Table 3.

Results from M1 and M4. M1 is the joint model that shares both the random intercept and slope from the longitudinal sub-model with the random intercept from the survival model. M4 is the interval censored survival model with the longitudinal measurements as a time-varying covariate

	M1: Shared Random Effects				M4: Time Varying Covariate
			Lower	Upper				Lower	Upper
Parameter	Estimate	SD	95% CrI	95% CrI		Estimate	SD	95% CrI	95% CrI
Linear Sub-Model
b 0	7.24	0.06	7.12	7.36	-	-	-	-	-
b 1	-0.05	0.005	-0.06	-0.04	-	-	-	-	-
${\sigma }_e^2$	7.44	0.09	7.26	7.63	-	-	-	-	-
${\sigma }_0^2$	1.66	0.14	1.40	1.94	-	-	-	-	-
${\sigma }_1^2$	0.004	0.0006	0.003	0.005	-	-	-	-	-
ρ	-0.38	0.07	-0.51	-0.24	-	-	-	-	-
Survival Sub-Model
α	0.57	0.06	0.47	0.69	α tvc	0.46	0.03	0.40	0.53
	Hazard					Hazard
	Ratio					Ratio
β 0	0.03	0.01	0.01	0.06	γ 0	0.17	0.06	0.08	0.30
β1 (HLA Mismatch Number)	1.26	0.07	1.13	1.40	γ 1	1.29	0.06	1.17	1.43
β2 (African American)	2.09	0.56	1.23	3.39	γ 2	1.79	0.40	1.11	2.70
β3 (Hispanic)	1.60	0.33	1.05	2.31	γ 3	1.67	0.31	1.14	2.33
β4 (Other Race)	1.14	0.56	0.34	2.41	γ 4	1.12	0.47	0.40	2.20
β5 (30-49 years)	0.57	0.15	0.32	0.93	γ 5	0.67	0.17	0.42	1.05
β6 (≥50 years)	0.30	0.08	0.17	0.49	γ 6	0.41	0.10	0.25	0.65
λ 0	0.64	0.06	0.52	0.75	η	0.80	0.03	0.75	0.85
λ1 (per 0.05 change)	0.43	0.07	0.32	0.58	-	-	-	-	-

For M1, the posterior mean and 95% credible intervals are presented for the linear portion of the model, the survival portion of the model, and the association parameters. The longitudinal portion is comprised of a fixed intercept (b₀), a fixed slope (b₁), and a random error term ($\sim N(0,{\sigma }_e^2)$). There is also a random intercept ($a_{0i}\sim N(0,{\sigma }_0^2)$) and a random slope for each individual ($a_{1i}\sim N(0,{\sigma }_1^2)$), which have a correlation parameter ρ. The survival model is comprised of fixed covariates (β), the Weibull association parameter α, and a random intercept for each individual that is related to the random intercept and slope of the longitudinal sub-model through two association parameters. The first association parameter (λ₀) links the two sub-models through their shared random intercepts. The second association parameter (λ₁) links the two sub-models through the longitudinal random slope and the survival random intercept. M4 contains the Weibull scale parameter, α_tvc, baseline covariates with parameter γ, and the coefficient for the time-varying covariate, η