| |
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
|
-
|
-
|
-
|
-
|
-
|
|
\(\sigma ^{2}_{e}\)
|
7.44
|
0.09
|
7.26
|
7.63
|
-
|
-
|
-
|
-
|
-
|
|
\(\sigma ^{2}_{0}\)
|
1.66
|
0.14
|
1.40
|
1.94
|
-
|
-
|
-
|
-
|
-
|
|
\(\sigma ^{2}_{1}\)
|
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 (\(\sim N(0,\sigma ^{2}_{e})\)). There is also a random intercept (\(a_{0i}\sim N(0,\sigma ^{2}_{0})\)) and a random slope for each individual (\(a_{1i}\sim N(0,\sigma ^{2}_{1})\)), 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, αtvc, baseline covariates with parameter γ, and the coefficient for the time-varying covariate, η
