Left Truncation and Late Entry into the Risk Set

In standard treatments of partial likelihood, it is assumed that every individual is at risk of an event at time 0 and continues to be at risk until either the event of interest occurs or the observation is censored. At that point the individual is removed from the risk set, never to return. It doesn’t have to be this way, however. If there are periods of time when it is known that a particular individual is not at risk for some reason, the partial likelihood method allows for the individual to be removed from the risk set and then to be returned at some later point in time. Unfortunately, the vast majority of partial likelihood programs are not set up to handle this possibility.

The most common ...

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