I am interested in identifying factors that lead to long-term survival among patients undergoing surgery. My sense is that such factors and their magnitude of effect can be identified using available Cox model methods and time-dependent covariates. However, it has been suggested that the sample of patients be modified from all persons undergoing surgery and all subsequent times points to a sample only including persons failing within a specific time or those never failing beyond a specific time. I contend that removing patients censored as alive or those censored as dead during certain intervals will violate one or more assumptions of the Cox model so much so as to render the results useless.
My questions are:
1) Are there examples of an approach to long-term survivor analysis that differs from traditional survival analysis methods?
2) If dividing the sample into early failure and long-term survivors is done can a time-to-event approach be justified in any way?
I have performed a literature search, but can only find standard Kaplan-Meier and Cox analyses as references. There is "Survival Analysis with Long-term Survivors" by Maller and Zhou, but this book is not available to me.