Table 1 Key quantities in estimation of Cox model parameters and their variance
Cox PL | Influence Weights | Plus Sampling Weights |
|---|---|---|
\(S^{(0)}(\beta,t) = \sum \limits _{j:t_{j} \geq t} e^{\beta ' z_{j}}\) | \(S_{r}^{(0)}(\beta,t) = \sum \limits _{j:t_{j} \geq t} A(t,z_{j}) e^{\beta ' z_{j}}\) | \(S_{wr}^{(0)}(\beta,t) = \sum \limits _{j:t_{j} \geq t} w_{j} A(t,z_{j}) e^{\beta ' z_{j}}\) |
\(S^{(1)}(\beta,t) = \sum \limits _{j:t_{j} \geq t} z_{j} e^{\beta ' z_{j}}\) | \(S_{r}^{(1)}(\beta,t) = \sum \limits _{j:t_{j} \geq t} A(t,z_{j}) z_{j} e^{\beta ' z_{j}}\) | \(S_{wr}^{(1)}(\beta,t) = \sum \limits _{j:t_{j} \geq t} w_{j} A(t,z_{j}) z_{j} e^{\beta ' z_{j}}\) |
\(S^{(2)}(\beta,t) = \sum \limits _{j:t_{j} \geq t} z_{j} z_{j}' e^{\beta ' z_{j}}\) | \(S_{r}^{(2)}(\beta,t) = \sum \limits _{j:t_{j} \geq t} A(t,z_{j}) z_{j} z_{j}' e^{\beta ' z_{j}}\) | \(S_{wr}^{(2)}(\beta,t) = \sum \limits _{j:t_{j} \geq t} w_{j} A(t,z_{j}) z_{j} z_{j}' e^{\beta ' z_{j}}\) |
\(\bar {z}(\beta,t) = \frac {S^{(1)}(\beta,t)}{S^{(0)}(\beta,t)}\) | \(\bar {z}_{r}(\beta,t) = \frac {S_{r}^{(1)}(\beta,t)}{S_{r}^{(0)}(\beta,t)}\) | \(\bar {z}_{wr}(\beta,t) = \frac {S_{wr}^{(1)}(\beta,t)}{S_{wr}^{(0)}(\beta,t)}\) |