I'm trying to learn about methods for conducting survival analysis when the data consists of, for example, yearly tests. In other words, when it is discovered that an event has occurred, it's only known that it occurred sometime in the last year. Right censoring would also typically be present.
I'm finding it a little hard to piece together the concepts I'm researching. I have a few questions so I'll just list them out.
- What is the "thing" you're trying to overcome when you have interval censoring? Obviously the issue is that you don't know when exactly the event occurred, but what does a successful approach accomplish that, say, using a Kaplan-Meier estimate at the midpoint of the intervals doesn't? Particularly, what is the conceptual approach that the nonparametric estimators take?
- What are the current approaches to dealing with this (parametric, semi-parametric, nonparametric)? I know that the Turnbull method is used as a nonparametric estimator of the survival function. What is the advantage to a parametric method or a nonparametric method in this case?
- Do approaches change if the goal is to obtain the survival function vs. the hazard function vs. the cumulative hazard function? Although they are related it may sometimes be hard to convert between them, so if the goal is to have the hazard function in hand then what is a preferable approach?
- If you could say anything briefly about how covariates are incorporated for different methods, that would also be helpful.