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 include individuals whose left truncation times exceed the given event time. Thus, any contribution to the likelihood must be conditional on the truncation limit having been exceeded.

An alternative way to specify left truncation in PROC PHREG is through the counting process style of input. The following specifications are equivalent:

   proc phreg data=one;
      model t2*dead(0)=x1-x10/entry=t1;
      title 'The ENTRY= option is Specified';
   run;
    
   proc phreg data=one;
      model (t1,t2)*dead(0)=x1-x10;
      title 'Counting Process Style of Input';
   run;