Mixed models for nested data

[Abishekaa]

This is a sample dataset: Each patient has multiple glucose levels that are categorized into episodes based on the time that glucose test date. Eg: Patient 2 has 3 glucose readings, the first two (80,85) carried out on the same day - therefore it is one episode. The third reading (160) carried out another day - hence its the second episode. 

ID Glucose episode
1    140         1
1    145         2
2    80          1 
2    85          1
2    160         2

1) I would like to fit a variance component mode to identify variability within & across episodes, and across patients.  I have tried the below code, and also using 'subject=episode(ID)' since the episodes are nested within each ID. Could you please explain what would be the best way to fit this model / if this is the right direction?

proc mixed data=test;
class ID episode;
model glucose = ;
random int episode/subject=ID;
run;

[SteveDenham · Accepted solution]

Looks good - you should probably add the SOLUTION option to your RANDOM statement.

SteveDenham

[Abishekaa]

Hi Steve, Thank you! Could you please explain how the above code takes nesting into account? And, how would the model differ from using the below code?

proc mixed data=test;
class ID episode;
model glucose = ;
random int /subject=episode(ID);
run;

[SteveDenham]

This code fits two variance components:

random int  episode/subject=ID

and is equivalent to:

random ID episode*ID;

While this code fits one variance component 

random int /subject=episode(ID)

and is equivalent to

random episode*ID;

The key here is that the matrix representation of nested effects is identical to the matrix representation of crossed effects (see the documentation of the RANDOM statement).

It comes down to partitioning the variability between ID and episode*ID, with the remainder, if any, in the residual.  All of this is going to be very data dependent.

SteveDenham

[Abishekaa]

Thanks so much for the clear explanation, Steve. This is extremely helpful!