The ICPHREG Procedure

Left-Truncation of Failure Times

Left-truncation occurs when individuals are not observed at the natural time origin of the phenomenon under study but come under observation at some known later time (called the left-truncation time). Any individuals whose left-truncation time exceeds the event time cannot be observed. Thus, any contribution to the likelihood must be conditional on the truncation limit having been exceeded.

You use the ENTRY= option to specify the variable that represents the left-truncation time. Suppose T1 and (T2, T3) represent the left-truncation time and the observed interval, respectively. To account for left-truncation, you specify the following statements:

proc icphreg;
   model (T2,T3)=X1-X10/entry=T1;
   title 'The ENTRY= option is Specified';

For the specified truncation time to be meaningful, its value must be smaller than the values of the interval boundaries. Otherwise, the observation is removed from the analysis.