Table 1.

Comparison of approaches by Shen et al. (2016) with the IPW methods, using equations (3) and (4), and the unadjusted Cox regression that ignores truncation (UNADJ). bias, SD and SE are, respectively, the bias and, standard deviation of $\widehat{\beta },$ average of asymptotic estimators of $SE(\widehat{\beta }),$ where SE for IPW-S is an analytical estimate, and for IPW-NS is a bootstrap estimator of $SE(\widehat{\beta })$ based on bootstrap distribution with 500 replications. CP is a coverage probability of 95% confidence interval using normal approximation and SE for IPW-S, and it is a coverage probability of 95% confidence interval $\left({\widehat{\beta }}_{0.025}^{bs},{\widehat{\beta }}_{0.925}^{bs}\right)$ based on bootstrap distribution with 500 replications for IPW-NS. MSE is an empirical mean squared error. r₍₅₀₀₎ is an n^th-order statistic of $R_1^{*},\dots ,R_n^{*}$ in the samples with n = 500, ${\overline{r}}_{(500)}$ is an average of r₍₅₀₀₎ over 1000 samples. Results are based on 1000 replications.

		β1 = 1					β2 = 1
Light truncation: R ~ Exp(2.5), P(T > R) = 0.16, avg P(T > r(500)) = 0.0001, ${\overline{r}}_{(500)}$ = 2.79
	n	$\mathrm{bias}\left({\widehat{\beta }}_1\right)$	SD	SE	MSE	CP	$\mathrm{bias}\left({\widehat{\beta }}_2\right)$	SD	SE	MSE	CP
Shen-EE	100	−0.023	0.205	0.192	0.043	0.940	−0.025	0.404	0.381	0.164	0.939
	300	−0.015	0.116	0.107	0.014	0.943	−0.029	0.249	0.238	0.063	0.943
	500	−0.009	0.073	0.069	0.005	0.950	−0.011	0.178	0.173	0.032	0.946
Shen-cMLE	100	−0.093	0.116	0.108	0.022	0.937	−0.091	0.239	0.225	0.065	0.936
	300	−0.051	0.083	0.078	0.009	0.941	−0.051	0.151	0.143	0.025	0.942
	500	−0.012	0.053	0.050	0.003	0.947	−0.044	0.108	0.102	0.014	0.947
IPW-S	100	0.017	0.145	0.156	0.021	0.960	0.013	0.267	0.256	0.071	0.946
	300	0.000	0.080	0.090	0.006	0.976	0.000	0.153	0.150	0.023	0.942
	500	0.003	0.063	0.072	0.004	0.980	−0.003	0.120	0.118	0.014	0.950
IPW-NS	100	0.015	0.149	0.151	0.023	0.938	0.010	0.284	0.277	0.081	0.941
	300	0.000	0.084	0.085	0.007	0.951	0.001	0.169	0.158	0.029	0.935
	500	0.002	0.068	0.067	0.005	0.953	−0.002	0.136	0.125	0.018	0.933
UNADJ	500	−0.125	0.052	0.054	0.018	0.363	−0.134	0.096	0.096	0.027	0.699
Moderate truncation: R ~ Exp(7.5), P(T > R) = 0.32, avg P(T > r(500)) = 0 01, ${\overline{\mathrm{r}}}_{(500)}$ = 0.96
	n	$\mathrm{bias}\left({\widehat{\beta }}_1\right)$	SD	SE	MSE	CP	$\mathrm{bias}\left({\widehat{\beta }}_2\right)$	SD	SE	MSE	CP
Shen-EE	100	−0.033	0.227	0.214	0.053	0.938	−0.073	0.473	0.443	0.229	0.937
	300	−0.028	0.157	0.147	0.025	0.941	−0.051	0.291	0.274	0.087	0.941
	500	−0.023	0.106	0.097	0.012	0.944	−0.017	0.216	0.207	0.047	0.944
Shen-cMLE	100	−0.159	0.107	0.099	0.037	0.575	−0.163	0.246	0.218	0.087	0.826
	300	−0.114	0.086	0.072	0.020	0.658	−0.125	0.168	0.159	0.044	0.852
	500	−0.085	0.055	0.052	0.010	0.714	−0.096	0.112	0.106	0.022	0.883
IPW-S	100	−0.013	0.182	0.227	0.033	0.975	−0.026	0.317	0.323	0.101	0.948
	300	−0.019	0.113	0.136	0.013	0.977	−0.027	0.208	0.198	0.044	0.943
	500	−0.016	0.094	0.110	0.009	0.978	−0.029	0.167	0.159	0.029	0.945
IPW-NS	100	−0.027	0.205	0.181	0.043	0.938	−0.044	0.394	0.353	0.157	0.934
	300	−0.030	0.134	0.112	0.019	0.902	−0.040	0.286	0.228	0.084	0.910
	500	−0.029	0.116	0.092	0.014	0.892	−0.062	0.240	0.191	0.059	0.911
UNADJ	500	−0.259	0.052	0.053	0.070	0.003	−0.253	0.095	0.096	0.073	0.267
Heavy truncation: R ~ Exp (15), P(T > R) = 0.45, avg P(T > r(500)) = 0.04, ${\overline{\mathrm{r}}}_{(500)}$ = 0.49
	n	$\mathrm{bias}\left({\widehat{\beta }}_1\right)$	SD	SE	MSE	CP	$\mathrm{bias}\left({\widehat{\beta }}_2\right)$	SD	SE	MSE	CP
Shen-EE	100	−0.078	0.272	0.254	0.080	0.935	−0.085	0.519	0.487	0.277	0.935
	300	−0.034	0.185	0.174	0.035	0.939	−0.042	0.348	0.332	0.123	0.939
	500	−0.025	0.157	0.151	0.025	0.942	−0.036	0.287	0.271	0.084	0.942
Shen-cMLE	100	−0.181	0.117	0.109	0.046	0.285	−0.194	0.268	0.252	0.109	0.720
	300	−0.146	0.091	0.086	0.030	0.376	−0.152	0.176	0.164	0.054	0.765
	500	−0.107	0.068	0.064	0.016	0.442	−0.116	0.135	0.129	0.032	0.817
IPW-S	100	−0.076	0.208	0.305	0.049	0.970	−0.068	0.367	0.412	0.140	0.949
	300	−0.056	0.140	0.205	0.023	0.965	−0.060	0.242	0.280	0.062	0.949
	500	−0.045	0.124	0.184	0.017	0.960	−0.060	0.201	0.250	0.044	0.952
IPW-NS	100	−0.106	0.240	0.208	0.069	0.874	−0.103	0.480	0.407	0.241	0.912
	300	−0.086	0.173	0.138	0.037	0.834	−0.091	0.367	0.285	0.143	0.905
	500	−0.074	0.160	0.117	0.031	0.811	−0.096	0.334	0.249	0.120	0.888
UNADJ	500	−0.370	0.051	0.053	0.140	0.000	−0.343	0.092	0.096	0.126	0.048