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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.

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You can get the median survival from your adjusted Cox model by calculating the predicted survival for a given set of covariate values and then finding the time at which survival = 0.5. There are several estimators that can be used to get the predicted survival from a Cox model. The Kalbfleisch/Prentic estimator is closest in concept to the Kaplan-Meier estimator, but can give you median survival for strata with specific values of covariates.

To get the mean survival, I think you need to assume a distribution for survival and use a parametric model to estimate survival. Common distributions are exponential, Weibull, log-normal, and gamma. The mean is usually quite dependent on the distribution selected, you will need to carefully decide which is appropriate.

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