SAS code for a model with 3 change points

[mmaximos]

Hello SAS experts and enthusiasts,

I am trying to translate the following modeled equation into a proc genmod function for running a regression for the purpose of an interrupted time series analysis. There are 3 change points that I am interested in, hence 7 Beta coefficients .

Where:

y= prescriptions

Bo= y-intercept

Bx*time(t)= estimated level change in prescriptions from start of observation period

Bx*time after intervention X (t)= time after the intervention has occurred in months (slope change)

Et= random variability error term

This is the code that I've generated to test the fitted model:

proc genmod data=its;  

    model prescriptions= obs intervention t_int1 intervention2 t_int2  intervention3 t_int3/ link=identity dist=normal;  

    output pred=pred;  

run;  

Would this be sufficient or do I have to enter the SAS code in the same manner as the model is written and if so, what would that look like?

Thank you!

[Rick_SAS]

You might want to start by reading the article, "Piecewise regression models and spline effects":

https://blogs.sas.com/content/iml/2017/04/05/nonsmooth-models-spline-effects.html

In that article, there is one CLAS variable that describes the time intervals. I guess your intervals are

"Before 1", 
"After 1 before 2"

"After 2 before 3"

and

"After 3"

You did not tell us whether the model is continuous at the changepoints. The article shows how to use GLM  and a CLASS statement for models that have a jump discontinuity at the intervention point. For continuous models, you can move to PROC GLMMIX and use the EFFECT statement to create a spline effect where the knots are placed at the intervention locations.

BTW, your model can also be handled by PROC GLM.

[mmaximos]

Thank you @Rick_SAS  for your guidance and I will read the article. The model is continuous at the changepoints. I am aware I can use the PROC GLM function, thank you; I was hoping to use the PROC GENMOD function for the purpose of practice.