Table 4.

Parameter estimates and 95% posterior intervals for simulation studies comparing joint models and separate analyses

Parameters	True values	Joint model	Marginal modelsa
Scenario A: biomarker variability not associated with survival
Longitudinal
Intercept(β0)	24.0	23.98 (23.68,24.28)	24.02 (23.72, 24.32)
Time(β1)	−0.5	−0.49 (−0.67, −0.30)	−0.72 (−0.87, −0.56)
Covariate X (β2)	1.0	0.97 (0.68, 1.27)	0.93 (0.64, 1.22)
${\sigma }_I^2$	5.0	5.04 (4.03, 6.21)	4.85 (3.87, 5.99)
${\sigma }_S^2$	0.25	0.29 (0.14, 0.51)	0.24 (0.12, 0.42)
μV	1.5	1.51 (1.36, 1.64)	1.51 (1.37, 1.64)
${\sigma }_V^2$	0.5	0.51 (0.33, 0.73)	0.53 (0.34, 0.75)
Survival
Shape (ρ)	2.0	2.43 (1.71, 3.69)	1.84 (1.62, 2.109)
α0	−1.5	−1.49 (−2.36, −0.93)	−4.79 (−5.77, −3.90)
Covariate X (α1)	0.5	0.50 (0.32, 0.79)	0.26 (0.16, 0.37)
γ1	0.2	0.21 (0.13, 0.32)	0.14 (0.10, 0.18)
γ2	1.0	1.14 (0.22, 2.44)	0.09 (0.05, 0.13)
γ3	0	0.01 (−0.33, 0.33)	−0.10(−0.16, −0.03)
Scenario B: biomarker variability associated with survival
Longitudinal
Intercept(β0)	24.0	23.97 (23.67, 24.28)	24.00 (23.70, 24.30)
Time(β1)	−0.5	−0.48 (−0.68, −0.26)	−0.72 (−0.88, −0.56)
Covariate X (β2)	1.0	0.99 (0.70, 1.28)	0.95 (0.66, 1.24)
${\sigma }_I^2$	5.0	4.93 (3.92, 6.11)	4.83 (3.84, 5.97)
${\sigma }_S^2$	0.25	0.29 (0.13, 0.51)	0.23 (0.10, 0.42)
μV	1.5	1.51 (1.37, 1.65)	1.47 (1.33, 1.61)
${\sigma }_V^2$	0.5	0.52 (0.34, 0.74)	0.53 (0.34, 0.76)
Survival
Shape (ρ)	2.0	2.50 (1.72, 3.82)	1.69 (1.49, 1.91)
α0	−1.5	−2.02 (−3.14, −1.29)	−4.66 (−5.68, −3.64)
Covariate X (α1)	0.5	0.51 (0.32, 0.80)	0.26 (0.15, 0.37)
γ1	0.2	0.21 (0.12, 0.33)	0.14 (0.10, 0.18)
γ2	1.0	1.10 (0.20, 2.36)	0.08 (0.04, 0.11)
γ3	0.5	0.53 (0.21, 0.99)	−0.01 (−0.08, 0.07)

^aMarginal survival models only based on subjects with ≥3 longitudinal measurements