Journal of Probability and Statistics

Research Article

Two-Stage Joint Model for Multivariate Longitudinal and Multistate Processes, with Application to Renal Transplantation Data

Table 3

The results of the multistate models (Stage 2) for different association structures between longitudinal and multistate processes.


Association structure: true slope of longitudinal biomarkers
	Transition 1 to 2				Transition 2 to 3			Transition 1 to 3
Variables	Coef (SE)		HR (95% CI)	-value	Coef (SE)	HR (95% CI)	-value	Coef (SE)	HR (95% CI)	-value

DRG	0.12 (0.11)		1.13 (0.91, 1.40)	0.258	0.22 (0.12)	1.24 (0.98, 1.57)	0.069	−0.32 (0.35)	0.73 (0.98, 1.57)	0.370
Recipient age	−0.01 (0.01)		0.99 (0.97, 1.01)	0.317	0.04 (0.02)	1.04 (1.00, 1.08)	0.045	0.005 (0.01)	1.00 (0.98, 1.03)	0.709
Creatinine	0.22 (0.12)		1.25 (0.98, 1.58)	0.067	0.49 (0.26)	1.63 (0.98, 2.72)	0.059	1.05 (0.54)	2.87 (0.99, 8.31)	0.052
Hemoglobin	−0.15 (0.08)		0.86 (0.74, 1.01)	0.061	−0.17 (0.09)	0.84 (0.71, 1.01)	0.058	0.36 (0.26)	1.44 (0.86,2.42)	0.168
BUN	0.02 (0.01)		1.02 (1.00, 1.04)	0.045	−0.01 (0.01)	0.99 (0.98, 1.00)	0.143	0.01 (0.01)	1.01 (0.99, 1.03)	0.176
−2(loglikelihood)	5714.38

Association structure: true value of longitudinal biomarkers
	Transition 1 to 2				Transition 2 to 3			Transition 1 to 3
Variables	Coef (SE)		HR (95% CI)	-value	Coef (SE)	HR (95% CI)	-value	Coef (SE)	HR (95% CI)	-value

DRG	0.02 (0.11)		1.02 (0.83, 1.27)	0.837	−0.07 (0.12)	0.93 (0.74, 1.18)	0.554	−0.17 (0.37)	0.85 (0.41, 0.74)	0.651
Recipient age	−0.02 (0.02)		0.98 (0.94, 1.02)	0.317	0.12 (0.05)	1.13 (1.02,1.24)	0.016	0.01 (0.02)	1.01 (0.97, 1.05)	0.617
Creatinine	0.45 (0.22)		1.57 (1.02, 2.41)	0.040	0.13 (0.26)	1.14 (0.68, 1.89)	0.617	0.67 (0.35)	1.95 (0.98, 3.88)	0.055
Hemoglobin	−0.68 (0.05)		0.51 (0.46, 0.56)	<0.001	−0.44 (0.22)	0.64 (0.42, 0.99)	0.045	−0.06 (0.07)	0.94 (0.82, 1.09)	0.454
BUN	0.03 (0.01)		1.03 (1.01, 1.05)	0.003	0.01 (0.01)	1.01 (0.99, 1.03)	0.317	−0.01 (0.01)	0.99 (0.97, 1.01)	0.381
−2(loglikelihood)	5061.89

Association structure: both true slope and true value of longitudinal biomarkers
	Transition 1 to 2				Transition 2 to 3			Transition 1 to 3
Variables	Coef (SE)		HR (95% CI)	-value	Coef (SE)	HR (95% CI)	-value	Coef (SE)	HR (95% CI)	-value

DRG	−0.01 (0.11)		0.99 (0.80, 1.23)	0.927	−0.03 (0.12)	0.97 (0.77, 1.23)	0.807	−0.13 (0.37)	0.88 (0.42, 1.82)	0.728
Recipient age	−0.015 (0.01)		0.98 (0.96, 1.00)	0.134	0.01 (0.005)	1.01 (1.00, 1.02)	0.024	0.01 (0.01)	1.01 (0.98, 1.04)	0.374
Creatinine		1.31 (0.38)	3.71 (1.76, 7.83)	<0.001	0.08 (0.32)	1.08 (0.59, 2.03)	0.802	1.44 (0.62)	4.22 (1.25, 14.29)	0.020
Creatinine		−1.85 (0.41)	0.16 (0.07, 0.35)	<0.001	0.54 (0.36)	1.72 (0.85, 3.47)	0.134	1.13 (0.59)	3.09 (0.97, 9.83)	0.055
Hemoglobin		−0.83 (0.06)	0.44 (0.39, 0.49)	<0.001	−0.47 (0.07)	0.62 (0.54, 0.72)	<0.001	0.06 (0.09)	1.06 (0.89, 1.27)	0.484
Hemoglobin		−0.11 (0.07)	0.89 (0.78, 1.01)	0.083	−0.05 (0.08)	0.95 (0.81, 1.12)	0.571	0.43 (0.21)	1.54 (1.03, 2.31)	0.035
BUN		0.01 (0.01)	1.01 (0.99,1.03)	0.074	0.01 (0.01)	1.01 (0.99, 1.02)	0.480	−0.01 (0.01)	0.98 (0.97, 1.00)	0.120
BUN		0.05 (0.01)	1.05 (1.04, 1.06)	<0.001	0.03 (0.02)	1.03 (0.99, 1.07)	0.134	0.05 (0.03)	1.05 (0.99, 1.11)	0.095
−2(loglikelihood)	4981.07

Association structure: the area under the biomarkers’ trajectories
	Transition 1 to 2				Transition 2 to 3			Transition 1 to 3
Variables	Coef (SE)		HR (95% CI)	-value	Coef (SE)	HR (95% CI)	-value	Coef (SE)	HR (95% CI)	-value

DRG	0.04 (0.11)		0.96 (0.78, 1.19)	0.742	0.26 (0.12)	1.30 (1.03, 1.64)	0.200	−0.47 (0.37)	0.62 (0.30, 1.28)	0.203
Recipient age	−0.05 (0.02)		0.95 (0.91, 0.99)	0.013	0.13 (0.05)	1.14 (1.03, 1.26)	0.009	0.01 (0.01)	1.01 (0.98, 1.04)	0.425
Creatinine	0.09 (0.04)		1.10 (1.01, 1.18)	0.024	0.07 (0.04)	1.07 (0.99, 1.16)	0.080	0.15 (0.08)	1.16 (0.99, 1.36)	0.061
Hemoglobin	−0.10 (0.04)		0.90 (0.84, 0.98)	0.012	−0.09 (0.04)	0.91 (0.84, 0.99)	0.023	−0.02 (0.01)	0.98 (0.97, 1.00)	0.134
BUN	0.12 (0.05)		1.13 (1.02, 1.24)	0.016	0.02 (0.01)	1.02 (1.00, 1.04)	0.069	−0.001 (0.001)	1.00 (0.99, 1.01)	0.133
−2(loglikelihood)	4013.425