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.