Table 2.

Nonlinear model: simulation results of parameter estimations

	Time-dependent Cox model				Proposed PLSI-Cox model
	Bias	SD	SE	CP	Bias	SD	SE	CP
N = 500 with censoring rate 25% (99.8% converged)
${\beta }_1$	−0.344	0.350	0.247	0.634	0.000	0.014	0.014	0.946
${\beta }_2$	0.343	0.338	0.245	0.660	0.000	0.015	0.014	0.938
${\beta }_3$	−0.359	0.340	0.248	0.638	0.000	0.014	0.014	0.932
${\beta }_4$	0.357	0.326	0.244	0.636	0.000	0.015	0.014	0.930
${\beta }_5$	−0.344	0.349	0.246	0.638	−0.002	0.014	0.014	0.948
${\beta }_6$	−0.370	0.381	0.275	0.650	0.000	0.017	0.017	0.958
${\beta }_7$	0.360	0.374	0.268	0.670	−0.001	0.016	0.015	0.934
${\beta }_8$	−0.350	0.369	0.275	0.690	0.000	0.017	0.017	0.952
${\alpha }_1$	−0.488	0.431	0.431	0.774	−0.067	0.408	0.423	0.954
${\alpha }_2$	0.455	0.409	0.430	0.848	0.053	0.398	0.425	0.974
${\alpha }_3$	−0.231	0.097	0.099	0.380	−0.023	0.099	0.099	0.948
N = 500 with censoring rate 50% (100% converged)
${\beta }_1$	−0.362	0.344	0.250	0.650	0.000	0.014	0.014	0.938
${\beta }_2$	0.361	0.342	0.249	0.638	0.001	0.015	0.014	0.938
${\beta }_3$	−0.341	0.327	0.250	0.672	−0.001	0.014	0.014	0.952
${\beta }_4$	0.379	0.342	0.247	0.632	0.001	0.013	0.014	0.958
${\beta }_5$	−0.349	0.346	0.251	0.670	−0.001	0.015	0.014	0.940
${\beta }_6$	−0.330	0.387	0.275	0.678	−0.001	0.017	0.017	0.950
${\beta }_7$	0.357	0.359	0.270	0.660	0.000	0.016	0.015	0.938
${\beta }_8$	−0.364	0.378	0.278	0.672	0.002	0.018	0.017	0.938
${\alpha }_1$	−0.481	0.419	0.430	0.798	−0.089	0.394	0.422	0.962
${\alpha }_2$	0.471	0.431	0.429	0.814	0.093	0.423	0.422	0.952
${\alpha }_3$	−0.232	0.092	0.099	0.348	−0.022	0.096	0.099	0.952
N = 300 with censoring rate 25% (99.8% converged)
${\beta }_1$	−0.321	0.336	0.245	0.688	−0.001	0.018	0.019	0.962
${\beta }_2$	0.356	0.343	0.243	0.638	0.001	0.017	0.019	0.960
${\beta }_3$	−0.359	0.340	0.244	0.622	0.000	0.019	0.019	0.952
${\beta }_4$	0.355	0.350	0.241	0.618	0.001	0.018	0.019	0.968
${\beta }_5$	−0.347	0.353	0.245	0.628	−0.001	0.019	0.019	0.944
${\beta }_6$	−0.340	0.372	0.272	0.668	0.000	0.022	0.024	0.966
${\beta }_7$	0.335	0.367	0.266	0.676	−0.001	0.020	0.021	0.968
${\beta }_8$	−0.333	0.365	0.274	0.700	0.000	0.021	0.024	0.966
${\alpha }_1$	−0.447	0.556	0.574	0.882	−0.026	0.572	0.567	0.956
${\alpha }_2$	0.481	0.564	0.575	0.872	0.094	0.532	0.571	0.968
${\alpha }_3$	−0.235	0.134	0.132	0.594	−0.026	0.127	0.133	0.954
N = 300 with censoring rate 50% (100% converged)
${\beta }_1$	−0.401	0.346	0.248	0.600	−0.002	0.019	0.019	0.948
${\beta }_2$	0.392	0.333	0.247	0.600	0.000	0.018	0.019	0.956
${\beta }_3$	−0.361	0.346	0.250	0.630	0.000	0.019	0.020	0.958
${\beta }_4$	0.367	0.342	0.245	0.648	0.002	0.018	0.019	0.954
${\beta }_5$	−0.379	0.335	0.250	0.618	−0.001	0.019	0.019	0.942
${\beta }_6$	−0.354	0.381	0.276	0.660	0.000	0.023	0.024	0.962
${\beta }_7$	0.355	0.360	0.268	0.644	−0.001	0.021	0.021	0.948
${\beta }_8$	−0.364	0.379	0.277	0.662	−0.001	0.024	0.024	0.936
${\alpha }_1$	−0.420	0.565	0.572	0.902	−0.011	0.566	0.567	0.936
${\alpha }_2$	0.440	0.553	0.572	0.878	0.018	0.568	0.566	0.956
${\alpha }_3$	−0.236	0.130	0.132	0.598	−0.030	0.125	0.131	0.962