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Table 2 Results from all models

From: Dynamic prediction based on variability of a longitudinal biomarker

Parameter

Model 1

Model 2

Model 3

Model 4

Linear Sub-Model

Estimate (95% CrI)

Estimate (95% CrI)

Estimate (95% CrI)

Estimate (95% CrI)

b1

-0.059 (-0.071, -0.047)

-0.056 (-0.068, -0.044)

-0.056 (-0.068, -0.044)

-0.056 (-0.069, -0.045)

b0

7.254 (7.094, 7.411)

7.177 (7.007, 7.324)

7.182 (7.014, 7.338)

7.178 (7.027, 7.32)

ρ

-0.419 (-0.562, -0.264)

-0.427 (-0.564, -0.275)

-0.422 (-0.555, -0.268)

-0.424 (-0.563, -0.268)

\(\sigma ^{2}_{0}\)

1.769 (1.455, 2.124)

1.716 (1.42, 2.074)

1.711 (1.394, 2.069)

1.713 (1.397, 2.072)

\(\sigma ^{2}_{1}\)

0.005 (0.003, 0.007)

0.005 (0.003, 0.006)

0.005 (0.003, 0.007)

0.005 (0.003, 0.007)

\(\sigma ^{2}_{e}\)

7.146 (6.931, 7.359)

NA (NA, NA)

NA (NA, NA)

NA (NA, NA)

Survival Sub-Model

Hazard Ratio (95% CrI)

Hazard Ratio (95% CrI)

Hazard Ratio (95% CrI)

Hazard Ratio (95% CrI)

α

0.555 (0.439, 0.698)

0.514 (0.413, 0.623)

0.535 (0.426, 0.666)

0.524 (0.421, 0.647)

β0

0.035 (0.012, 0.075)

0.043 (0.018, 0.085)

0.024 (0.006, 0.057)

0.045 (0.014, 0.107)

β1 (HLA Mismatch Number)

1.262 (1.115, 1.437)

1.239 (1.098, 1.393)

1.236 (1.086, 1.394)

1.238 (1.100, 1.403)

β2 (African American)

2.015 (1.003, 3.644)

1.612 (0.857, 2.717)

1.673 (0.872, 2.805)

1.634 (0.857, 2.794)

β3 (Hispanic)

1.466 (0.842, 2.324)

1.54 (0.919, 2.365)

1.398 (0.836, 2.232)

1.540 (0.899, 2.420)

β4 (Other Race)

1.092 (0.21, 2.909)

0.949 (0.192, 2.465)

0.944 (0.168, 2.459)

0.951 (0.189, 2.484)

β5 (Middle Age)

0.721 (0.35, 1.37)

0.803 (0.41, 1.482)

0.784 (0.398, 1.463)

0.802 (0.405, 1.472)

β6 (Older Age)

0.307 (0.137, 0.616)

0.34 (0.168, 0.627)

0.338 (0.163, 0.655)

0.335 (0.165, 0.623)

λ0

0.659 (0.515, 0.813)

0.66 (0.539, 0.802)

0.644 (0.517, 0.78)

0.661 (0.491, 0.845)

λ1 (per 0.05 change)

0.478 (0.315, 0.646)

0.578 (0.441, 0.731)

0.559 (0.41, 0.714)

0.569 (0.410, 0.749)

λ2

NA (NA, NA)

NA (NA, NA)

1.254 (1.004, 1.543)

1.400 (0.119, 5.026)

  1. 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 (\(\sim N(0,\sigma ^{2}_{e})\)). In Models 2-4, the random error term is individual specific (\(\sim N(0,\sigma ^{2}_{ie})\)) 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, slope, and some function of the estimated longitudinal trajecotry, through 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. In Models 2-4, λ2 links the two sub-models through the longitudinal individual-specific SD (Model 3) or CV (Model 4) term. Middle age=30-49 years, Older age=50+ years. Model 1 (M1)=base model, shared random intercept and slope only, Model 2 (M2)=allow for individual specific random error term, Model 3 (M3)=share the individual specific standard deviation with hazard, Model 4 (M4)=share the individual specific CV with hazard. Training cohort, N=358
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BMC Medical Research Methodology

ISSN: 1471-2288

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