mixed model specification

[Jognnewsas]

I have a dataset (see attached), which basically involves 4 treatments for a chemotherapy drug. Samples were taken from 2 biopsy locations, and biopsy were taken at 2 time points. So biopsy location and time are nested within subject, and thus each subject has 4 data points (from 2 biopsy locations and 2 time points). The objective is to study treatment difference.

time is 2-level factor (Day 4, Day 10)

biopsysite is 2-level factor (S1 and S2)

trt is 4-level factor (A, B, C, D)

An exmple part of the dataet looks like:

pid trt  time   biopsysite      y age

P2   A DAY 4           S1 -0.122  49

P2   A DAY 4           S2 -0.442  49

P2   A DAY 10          S1  0.229  49

P2   A DAY 10          S2 -0.007  49

P8   B DAY 4           S2  0.748  62

P8   B DAY 4           S1  0.086  62

P8   B DAY 10          S2  0.090  62

P8   B DAY 10          S1  0.076  62

:

:

:

I would like to fit a mixed model with age, time, trt and time by trt as fixed factor. "time" as repeated measure using AR1(), and "biopsysite" as random with compound symmetry covariance structure between the 2 biopsy locations.

How should I specify the mixed model? Is the following correct?

proc mixed;

  class pid trt time biopsysite;

  model y = age trt time trt*time / s;

  random biopsysite / type=cs subject=pid g;

  repeated / type=ar(1) subject=pid*biopsysite r;

  lsmeans trt*time/cl pdiff;

run;

Or what about this one, does it make sense?

proc mixed data=test;
class time trt pid biopsysite;
model y=age time trt time*trt/s;
random biopsysite/type=cs  g;
repeated pid / type=ar(1) r;

lsmeans trt*time / cl pdiff alpha=0.2;

run;

[trekvana]

i am thinking

proc mixed data=test;
class time trt pid biopsysite;
model y=age time trt time*trt/s;
random biopsysite /  type=cs subject=pid  g;
repeated time / type=ar(1) subject=pid r;

lsmeans trt*time / cl pdiff alpha=0.2;

run;

[Jognnewsas]

Thanks for suggestion. The reason I was using "subject=pid*biopsysite" in repeated statement was because the 2 time points thar were repeated were per each biopsy site, by specifying pid*biopsite intereaction, I was making sure the ar(1) covariance structure is applied to the 2 time point within biopsy site within subject. Accoording to MIXED manual:

"use the SUBJECT= option to define the blocks of and the TYPE= option to define their covariance structure"

The block of R in my example is within biopsy site within subject.

Am I understanding this correctly?

Thanks

[trekvana]

ah in that case do repeated time / type=ar(1) subject=biopsysite(pid)

the subject=biopsysite(pid) specifies that each biopsysite is nested with each pid. you may also want to try random intercept / type=un subject=pid that way you are fitting a random intercept for each person as well as an ar(1) covariance structure for the time points

this ultimately gives you a hybrid covariance structure. i can't think of the complete details off the top of my head (i'll have to reference back to my old school notes if you want more info)

cheers

[Jognnewsas]

Thank you very much!