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RaphaelS1 committed Nov 18, 2024
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Expand Up @@ -360,7 +360,7 @@ Following @Klein2003, we can define the likelihood contributions for the differe
- $\delta_i = 1$: $P(Y_i = t_i|Y_i \leq t_i^R|\bstheta) = \frac{f_Y(t_i|\bstheta)}{F_Y(t_i^R|\bstheta)}$
- $\delta_i = 0$: $P(Y_i \geq t_i|Y_i \leq t_i^R|\bstheta) = \frac{F_Y(t_i^R|\bstheta) - F_Y(t_i|\bstheta)}{F_Y(t_i^R|\bstheta)}$
Let $\mathcal{O}$, $\mathcal{RC}$, $\mathcal{LC}$, $\mathcal{IC}$, $\mathcal{LT}$, $\mathcal{RT} \subset \mathcal{D}$ subsets of the observed data for subjects with observed event times, right-censoring, left-censoring, interval-censoring, left-truncation and right-truncation, respectively.
Let $\mathcal{O}$, $\mathcal{RC}$, $\mathcal{LC}$, $\mathcal{IC}$, $\mathcal{LT}$, $\mathcal{RT} \subset \mathcal{D}$ be subsets of the observed data for subjects with observed event times, right-censoring, left-censoring, interval-censoring, left-truncation and right-truncation, respectively.
Then, assuming independence between observations, the objective function for the observed data can be defined as
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