Modified Cox–Snell residual ($Y^{\ast }=H(\min (T,C))+1-\Delta$)

For an observed transformed time $Y=H(\min (T,C))$ and event indicator $\Delta$, the correction $Y^{\ast }=Y+1-\Delta$ has mean one under independent censoring. Its complement $1-Y^{\ast }=\Delta -Y$ is the corresponding martingale residual.