 Terminal-observation invariance of Cox martingale residuals

In an untied Cox proportional-hazards model with a single subject remaining after all other observed exit times, that subject's event contributes the constant factor one to Cox partial likelihood. Replacing its terminal censoring time by a later event therefore preserves the fitted coefficients and every earlier Breslow estimator increment. At its new event, the subject's fitted cumulative hazard increases by one, cancelling the increase of one in its event indicator. Every martingale residual is unchanged. This property relies on the subject being alone in the terminal risk set and the same covariate history being retained.