Table 1 Estimated bias, RMSE, SE and approximated 95% coverage probabilities for the TN frailty model with basal distribution PE under different scenarios (cases censoring 10% and 25%).

From: The multivariate shared truncated normal frailty model with application to medical data

Censoring	\(\theta\)	Parameter	Scenario 1				Scenario 2				Scenario 3
Censoring	\(\theta\)	Parameter	Bias	RMSE	SE	CP	Bias	RMSE	SE	CP	Bias	RMSE	SE	CP
\(10\%\)	0.20	\(\theta\)	−0.003	0.109	0.106	0.894	0.003	0.074	0.073	0.922	−0.011	0.081	0.076	0.887
		\(\beta\)	0.005	0.299	0.286	0.941	−0.026	0.213	0.201	0.940	−0.020	0.201	0.193	0.945
		\(\lambda _1\)	0.076	0.243	0.261	0.941	0.019	0.171	0.166	0.863	0.028	0.177	0.173	0.875
		\(\lambda _2\)	0.053	0.645	0.599	0.877	0.071	0.460	0.413	0.854	0.049	0.483	0.445	0.874
		\(\lambda _3\)	−0.073	0.462	0.414	0.857	−0.089	0.331	0.279	0.819	−0.059	0.333	0.290	0.848
	0.50	\(\theta\)	−0.076	0.204	0.210	0.806	−0.044	0.150	0.152	0.871	−0.077	0.173	0.160	0.793
		\(\beta\)	−0.053	0.322	0.287	0.913	−0.046	0.238	0.193	0.877	−0.044	0.206	0.188	0.918
		\(\lambda _1\)	0.086	0.265	0.203	0.708	0.026	0.193	0.096	0.494	0.024	0.191	0.129	0.655
		\(\lambda _2\)	0.058	0.741	0.457	0.615	0.004	0.511	0.224	0.425	0.022	0.558	0.341	0.604
		\(\lambda _3\)	−0.224	0.595	0.377	0.601	−0.237	0.453	0.197	0.460	−0.186	0.448	0.255	0.598
	0.75	\(\theta\)	−0.226	0.307	0.26	0.695	−0.172	0.237	0.202	0.750	−0.182	0.261	0.220	0.726
		\(\beta\)	−0.082	0.329	0.282	0.888	−0.092	0.246	0.193	0.859	−0.047	0.213	0.186	0.920
		\(\lambda _1\)	0.080	0.265	0.162	0.569	0.039	0.203	0.068	0.345	0.025	0.191	0.105	0.546
		\(\lambda _2\)	−0.081	0.790	0.357	0.464	−0.048	0.538	0.15	0.278	−0.047	0.642	0.285	0.456
		\(\lambda _3\)	−0.419	0.708	0.300	0.443	−0.413	0.578	0.153	0.304	−0.274	0.522	0.226	0.463
\(25\%\)	0.20	\(\theta\)	0.038	0.149	0.137	0.937	0.030	0.102	0.089	0.942	0.006	0.095	0.087	0.915
		\(\beta\)	−0.052	0.344	0.307	0.917	−0.053	0.234	0.216	0.922	−0.044	0.225	0.210	0.940
		\(\lambda _1\)	0.099	0.258	0.285	0.977	0.027	0.226	0.179	0.903	0.030	0.199	0.182	0.919
		\(\lambda _2\)	0.086	0.673	0.647	0.924	0.066	0.467	0.455	0.915	0.047	0.491	0.482	0.932
		\(\lambda _3\)	−0.119	0.548	0.478	0.852	−0.180	0.401	0.325	0.817	−0.154	0.400	0.330	0.829
	0.50	\(\theta\)	−0.048	0.200	0.239	0.856	0.001	0.171	0.187	0.915	−0.045	0.187	0.185	0.830
		\(\beta\)	−0.105	0.353	0.307	0.903	−0.103	0.261	0.217	0.886	−0.070	0.230	0.209	0.919
		\(\lambda _1\)	0.107	0.277	0.248	0.823	0.037	0.184	0.141	0.717	0.044	0.187	0.168	0.831
		\(\lambda _2\)	0.060	0.771	0.565	0.736	0.045	0.519	0.362	0.659	0.042	0.568	0.468	0.792
		\(\lambda _3\)	−0.416	0.687	0.415	0.606	−0.398	0.554	0.274	0.508	−0.295	0.519	0.331	0.658
	0.75	\(\theta\)	−0.195	0.288	0.298	0.771	−0.119	0.218	0.243	0.838	−0.173	0.254	0.241	0.763
		\(\beta\)	−0.126	0.370	0.309	0.901	−0.117	0.272	0.216	0.876	−0.099	0.242	0.208	0.915
		\(\lambda _1\)	0.104	0.277	0.229	0.762	0.050	0.207	0.122	0.590	0.040	0.201	0.149	0.720
		\(\lambda _2\)	0.003	0.817	0.531	0.653	−0.025	0.541	0.299	0.531	−0.025	0.659	0.426	0.659
		\(\lambda _3\)	−0.600	0.813	0.366	0.459	−0.561	0.672	0.225	0.353	−0.411	0.594	0.298	0.508

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Table 1 Estimated bias, RMSE, SE and approximated 95% coverage probabilities for the TN frailty model with basal distribution PE under different scenarios (cases censoring 10% and 25%).

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