Table 7.

Maximum likelihood estimate (MLEs), standard error (SE), $95\mathrm{\%}$ asymptotic confidence intervals (CI), AIC value obtained for the CLL Gamma and CLL IG frailty models categorized by surgery, age and gender fitted for the melanoma dataset.

Model	Extended CLL				CLL PVF frailty
			CI(95%)				CI(95%)
Parameter	MLE	SE	Lower	Upper	MLE	SE	Lower	Upper
${\alpha }_0$	0.184	0.010	0.165	0.203	0.135	0.015	0.105	0.165
${\alpha }_{1_{\text{(Yes)}}}$	−0.145	0.010	−0.164	−0.125	−0.110	0.015	−0.139	−0.081
${\alpha }_{2_{\text{(Older)}}}$	0.007	0.007	−0.006	0.020	0.005	0.007	−0.009	0.018
${\alpha }_{3_{\text{(Male)}}}$	0.019	0.007	0.006	0.032	0.007	0.007	−0.007	0.021
λ	0.916	0.057	0.805	1.027	1.347	0.128	1.095	1.598
${\mathrm{\text{β}}}_{1_{\text{(Yes)}}}$	1.093	0.028	1.037	1.148	1.217	0.035	1.148	1.286
${\mathrm{\text{β}}}_{2_{\text{(Age)}}}$	−0.143	0.031	−0.204	−0.083	−0.163	0.031	−0.225	−0.102
${\mathrm{\text{β}}}_{3_{\text{(Male)}}}$	−0.213	0.029	−0.270	−0.156	−0.203	0.030	−0.262	−0.143
γ	–	–	–	–	0.329	0.126	0.082	0.576
θ	–	–	–	–	1.511	0.266	0.989	2.033
max $\ell (\cdot )$	$-6639.61$				$-6609.39$
AIC	$\mathrm{13,295.22}$				$\mathrm{13,238.78}$
Model	CLL Gamma frailty				CLL IG frailty
${\alpha }_0$	0.125	0.016	0.093	0.156	0.153	0.012	0.130	0.176
${\alpha }_{1_{\text{(Yes)}}}$	−0.098	0.016	−0.129	−0.068	−0.125	0.012	−0.148	−0.102
${\alpha }_{2_{\text{(Older)}}}$	0.001	0.007	−0.012	0.014	0.003	0.007	−0.010	0.016
${\alpha }_{3_{\text{(Male)}}}$	0.003	0.007	−0.011	0.016	0.009	0.007	−0.004	0.022
λ	1.655	0.163	1.335	1.975	1.413	0.134	1.150	1.676
${\mathrm{\text{β}}}_{1_{\text{(Yes)}}}$	1.267	0.034	1.201	1.334	1.221	0.034	1.156	1.287
${\mathrm{\text{β}}}_{2_{\text{(Older)}}}$	−0.145	0.030	−0.203	−0.087	−0.149	0.031	−0.209	−0.089
${\mathrm{\text{β}}}_{3_{\text{(Male)}}}$	−0.177	0.028	−0.233	−0.121	−0.194	0.029	−0.251	−0.137
γ	–	–	–	–	–	–	–	–
θ	1.457	0.194	1.078	1.837	1.468	0.302	0.877	2.059
max $\ell (\cdot )$	$-6602.22$				$-6612.81$
AIC	$\mathrm{13,222.44}$				$\mathrm{13,243.62}$