$\xi_{ij} = {1 + \exp(\gamma_{0j})}^{-\exp{\beta^\top\Psi(Z_i)}}$
$\Gamma_i = {\prod_{j = 1}^{t_i^0} \phi_j} {(1 - \phi_{t_i^0}) / \phi_{t_i^0}}^{d_i^0}$
$\Delta_{i k} = {\prod_{j=1}^{k-1} \phi_j} {\prod_{j=k}^{t_i^0} (1 - \theta_{j - k})} {\theta_{t_i^0 - k} / (1 - \theta_{t_i^0 - k})}^{d_i^0}$
$f(t_i^0, d_i^0, Z_i; \beta, \gamma_0, \theta, \phi) = \Gamma_i \prod_{j=1}^{t_i^0} \xi_{ij} + \sum_{k = 1}^{t_i^0} { \Delta_{ik} (1 - \xi_{ik}) \prod_{j=1}^{k - 1} \xi_{ij} }$
$L(\beta, \gamma_0, \theta, \phi) = \prod_{i=1}^n f(t_i^0, d_i^0, Z_i; \beta, \gamma_0, \theta, \phi)$
$l(\beta, \gamma_0, \theta, \phi) = \sum_{i=1}^n \log f(t_i^0, d_i^0, Z_i; \beta, \gamma_0, \theta, \phi)$
Meier, A.S., Richardson, B.A. and Hughes, J.P. (2003), Discrete Proportional Hazards Models for Mismeasured Outcomes. Biometrics, 59: 947-954. https://doi.org/10.1111/j.0006-341X.2003.00109.x
Magaret, A.S. (2008), Incorporating validation subsets into discrete proportional hazards models for mismeasured outcomes. Statist. Med., 27: 5456-5470. https://doi.org/10.1002/sim.3365
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