I am analysing data from a longitudinal study in SAS and see time-dependent patterns in the residuals.
Subjects in four groups (A to D) were given a treatment at time=0; and continuous response variable y was measured at time = 0, 0.5, ... to 4. I want to know if there is a difference in response to the treatment between groups. We expect a non-linear trend of the response variable over time regardless of treatment and group and a group-specific effect that could change over time.
I use Group, Time, and their interaction as fixed effects and assume heterogeneous autocorrelation between measurements taken from the same subject on the same day. ARH(1) was chosen because autocorrelation seemed logical in this type of study, trying UN revealed that ARH(1) might be a better option and AIC of ARH(1) was lower than AR(1).
my SAS code looks like this:
proc mixed data=Data; class Group Time Treatment ; model logResponse= Group|Time / DDFM=KENWARDROGER(firstorder) CL ; repeated Time / subject=Subject type=ARH(1) R; run;
The problem is that my residuals are much larger for certain Time-points than for others. There is a logical biological explanation to this. Shortly after treatment the subjects all show the same strong response thus there is little variation, as time passes the effect of treatment reduces and there is more variation in response variable.
So, what do I do?