Journal of Probability and Statistics / 2012 / Article / Tab 2 / Research Article
A Two-Stage Joint Model for Nonlinear Longitudinal Response and a Time-to-Event with Application in Transplantation Studies Table 2 Parameter estimates, SE, and 95% confidence/credibility intervals from proportional hazards Cox model for graft survival for plug-in method (a), sampled covariates (b), and fully Bayesian approach (c, d, e).
(a) Graft survival, plug-inEffect Parameter log(HR) SE (95% CI)
e
x
p
(
𝜙
1
)
𝛾
1
0.052 0.022 (0.009; 0.095)
e
x
p
(
𝜙
2
)
𝛾
2
−0.005 0.005 (−0.015; 0.005)
e
x
p
(
𝜙
3
)
𝛾
3
0.053 0.158 (−0.257; 0.363)
(b) Graft survival, sampling two-stageEffect Parameter log(HR) SE (95% CI)
e
x
p
(
𝜙
1
)
𝛾
1
0.053 0.024 (0.006; 0.100)
e
x
p
(
𝜙
2
)
𝛾
2
−0.006
0.008 (−0.022; 0.010)
e
x
p
(
𝜙
3
)
𝛾
3
0.055 0.185 (−0.308; 0.418)
(c) Graft survival, fully Bayesian, WeibullEffect Parameter log(HR) SE (95% HPD)
e
x
p
(
𝜙
1
)
𝛾
1
0.058 0.023 (0.013; 0.103)
e
x
p
(
𝜙
2
)
𝛾
2
−0.005
0.008 (−0.020; 0.011)
e
x
p
(
𝜙
3
)
𝛾
3
0.056 0.180 (−0.299; 0.411)
(d) Graft survival, fully Bayesian, CoxEffect Parameter log(HR) SE (95% HPD)
e
x
p
(
𝜙
1
)
𝛾
1
0.056 0.023 (0.010; 0.101)
e
x
p
(
𝜙
2
)
𝛾
2
−0.006
0.008 (−0.022; 0.010)
e
x
p
(
𝜙
3
)
𝛾
3
0.055 0.171 (−0.280; 0.390)
(e) Graft survival, fully Bayesian, piecewise constant hazardEffect Parameter log(HR) SE (95% HPD)
e
x
p
(
𝜙
1
)
𝛾
1
0.054 0.024 (0.007; 0.102)
e
x
p
(
𝜙
2
)
𝛾
2
−0.005
0.009 (−0.022; 0.012)
e
x
p
(
𝜙
3
)
𝛾
3
0.054 0.179 (−0.297; 0.405)
