From: Revisiting methods for modeling longitudinal and survival data: Framingham Heart Study
Exams | (Ui1, Ui2) | Residual | Age | Sex | Link | Censoring Distribution |
---|---|---|---|---|---|---|
6 | (4.250, 0.250) | σ2 = 0.1161 | 0.050 | −0.500 | Varying | Uniform (25, 30) |
\( \mathbf{Random}\ \mathbf{Effects}\ \mathbf{Covariance}\ \mathbf{Matrix}:\kern1em G=\left[\begin{array}{cc}0.29& -0.00465\\ {}-0.00465& 0.000320\end{array}\right] \) | ||||||
Longitudinal Trajectories : φβ(tij) = Ui1 + Ui2 ∗ tij + α ∗ Agei | ||||||
Survival Model : h(t) = h0(t) exp {α1Age + α2Sex + γφβ(t)} | ||||||
\( \mathbf{Survival}\ \mathbf{Time}\ \left(\mathbf{Exponential}\right):\kern1em T=\frac{1}{\left(\ \gamma \ast {U}_{i2}\right)}L\left(\frac{-\gamma \left({U}_{i2}\right)\mathit{\log}(M)}{\lambda exp\left({X}^{\prime}\beta +\gamma \left({U}_{i1}\right)\right)}\right) \) | ||||||
\( \mathbf{Survival}\ \mathbf{Time}\ \left(\mathbf{Weibull}\right):\kern1em T=\frac{1}{\gamma \left({U}_{i2}\ast \frac{1}{\nu}\right)}L\left(\gamma \left({U}_{i2}\ast \frac{1}{\nu}\right)\ast {\left(\frac{-\mathit{\log}(M)}{\lambda exp\left\{{X}^{\prime}\beta +\gamma \left({U}_{i1}\right)\right\}}\right)}^{\frac{1}{\nu }}\right) \) |