I am working with the standard proportional hazards model given by $\lambda(t|Z) = \lambda_0(t)e^{Z\beta}$ for a special type of data that requires an EM algorithm to estimate a discretized version of $\lambda_0$, and $\beta$. I have another data set consisting of right-censored failure time data that I want to include in this EM algorithm procedure. I am aware that the partial likelihood is the standard procedure however I cannot use this approach I am constrained to using an EM algorithm.
Question:
Can an EM algorithm be applied to right-censored failure time under a proportional hazards model to estimate the unknown parameters? If so, are there any references which cite this approach and if not, what would be the justification against its use?
Any help with this problem would be greatly appreciated. Thank you.
Edits:
Thank you to @EdM. I am trying to use the following algorithm. Let $$(X_i, \delta_i, Z_i): i = 1, 2, ..., n$$ be right-censored data with covariates Z. Defining the "missing" data as those failure times that are censored, the expected log-likelihood function is given by: $$l_{E}(\beta, \lambda) = \sum_{i=1}^{n} \sum_{j=1}^{k} w_{ij} \log(f_i(t_j))$$ where $w_{ij} = \mathbb{E}(1(T_i = t_j) | O) = \delta_i 1(X_i = t_j) + (1-\delta_i) \frac{p_{ij}1_(X_i \leq t_j)}{\sum_{j=1}^{k} p_{ij}1(X_i \leq t_j)}$ with $$p_{ij} = \lambda_j \exp(\beta Z_i) \exp( \sum_{l=1}^{j} \lambda_l \exp(\beta Z_i))$$ and $$f_{i}(t_j) = \lambda_j \exp(\beta Z_i) \exp( \sum_{l=1}^{j} \lambda_l \exp(\beta Z_i))$$ The algorithm would proceed by computing the $w_{ij}$ weights, maximizing the function with respect to the baseline hazards $\lambda_j$ and coefficients $\beta$ and then iterating until convergence. I assumed the last observed time is a failure so no probability mass was lost in the tail but the algorithm does not appear to be working. I also cannot find any mention of this approach in the literature.