Table 2.

Simulation results for lognormal frailty: AVG, average number of events per subject; SD, sample standard deviation; SE, mean of estimated standard errors; CP, empirical coverage probability of 95% Wald-type confidence interval; RE, relative efficiency of NPMLE compared with GehanR.

						NPMLE			GehanR
AVG	σ2	Bias	SD	β	Bias	SD	SE	CP(%)	Bias	SD	RE
Λ0(t)=log(t + 1)
2	2.320	−0.308	.769	−1	0.052	.491	.469	93.4	−0.001	.730	2.210
				1	−0.027	.414	.417	94.6	−0.029	.587	2.010
4	2.320	−0.136	.779	−1	0.046	.398	.460	96.4	0.019	1.085	7.432
				1	−0.022	.367	.411	95.8	−0.025	.876	5.697
2	1.718	−0.121	.572	−1	0.055	.475	.464	94.0	0.003	.663	1.948
				1	0.04	.406	.415	95.2	−0.022	.556	1.875
4	1.718	−0.045	.523	−1	0.016	.406	.410	94.8	0.015	.985	5.886
				1	−0.014	.382	.363	94.0	−0.011	.773	4.095
2	0.649	0.128	.235	−1	0.009	.405	.439	95.4	−0.022	.479	1.399
				1	−0.000	.374	.390	95.8	0.009	.414	1.225
4	0.649	0.061	.189	−1	−0.006	.378	.392	95.8	0.001	.692	3.351
				1	0.028	.344	.346	94.8	0.012	.575	2.794
Λ0(t)=−log{1 − Φ(log t)}
2	2.320	−0.371	.731	−1	0.045	.329	.309	96.0	−0.015	.413	1.576
				1	−0.054	.287	.279	93.2	−0.011	.359	1.565
4	2.320	−0.305	.744	−1	0.052	.337	.337	95.0	−0.009	.506	2.254
				1	−0.018	.299	.297	94.2	−0.015	.413	1.908
2	1.718	−0.153	.572	−1	0.009	.293	.282	93.8	−0.019	.377	1.656
				1	−0.018	.262	.254	94.4	−0.009	.328	1.567
4	1.718	−0.216	.484	−1	0.052	.286	.292	95.0	−0.009	.451	2.487
				1	−0.05	.257	.257	93.6	−0.012	.370	2.073
2	0.649	0.088	.257	−1	−0.009	.281	.272	94.0	−0.02	.296	1.110
				1	0.026	.233	.245	96.4	0.005	.244	1.097
4	0.649	−0.011	.177	−1	0.006	.243	.249	95.0	−0.017	.322	1.756
				1	−0.012	.215	.222	95.6	0.008	.265	1.519