I need to analyze the treatment effect on survival using CoxPH models from observational data (registry data). Patients are diagnosed having a disease (at t0), and some of these patients are at some time later treated with drug X (every patient is treated at a different time after diagnosis, some very early, others years later). Simply comparing treated to untreated patients leads to an “immortal time bias”, because the treated patients must obviously have survived until the time they received the treatment. I read that a landmark analysis is a way to eliminate or correct for this kind of bias, but I can only find examples where the landmarking is about a co-variable and not the variable of interest (here: treatment). An example is here.
Is it possible to use the landmark analysis in this context?
What patients are labelled as “treated” then (among those that survived the landmark time)? All patients been treated only before the landmark time, or all patients that have been treated any time?
As a related but a bit different approach I thought to select patients that have been treated within a short period of time after t0 and compare only those to the patients that have not been treated at all. This ignores data from all patients that are treated somewhat later after diagnosis. This may limit the power, but if the registry is large enough and the treatment effect is statistically significant - is there any strong argument against it (e.g. because this introduces another kind of bias)?
Thank you for any help!