Landmark analysis with a variable landmark time


In landmark analyses I have seen, a common landmark time is chosen, say, 3 months after transplant, people are classified as having experienced rejection or not and then are followed until 60 months for various outcomes.

The scenario I’m looking at is a bit different. A study followed people from time of hospital admission to 1 year after the admission. People had various complications arise during their hospital stay, some died, but most lived to go home. At the time of hospital discharge, clinicians have to make decisions about plans for follow-up and additional tests to be done after someone is discharged so it is natural for them to want to know about the short to medium term prognosis of their patients who survived to discharge. I am considering setting the day of discharge from hospital as the landmark time (time 0) and setting as fixed covariates the medical events that occurred during the hospital stay (along with pre-hospital medical history, age, etc) and the dependent variable as some outcome (say mortality) that occurred between discharge and 1 year after hospital admission.

Note that the last possible day of follow-up is fixed at 1 year after hospital admission (not hospital discharge) so this creates a situation where maximum follow-up time varies with the duration of hospital stay. People who stayed in hospital longer will have shorter followups. In essence, they are censored earlier but the time to censorship is obviously going to be affected by the duration of hospital stay and duration of hospital stay likely carries prognostic information with respect to the outcome, so the censoring is informative. I suppose it is informative in a way where you are less likely to observe the outcome for people who stayed in hospital longer simply because you follow them for a shorter time. Of course, the outcome I think is more likely to occur sooner in these folks.

It seems to me that simply adjusting for the duration of hospital stay would attenuate the relationship between in-hospital complications (which will typically prolong length of stay) and the outcome. On the other hand, it is also possible that people who stayed in hospital longer had more time to have more complications observed and therefore classified as “in hospital” events, but I think the latter point is much less of an issue than the former.

Does anyone have insights into this? The lengths of stay are short (on the order of 1-3 weeks) compared to the duration of maximum followup and for this reason I suspect it will be a minor issue. I just have not seen such variable landmark times being used, where the landmark time is essentially patient-dependent.



What a great question to ask. I’ve taken for granted that the censoring is non-informative upon conditioning on length of stay but have never thought it through. I hope you get some good responses.

Thank you for promoting the question widely!

I suspect in most contexts it will play out fine if

  1. Total follow-up duration greatly exceeds the median length of stay
  2. Events are not truly clustered near the end of the follow-up period (such that you are vulnerable to differentially missing events in the group of people with effectively shorter follow-up due to longer length of stay).
  3. There is substantial overlap in the distribution of length of hospital stay in the two groups of patients being compared (with exposure of interest vs without). I suppose one could estimate those distributions conditional on other covariates to better even the playing field. Said another way, the exposure of interest is not very strongly associated with of length of stay. How strong is too strong? Depends.

There are many arbitrary statements there, so sensitivity analyses seem in order.
Thinking through some sensible ones, perhaps:
i) Excluding people with very long hospital stays (defined by some quantile). This would bias toward the null, but a “non-zero” association would still remain evident conditional on power. Not ideal, but perhaps readers feel more comfortable with sample restriction than with the magic of covariate adjustment.
ii) Including length of stay as a covariate. This would also attenuate the magnitude of association but I suspect not very much if you are already including in-hospital complications and pre-admission characteristics that would affect length of stay. Length of stay does tell us something more about the severity of what went on beyond binary representations of complications, but it is not without its noise. It would be somewhat collinear with the other variables.