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). The risk set just prior to an event time does not include individuals whose left-truncation times exceed that event time. 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 represent the left-truncation time and the survival time, respectively. To account for left-truncation, you specify the following statements:
proc surveyphreg;
model T2*Dead(0)=X1-X10/entry=T1;
title 'The ENTRY= option is Specified';
run;
Equivalently, you can use the counting process style of input for left-truncation:
proc surveyphreg;
model (T1,T2)*Dead(0)=X1-X10;
title 'Counting Process Style of Input';
run;