I am running stepwise variable selection for a Cox proportional hazards model and use log-likelihood test statistic for that.
But I feel uncomfortable using LR test (which is advised as the best choice) since it is actually using partial likelihood which is not the same thing as likelihood in classical regression models.
It seems strange to me that most textbooks omits this detail and states without references that partial LR statistic follows distribution.
I tried to find some justification for partial LR use in the same way as usual LR, but haven't succeeded yet.
Any thought on this or maybe someone know helpful source explaining the topic?