Comparing Different Types of Survival Models Suppose there is a system in which individuals are measured only at discrete time points (e.g. blood pressure is measured once every year) and these individuals have the ability to transition between multiple states (e.g. disease free, disease stage 1, disease stage 2, death by disease of interest , death by comorbidity, lost to follow up  etc.) until one of the absorbing states is reached or the period of study is over. The goal of the analysis is to understand what how different cohorts of patients and patient characteristics contribute to the transitions between these states.
I am trying to understand what types of Survival Models are generally used for this type of problem.
At first I thought that perhaps the competing risk model might be suitable seeing as there are "competing absorption states" (e.g. death by disease of interest vs death by comorbidity) - but I am not sure if a multistate/multistate-survival model is better suited for these types of problems.
Another approach that I have been considering is using several multinomial logistic regression. For example, if there are "n" states and "k" absorbing states  (i.e. "n - k" non-absorbing states):

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*Isolate all rows of data in "state 1" and create a multinomial logistic regression model where the outcomes are "state 1, state 2, state 3... state n"

*Repeat this process and create "n - k" multinomial logistic regression models

Thus, as a recap:

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*Approach 1: Discrete Competing Risks Model

*Approach 2: Discrete Multistate Survival Model

*Approach 3: Multinomial Logistic Regression

Can someone please comment which of these approaches (or perhaps some other approach) is generally used for these types of Discrete Time problems?
Thanks!

Offering a different perspective on the matter, this is a common issue in cancer clinical trials. The typical endpoint is PFS or progression-free survival - it is a composite endpoint of death and disease progression. Disease progression is surveilled by conducting periodic scans. So with a 3 (or 6) month interval between scans, if disease progression is detected, we have no idea at which exact timepoint the cancer grew - as early as the day after the previous scan to the day prior to the current scan. This interval censoring problem is well explored.
What's desired in this case is a consistent association measure to make inference that the survival is better in one group - provided the proportional hazards assumption is met. So this motivates the hazard ratio from a Cox proportional hazards model. What we also desire is a measure of person-time follow-up so that we can approximate the population-based incidence density by dividing events to follow-up.
In analyzing the data, the event timepoint is, for PFS events, date of death or cancer scan showing disease progression. For controls, they are censored back to latest evaluable scan, and subjects can be censored if they miss a certain number of scans because the interval censoring becomes intolerable.
You can do some relatively simple simulations to show that the extent of bias is relatively small and the power of the statistical test is acceptable and, most favorably, the analysis model is easy to specify, fit, replicate, and understand.
