When I have taught survival analysis in the past, one argument that I make is that continuous variables (i.e., time to the event) have more information than binary outcomes (i.e., indicator variable for event). One might take the naive approach of doing logistic regression and adjusting for follow up time (guilty…a long time ago), but I argue that causes collider bias, since the follow up time is caused by having the event.
Does that argument make sense?
I was recently watching one of @f2harrell talks on ordinal logistic models for longitudinal data, and he mentioned possibly including follow up time in the model. For the time-to-event outcomes, wouldn’t the same collider bias issues apply?
I think it makes sense. You don’t want to include anything related to Y as X in a regression model. Logistic models require everyone not having an event to be followed to the max, and even there are very inefficient.
Longitudinal models are altogether different. One includes follow-up time as a covariate to model time trends. These times are calendar times of time elapsed from start of treatment, etc., and are not event times or censoring times.
But what about when including events, or even absorbing states (e.g., death) as some of the outcomes. For example, let’s say that there is an ordinal variable from 0-5, and we are also interested in CHD events and total mortality. So a non-fatal CHD event is a 6 and any death is a 7. So, two example observations might be 3347 and 1677.
In that case, wouldn’t the time variable included as a covariate be a collider for the 6 and 7 outcomes?
Just like in the regular longitudinal setup I described, you always include a time effect. This is a fixed effect to allow the mean time-response profile to be non-flat.