The PHREG Procedure

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 the given 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 phreg;
   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 phreg;
   model (T1,T2)*Dead(0)=X1-X10;
   title 'Counting Process Style of Input';
run;

Since the product-limit estimator of the survivor function is not available for the counting process style of input, you cannot use PROC PHREG to obtain the product-limit estimate of the survivor function if you have data with left-truncation times. In the preceding PROC PHREG calls, if you also specify METHOD=PL in a BASELINE statement or an OUTPUT statement, it is defaulted to METHOD=BRESLOW.