 Solution

A baseline-group log-rank test is inappropriate. Receiving surgery is determined at month 3, so classifying patients by that future decision gives the surgery group guaranteed survival without treatment failure to the decision time, creating immortal time bias. Fitness also strongly confounds surgery and prognosis. One can perform a month-3 landmark analysis among patients still at risk, or model surgery as a time-dependent covariate, while adjusting for the clinical variables driving the decision.