I am analyzing data from an randomized controlled trial with a “strange” design where there are two phases (control and intervention) and individuals can enroll in either phases. Those who are enrolled in control may have the event of interest (or censoring) either in the control or in the intervention phase (i.e. they can carry-over to the intervention phase). Also, there is a number of NON time-dependent covariates that I need to adjust for. I have used a Cox model with intervention as a time dependent covariate, in order to investigate the effect of the intervention, controlling for the covariates.
What I am not sure how to do (and I have been asked for) is to provide estimates of median or mean survival times. I have thought of different options none of which seems satisfactory to me. One thing, one of those covariates (categorical) has a very high effect on the time-to-event and we also see a large imbalance of its distribution between the two phases. So ignoring it in the survival time estimates would be highly misleading.
Any suggestions would be very much appreciated.