Table 1.

Performance of the proposed joint model compared with the joint frailty model and shared frailty models ignoring Level-2 clustering

N=300	Proposed joint model (PJM)					Joint frailty model with Level-1 clustering only (JFM-L1)					Shared frailty model with Level-1 clustering only (SFM-L1)
Parameter	Estimate	Bias	SE	SEM	CP	Estimate	Bias	SE	SEM	CP	Estimate	Bias	SE	SEM	CP
β= −0.5	−0.483	3.4	0.215	0.190	0.944	−0.491	1.8	0.239	0.221	0.947	−0.327	52.9	0.153	0.152	0.787
α= −0.5	−0.502	0.4	0.262	0.284	0.958	−0.521	4.2	0.285	0.287	0.943			NA
γ2= 0.5	0.506	1.2	0.181	0.178	0.986			NA					NA
γ1= 0.5	0.495	1.0	0.236	0.227	0.972	0.514	2.8	0.156	0.151	0.960			NA
θ2 =1.0	0.942	5.8	0.261	0.244	0.901			NA					NA
θ1= 1.0	1.005	0.5	0.105	0.099	0.944	1.356	35.6	0.195	0.110	0.227	0.665	50.4	0.207	0.105	0.234
β= −0.5	−0.487	2.6	0.201	0.190	0.963	−0.501	0.2	0.221	0.221	0.950	−0.346	44.5	0.152	0.159	0.819
α= −0.5	−0.521	4.2	0.296	0.269	0.936	−0.473	5.4	0.297	0.288	0.940			NA
γ2= 1.0	1.060	6.0	0.242	0.207	0.938			NA					NA
γ1= 0.5	0.535	7.0	0.191	0.205	0.951	0.719	43.8	0.172	0.157	0.680			NA
θ2 =1.0	0.929	7.1	0.219	0.239	0.901			NA					NA
θ1= 1.0	0.989	1.1	0.089	0.099	0.988	1.348	34.8	0.187	0.113	0.223	0.673	48.6	0.230	0.117	0.305
β= −0.5	−0.505	1.0	0.209	0.200	0.952	−0.511	2.2	0.229	0.231	0.967	−0.307	62.9	0.167	0.163	0.768
α= −0.5	−0.480	4.0	0.282	0.251	0.912	−0.399	20.2	0.305	0.291	0.917			NA
γ2= 2.0	2.032	1.6	0.367	0.372	0.959			NA					NA
γ1= 0.5	0.534	6.8	0.231	0.218	0.966	0.905	81.0	0.234	0.190	0.413			NA
θ2 =1.0	0.920	8.0	0.256	0.245	0.878			NA					NA
θ1= 1.0	0.985	1.5	0.114	0.110	0.932	1.349	34.9	0.194	0.129	0.270	0.556	79.9	0.180	0.146	0.176

NA: Not Applicable; Percent Relative Bias = mean of $\left|\frac{\mathit{\text{observed}}-\mathit{\text{true}}}{\mathit{\text{true}}}\right|\times 100$; SE = Sampling standard error of the parameter estimate; SEM = Sampling mean of the standard error estimate (SEM); CP = Coverage probability of the corresponding 95% confidence interval