How to implement a piecewise linear regression model in PHREG procedure of SAS?
For example with one knot at X=T:
Y = β_10 + β_11 . X if X ≤ T
Y = β_20 + β_21 . X if X >T
Given the model with the constraint of continuity:
Y = β_10 + β_11 . X if X ≤ T
Y = β_10 + (β_11 - β_21) T + β_21 . X if X >T
i.e :
Y= β_0 + β_1 . X + S_1
where
S_1 = ( β_11 - β_21 ) T if X >T and 0 otherwise.
Finally i would like to include it in a Cox model:
Proc PHREG
Model time * cas (censure) = X S_1 ;
Run ;
But the problem is S_1 has unknown beta coefficients in it.
Thanks for your help!
