Left truncation arises when individuals come under observation only some known time after the natural time origin of the phenomenon under study. The risk set just prior to an event time does not ...

Roth, A. E., and U. G. Rothblum. "Truncation Strategies in Matching Markets--In Search of Advice for Participants." Econometrica 67, no. 1 (January 1999): 21–43.

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