Wei Song
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Transition Rates | |
Rate from naive state \(N\) to the first shock month \(S_{k\_1}\) | \[ r_{N \to S_{k\_1}}^{(i)} = \frac{\text{Events}_{N \to S_{k\_1}}^{(i)}} {\text{Person-Time}_{N}^{(i)}} \] |
Transition Probabilities | |
Probability of moving from \(N\) to \(S_{k\_1}\) | \[ p_{N \to S_{k\_1}}^{*(i)} = \bigl(1 - p_{N \to D}^{(i)}\bigr) \times \Bigl[\,1 - \exp\bigl(-\,r_{N \to S_{k\_1}}^{(i)}\bigr)\Bigr] \] |
Probability of remaining in \(N\) | \[ p_{N \to N}^{*(i)} = \bigl(1 - p_{N \to D}^{(i)}\bigr) \times \Bigl[\, 1 - \sum_{k=1}^{3} \Bigl(1 - \exp\bigl(-\,r_{N \to S_{k\_1}}^{(i)}\bigr)\Bigr) \Bigr] \] |
Probability of moving from \(S_{k\_j}\) to \(S_{k\_j+1}\) | \[ p_{S_{k\_j} \to S_{k\_j+1}}^{*(i)} = 1 - p_{S_{k\_j} \to D}^{(i)}, \quad j = 1,\dots,11 \] |
Probability of moving from \(S_{k\_12}\) to \(R\) | \[ p_{S_{k\_12} \to R}^{*(i)} = 1 - p_{S_{k\_12} \to D}^{(i)} \] |
Probability of remaining in \(R\) | \[ p_{R \to R}^{*(i)} = 1 - p_{R \to D}^{(i)} \] |
Probability of remaining in \(D\) | \[ p_{D \to D}^{*(i)} = 1 \] |
Cost | |
Monthly cost for non-death state \(X\) | \[ c_{X}^{(i)} = \frac{\text{Total-Cost}_{X}^{(i)}} {\text{Person-Time}_{X}^{(i)}} \] |
\( y_{it} = \alpha_0 + \alpha X_i + \beta d_i + \gamma \lambda + \color{orange}{\delta d_i \lambda} \) + \( u_{it} \)
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