Table 2 Clustered survival data structure from the scenario for which the number of patients is 50 and the number of considered molar teeth of each patient is 5.
From: On a Bayesian multivariate survival tree approach based on three frailty models
ID of patient (i) | Teeth (j) | Covariate \(({\varvec{{X}}})\) | Failure time \((Y_{ij})\) | Censoring time \((C_{ij})\) | \(\tau _{ij}\) | Event status \((\Delta _{ij})\) |
|---|---|---|---|---|---|---|
1 | 1 | \({\varvec{{X}}}_{11}=(X_1,X_2,X_3,\ldots ,X_p)_{11}\) | \(Y_{11}\) | \(C_{11}\) | \(\tau _{11}=min(Y_{11},C_{11})\) | \(\Delta _{11}=I(\tau _{11},Y_{11})\) |
2 | \({\varvec{{X}}}_{12}=(X_1,X_2,X_3,\ldots ,X_p)_{12}\) | \(Y_{12}\) | \(C_{12}\) | \(\tau _{12}=min(Y_{12},C_{12})\) | \(\Delta _{12}=I(\tau _{12},Y_{12})\) | |
3 | \({\varvec{{X}}}_{13}=(X_1,X_2,X_3,\ldots ,X_p)_{13}\) | \(Y_{13}\) | \(C_{13}\) | \(\tau _{13}=min(Y_{13},C_{13})\) | \(\Delta _{13}=I(\tau _{13},Y_{13})\) | |
4 | \({\varvec{{X}}}_{14}=(X_1,X_2,X_3,\ldots ,X_p)_{14}\) | \(Y_{14}\) | \(C_{14}\) | \(\tau _{14}=min(Y_{14},C_{14})\) | \(\Delta _{14}=I(\tau _{14},Y_{14})\) | |
5 | \({\varvec{{X}}}_{15}=(X_1,X_2,X_3,\ldots ,X_p)_{15}\) | \(Y_{15}\) | \(C_{15}\) | \(\tau _{15}=min(Y_{15},C_{15})\) | \(\Delta _{15}=I(\tau _{15},Y_{15})\) | |
2 | 1 | \({\varvec{{X}}}_{21}=(X_1,X_2,X_3,\ldots ,X_p)_{21}\) | \(Y_{21}\) | \(C_{21}\) | \(\tau _{21}=min(Y_{21},C_{21})\) | \(\Delta _{21}=I(\tau _{21},Y_{21})\) |
2 | \({\varvec{{X}}}_{22}=(X_1,X_2,X_3,\ldots ,X_p)_{22}\) | \(Y_{22}\) | \(C_{22}\) | \(\tau _{22}=min(Y_{22},C_{22})\) | \(\Delta _{22}=I(\tau _{22},Y_{22})\) | |
3 | \({\varvec{{X}}}_{23}=(X_1,X_2,X_3,\ldots ,X_p)_{23}\) | \(Y_{23}\) | \(C_{23}\) | \(\tau _{23}=min(Y_{23},C_{23})\) | \(\Delta _{23}=I(\tau _{23},Y_{23})\) | |
4 | \({\varvec{{X}}}_{24}=(X_1,X_2,X_3,\ldots ,X_p)_{24}\) | \(Y_{24}\) | \(C_{24}\) | \(\tau _{24}=min(Y_{24},C_{24})\) | \(\Delta _{24}=I(\tau _{24},Y_{24})\) | |
5 | \({\varvec{{X}}}_{25}=(X_1,X_2,X_3,\ldots ,X_p)_{25}\) | \(Y_{25}\) | \(C_{25}\) | \(\tau _{25}=min(Y_{25},C_{25})\) | \(\Delta _{25}=I(\tau _{25},Y_{25})\) | |
â‹® | â‹® | â‹® | â‹® | â‹® | â‹® | â‹® |
50 | 1 | \({\varvec{{X}}}_{50,1}=(X_1,X_2,X_3,\ldots ,X_p)_{50,1}\) | \(Y_{50,1}\) | \(C_{50,1}\) | \(\tau _{50,1}=min(Y_{50,1},C_{50,1})\) | \(\Delta _{50,1}=I(\tau _{50,1},Y_{50,1})\) |
2 | \({\varvec{{X}}}_{50,2}=(X_1,X_2,X_3,\ldots ,X_p)_{50,2}\) | \(Y_{50,2}\) | \(C_{50,2}\) | \(\tau _{50,2}=min(Y_{50,2},C_{50,2})\) | \(\Delta _{50,2}=I(\tau _{50,2},Y_{50,2})\) | |
3 | \({\varvec{{X}}}_{50,3}=(X_1,X_2,X_3,\ldots ,X_p)_{50,3}\) | \(Y_{50,3}\) | \(C_{50,3}\) | \(\tau _{50,3}=min(Y_{50,3},C_{50,3})\) | \(\Delta _{50,3}=I(\tau _{50,3},Y_{50,3})\) | |
4 | \({\varvec{{X}}}_{50,4}=(X_1,X_2,X_3,\ldots ,X_p)_{50,4}\) | \(Y_{50,4}\) | \(C_{50,4}\) | \(\tau _{50,4}=min(Y_{50,4},C_{50,4})\) | \(\Delta _{50,4}=I(\tau _{50,4},Y_{50,4})\) | |
5 | \({\varvec{{X}}}_{50,5}=(X_1,X_2,X_3,\ldots ,X_p)_{50,5}\) | \(Y_{50,5}\) | \(C_{50,5}\) | \(\tau _{50,5}=min(Y_{50,5},C_{50,5})\) | \(\Delta _{50,5}=I(\tau _{50,5},Y_{50,5})\) |
