Table 6 Open in new tab Estimation...

	JM	No Variability	PH
Survival
γ₁	–0.4095	0.1389	–0.4425	0.1386	–0.5974	0.1581
γ₂	–0.0967	0.1701	–0.1263	0.1658	–0.2679	0.1386
γ₃	0.7081	0.1228	0.7121	0.1264	0.6827	0.1159
γ₄	0.2219	0.1430	0.2215	0.1405	0.2280	0.1406
γ₅	0.3557	0.2142	0.3584	0.2110	0.3581	0.2092
α₁	0.3693	0.1659	0.3015	0.1372	–	–
α₂	0.2378	0.1035	–	–	–	–
Longitudinal
η₁	–0.0466	0.0106	–0.0471	0.0102	–	–
η₂	0.0330	0.0146	0.0328	0.0147	–	–
η₃	0.0928	0.0208	0.0927	0.0204	–	–
ξ	0.0789	0.0049	0.0796	0.0047	–	–
D₂₂	0.2189	0.0069	0.2219	0.0068	–	–
D₃₃	0.2161	0.0082	0.2206	0.0080	–	–
D₄₄	0.4064	0.0175	0.4090	0.0178	–	–
D₅₅	0.5362	0.0221	0.5395	0.0218	–	–
D₆₆	0.3037	0.0128	0.3036	0.0125	–	–
$σ^{2}$	0.1798	0.0016	0.1798	0.0016	–	–

	JM	No Variability	PH
Survival
γ₁	–0.4095	0.1389	–0.4425	0.1386	–0.5974	0.1581
γ₂	–0.0967	0.1701	–0.1263	0.1658	–0.2679	0.1386
γ₃	0.7081	0.1228	0.7121	0.1264	0.6827	0.1159
γ₄	0.2219	0.1430	0.2215	0.1405	0.2280	0.1406
γ₅	0.3557	0.2142	0.3584	0.2110	0.3581	0.2092
α₁	0.3693	0.1659	0.3015	0.1372	–	–
α₂	0.2378	0.1035	–	–	–	–
Longitudinal
η₁	–0.0466	0.0106	–0.0471	0.0102	–	–
η₂	0.0330	0.0146	0.0328	0.0147	–	–
η₃	0.0928	0.0208	0.0927	0.0204	–	–
ξ	0.0789	0.0049	0.0796	0.0047	–	–
D₂₂	0.2189	0.0069	0.2219	0.0068	–	–
D₃₃	0.2161	0.0082	0.2206	0.0080	–	–
D₄₄	0.4064	0.0175	0.4090	0.0178	–	–
D₅₅	0.5362	0.0221	0.5395	0.0218	–	–
D₆₆	0.3037	0.0128	0.3036	0.0125	–	–
$σ^{2}$	0.1798	0.0016	0.1798	0.0016	–	–

Table 6

Estimation results for MRC data under different models. JM refers to the proposed joint model; No Variability refers to the standard joint model with the restriction $α_{2} = 0$ and PH is the proportional hazards model involving baseline covariates only. ${SD}^{b}$ in both JM and No Variability denote the standard deviation based on 100 bootstrap samples and SD’s in PH are obtained from R function “coxph”.

	JM		No Variability		PH
Parameters	$\hat{θ}$	${SD}^{b}$	$\hat{θ}$	${SD}^{b}$	$\hat{θ}$	SD
Survival
γ₁	–0.4095	0.1389	–0.4425	0.1386	–0.5974	0.1581
γ₂	–0.0967	0.1701	–0.1263	0.1658	–0.2679	0.1386
γ₃	0.7081	0.1228	0.7121	0.1264	0.6827	0.1159
γ₄	0.2219	0.1430	0.2215	0.1405	0.2280	0.1406
γ₅	0.3557	0.2142	0.3584	0.2110	0.3581	0.2092
α₁	0.3693	0.1659	0.3015	0.1372	–	–
α₂	0.2378	0.1035	–	–	–	–
Longitudinal
η₁	–0.0466	0.0106	–0.0471	0.0102	–	–
η₂	0.0330	0.0146	0.0328	0.0147	–	–
η₃	0.0928	0.0208	0.0927	0.0204	–	–
ξ	0.0789	0.0049	0.0796	0.0047	–	–
D₂₂	0.2189	0.0069	0.2219	0.0068	–	–
D₃₃	0.2161	0.0082	0.2206	0.0080	–	–
D₄₄	0.4064	0.0175	0.4090	0.0178	–	–
D₅₅	0.5362	0.0221	0.5395	0.0218	–	–
D₆₆	0.3037	0.0128	0.3036	0.0125	–	–
$σ^{2}$	0.1798	0.0016	0.1798	0.0016	–	–

	JM		No Variability		PH
Parameters	$\hat{θ}$	${SD}^{b}$	$\hat{θ}$	${SD}^{b}$	$\hat{θ}$	SD
Survival
γ₁	–0.4095	0.1389	–0.4425	0.1386	–0.5974	0.1581
γ₂	–0.0967	0.1701	–0.1263	0.1658	–0.2679	0.1386
γ₃	0.7081	0.1228	0.7121	0.1264	0.6827	0.1159
γ₄	0.2219	0.1430	0.2215	0.1405	0.2280	0.1406
γ₅	0.3557	0.2142	0.3584	0.2110	0.3581	0.2092
α₁	0.3693	0.1659	0.3015	0.1372	–	–
α₂	0.2378	0.1035	–	–	–	–
Longitudinal
η₁	–0.0466	0.0106	–0.0471	0.0102	–	–
η₂	0.0330	0.0146	0.0328	0.0147	–	–
η₃	0.0928	0.0208	0.0927	0.0204	–	–
ξ	0.0789	0.0049	0.0796	0.0047	–	–
D₂₂	0.2189	0.0069	0.2219	0.0068	–	–
D₃₃	0.2161	0.0082	0.2206	0.0080	–	–
D₄₄	0.4064	0.0175	0.4090	0.0178	–	–
D₅₅	0.5362	0.0221	0.5395	0.0218	–	–
D₆₆	0.3037	0.0128	0.3036	0.0125	–	–
$σ^{2}$	0.1798	0.0016	0.1798	0.0016	–	–

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