	0.074	0.101	0.261	0.263	0.236
1	2	-0.250	-0.253	-0.247	-0.545	-0.550	-0.544
	1.5	-0.177	-0.175	-0.177	-0.285	-0.284	-0.284
	1	-0.096	-0.093	-0.097	-0.110	-0.107	-0.112
	0.5	-0.017	-0.020	-0.018	-0.022	-0.025	-0.023
	0	0.051	0.053	0.055	0.000	0.002	0.000
	-0.5	0.107	0.106	0.116	-0.007	-0.008	-0.009
	-1	0.152	0.153	0.177	0.000	0.000	0.002
	-1.5	0.193	0.191	0.232	0.057	0.053	0.055
	-2	0.230	0.232	0.280	0.175	0.176	0.157
1.5	2	-0.422	-0.423	-0.418	-0.605	-0.607	-0.602
	1.5	-0.285	-0.285	-0.284	-0.326	-0.325	-0.326
	1	-0.132	-0.133	-0.134	-0.133	-0.134	-0.134
	0.5	0.019	0.023	0.021	-0.028	-0.027	-0.029
	0	0.153	0.152	0.159	0.000	-0.004	0.000
	-0.5	0.261	0.266	0.274	-0.015	-0.012	-0.015
	-1	0.345	0.342	0.376	-0.030	-0.033	-0.027
	-1.5	0.412	0.412	0.461	-0.005	-0.008	-0.002
	-2	0.467	0.468	0.531	0.078	0.075	0.068
2	2	-0.574	-0.578	-0.571	-0.656	-0.656	-0.653
	1.5	-0.359	-0.360	-0.357	-0.362	-0.361	-0.359
	1	-0.122	-0.124	-0.122	-0.152	-0.153	-0.152
	0.5	0.111	0.115	0.112	-0.034	-0.032	-0.036
	0	0.317	0.320	0.324	0.000	0.003	0.002
	-0.5	0.481	0.479	0.494	-0.022	-0.026	-0.026
	-1	0.605	0.605	0.636	0.059	-0.059	-0.056
	-1.5	0.698	0.701	0.747	-0.069	-0.069	-0.063
	-2	0.769	0.770	0.833	-0.023	-0.024	-0.026

${\mathit{Bias}}_{2\mathit{sps}}^{\mathit{analytic}}$ - bias computed using analytic formula derived for 2SPS method; ${\mathit{Bias}}_{2\mathit{sps}}^{\mathit{AFT}}$ - bias computed via simulation for 2SPS Weibull accelerated failure time model; ${\mathit{Bias}}_{2\mathit{sps}}^{\mathit{Cox}}$ -bias computed via simulation for 2SPS Cox model; ${\mathit{Bias}}_{2\mathit{sri}}^{\mathit{analytic}}$ - bias computed using analytic formula derived for 2SRI method; ${\mathit{Bias}}_{2\mathit{sri}}^{\mathit{AFT}}$ -bias computed via simulation for 2SRI Weibull accelerated failure time model; ${\mathit{Bias}}_{2\mathit{sri}}^{\mathit{Cox}}$ -bias computed via simulation for 2SRI Cox model;