Table 1.

Simulation results PDS design.^†

			β 1				β 2
β 1	a	Method	Mean	SE	$\widehat{\mathrm{SE}}$	CI	Mean	SE	$\widehat{\mathrm{SE}}$	CI
			(n0, n1, n3) = (200, 100, 100)
0.0	1.0	${\widehat{\beta }}_X$	−0.002	0.038	0.038	0.948	−0.502	0.127	0.127	0.951
		${\widehat{\beta }}_{\mathit{PDS}1}$	0.000	0.043	0.041	0.930	−0.496	0.150	0.127	0.946
		${\widehat{\beta }}_{\mathit{PDS}2}$	0.000	0.037	0.037	0.950	−0.500	0.095	0.096	0.962
		${\widehat{\beta }}_{\mathit{ODS}}$	0.002	0.038	0.039	0.942	−0.505	0.120	0.123	0.958
		${\widehat{\beta }}_{\mathit{IPW}}$	0.000	0.046	0.046	0.952	−0.510	0.146	0.140	0.931
		${\widehat{\beta }}_{\mathit{SRS}}$	0.001	0.050	0.050	0.957	−0.502	0.150	0.154	0.955
		${\widehat{\beta }}_N$	0.001	0.047	0.048	0.956	−0.493	0.310	0.119	0.575
0.5	1.0	${\widehat{\beta }}_X$	0.499	0.038	0.038	0.957	−0.498	0.126	0.126	0.946
		${\widehat{\beta }}_{\mathit{PDS}1}$	0.501	0.039	0.041	0.954	−0.494	0.097	0.106	0.968
		${\widehat{\beta }}_{\mathit{PDS}2}$	0.500	0.043	0.042	0.936	−0.495	0.104	0.106	0.950
		${\widehat{\beta }}_{\mathit{ODS}}$	0.503	0.044	0.045	0.953	−0.505	0.128	0.131	0.954
		${\widehat{\beta }}_{\mathit{IPW}}$	0.502	0.047	0.046	0.941	−0.508	0.155	0.151	0.938
		${\widehat{\beta }}_{\mathit{SRS}}$	0.500	0.049	0.050	0.955	−0.496	0.156	0.154	0.944
		${\widehat{\beta }}_N$	0.633	0.060	0.052	0.302	−0.495	0.122	0.134	0.972
0.5	1.5	${\widehat{\beta }}_X$	0.502	0.032	0.032	0.951	−0.500	0.120	0.117	0.940
		${\widehat{\beta }}_{\mathit{PDS}1}$	0.499	0.037	0.037	0.938	−0.503	0.100	0.097	0.946
		${\widehat{\beta }}_{\mathit{PDS}2}$	0.499	0.038	0.038	0.942	−0.500	0.103	0.099	0.940
		${\widehat{\beta }}_{\mathit{ODS}}$	0.503	0.042	0.043	0.956	−0.495	0.118	0.120	0.963
		${\widehat{\beta }}_{\mathit{IPW}}$	0.504	0.055	0.052	0.934	−0.508	0.167	0.166	0.937
		${\widehat{\beta }}_{\mathit{SRS}}$	0.500	0.049	0.050	0.955	−0.496	0.156	0.154	0.944
		${\widehat{\beta }}_N$	0.694	0.108	0.049	0.178	−0.507	0.297	0.128	0.603
			(n0, n1, n3) = (300, 50, 50)
0.5	1.5	${\widehat{\beta }}_X$	0.498	0.038	0.038	0.951	−0.497	0.130	0.130	0.949
		${\widehat{\beta }}_{\mathit{PDS}1}$	0.501	0.042	0.042	0.952	−0.497	0.114	0.113	0.932
		${\widehat{\beta }}_{\mathit{PDS}2}$	0.499	0.043	0.044	0.966	−0.498	0.120	0.121	0.950
		${\widehat{\beta }}_{\mathit{ODS}}$	0.503	0.044	0.045	0.955	−0.495	0.126	0.129	0.960
		${\widehat{\beta }}_{\mathit{IPW}}$	0.502	0.046	0.045	0.942	−0.498	0.147	0.144	0.940
		${\widehat{\beta }}_{\mathit{SRS}}$	0.500	0.049	0.050	0.955	−0.496	0.156	0.154	0.944
		${\widehat{\beta }}_N$	0.623	0.072	0.050	0.367	−0.487	0.149	0.130	0.923
			(n0, n1, n3) = (100, 50, 50)
0.5	1.0	${\widehat{\beta }}_X$	0.499	0.051	0.053	0.956	−0.501	0.178	0.179	0.951
		${\widehat{\beta }}_{\mathit{PDS}1}$	0.494	0.058	0.056	0.934	−0.498	0.150	0.140	0.942
		${\widehat{\beta }}_{\mathit{PDS}2}$	0.502	0.059	0.058	0.948	−0.505	0.146	0.150	0.968
		${\widehat{\beta }}_{\mathit{ODS}}$	0.502	0.062	0.062	0.955	−0.505	0.188	0.187	0.937
		${\widehat{\beta }}_{\mathit{IPW}}$	0.508	0.066	0.064	0.929	−0.507	0.218	0.210	0.922
		${\widehat{\beta }}_{\mathit{SRS}}$	0.495	0.072	0.071	0.944	−0.499	0.219	0.219	0.955
		${\widehat{\beta }}_N$	0.636	0.084	0.074	0.544	−0.492	0.180	0.192	0.967

^†Results are based on the model Y = β₀ + β₁X + β₂I_log(|x|)+e>1 + ∊, where e ~ N(0, 1), ∊ ~ N (0, 1), and X ~ N (0, 1); the true parameter values are β₀ = 1.0 and (β₂ = −0.5. ${\widehat{\beta }}_X$, ${\widehat{\beta }}_{\mathit{PDS}1}$, ${\widehat{\beta }}_{\mathit{PDS}2}$, ${\widehat{\beta }}_{\mathit{ODS}}$, ${\widehat{\beta }}_{\mathit{SRS}}$, ${\widehat{\beta }}_{\mathit{IPW}}$, and ${\widehat{\beta }}_N$ are defined as in Section 3.1.