One of PROC LIFEREG’s more useful features is its ability to handle left censoring and interval censoring. Recall that left censoring occurs when we know that an event occurred earlier than some time t, but we don’t know exactly when. Interval censoring occurs when the time of event occurrence is known to be somewhere between times a and b, but we don’t know exactly when. Left censoring can be seen as a special case of interval censoring in which a = 0; right censoring is a special case in which b=∞.
Interval-censored data are readily incorporated into the likelihood function. The contribution to the likelihood for an observation censored between a and b is just
Si(a) – Si(b)
where Si(.) is the survivor ...