A note on a transformation under censoring with application to partial least squares regression

In many applications of statistics, one is interested in the characteristics of a time-to-event variable YY, which, by itself, is not observable. Instead, one observes T=min(Y,Z)T=min(Y,Z) where ZZ is a censoring variable. Such data are common in biomedical, engineering and other applications as well as in a competing risks set-up. In this note, we provide a transformation based on the survival function of the censoring variable which allows one to recover the conditional expectation of YY from the observable TT. We discuss various ramifications of this result and describe its application in partial least squares regression of censored time-to-event data.