= Terminal-observation invariance of Cox martingale residuals
{title2=$\widehat M_i=v_i-e^{\widehat\beta^Tz_i}\widehat H_0(x_i)$}
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.
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