Table 2.

Case B: (p, β₁₁, β₁₂, β₂₁, β₂₂) = (0.6, 1, −1, 1, 1); Simulation results for the estimation of parameters over 1000 replications under the subhazard correlated frailty model

Censoring	Sample Size	Parameter	True	Mean	SD	SE1	SE2
25%	n = 200 (q = 20, ni = 10)	β11	1	1.003	0.274	0.272	0.217
		β12	−1	−1.006	0.140	0.129	0.124
		${\sigma }_0^2$	0.5	0.505	0.372	0.357	–
		${\sigma }_1^2$	0.5	0.520	0.472	0.493	–
		σ01	−0.25	−0.254	0.353	0.347	–
	n = 400 (q = 20, ni = 20)	β11	1	0.991	0.215	0.217	0.152
		β12	−1	−1.004	0.093	0.088	0.087
		${\sigma }_0^2$	0.5	0.490	0.265	0.259	–
		${\sigma }_1^2$	0.5	0.493	0.321	0.315	–
		σ01	−0.25	−0.245	0.244	0.234	–
	n = 1000 (q = 50, ni = 20)	β11	1	0.983	0.145	0.137	0.095
		β12	−1	−0.999	0.057	0.056	0.054
		${\sigma }_0^2$	0.5	0.486	0.166	0.160	–
		${\sigma }_1^2$	0.5	0.477	0.192	0.191	–
		σ01	−0.25	−0.237	0.150	0.143	–
50%	n = 200 (q = 20, ni = 10)	β11	1	1.011	0.335	0.330	0.278
		β12	−1	−1.028	0.172	0.159	0.153
		${\sigma }_0^2$	0.5	0.527	0.458	0.490	–
		${\sigma }_1^2$	0.5	0.578	0.666	0.699	–
		σ01	−0.25	−0.279	0.477	0.486	–
	n = 400 (q = 20, ni = 20)	β11	1	0.986	0.257	0.251	0.193
		β12	−1	−1.006	0.118	0.108	0.106
		${\sigma }_0^2$	0.5	0.489	0.327	0.329	–
		${\sigma }_1^2$	0.5	0.518	0.411	0.449	–
		σ01	−0.25	−0.249	0.314	0.316	–
	n = 1000 (q = 50, ni = 20)	β11	1	0.983	0.164	0.157	0.121
		β12	−1	−1.002	0.068	0.068	0.066
		${\sigma }_0^2$	0.5	0.487	0.199	0.198	–
		${\sigma }_1^2$	0.5	0.478	0.248	0.249	–
		σ01	−0.25	−0.238	0.187	0.185	–

SE1, mean of estimated standard errors using $H_w^{-1}$ and ${(-{\partial }^2{p}_{\tau }(h_w^{\ast })/\partial {\theta }^2)}^{-1}$ for β₁ =(β₁₁, β₁₂)^T and $\theta ={({\sigma }_0^2,{\sigma }_1^2,{\sigma }_{01})}^T$, respectively, over 1000 simulations;

SE2, mean of estimated standard errors using $H_w^{-1}{H}_1{H}_w^{-1}$ for β = (β₁₁, β₁₂)^T over 1000 simulations; SD, standard deviation of estimates over 1000 simulations, is defined by ${\{{\sum }_i{({\widehat{\psi }}^{(i)}-\overline{\psi })}^2/999\}}^{1/2}$, where ${\widehat{\psi }}^{(i)}$ is the estimate of ψ in the ith replication and $\overline{\psi }={\sum }_i{\widehat{\psi }}^{(i)}/1000$ is the mean of ${\widehat{\psi }}^{(i)}’\mathrm{s}$, and ψ = β₁₁, β₁₂, ${\sigma }_0^2$, ${\sigma }_1^2$, or σ₀₁.