Dear Statisticians,

I have an experimental design in which core body temperature is measured under two different treatment factors of Drug treatment (group: 4 levels) at three different room temperatures (RT) over time.

It is in my simplistic terms a 2 Way ANOVA with a repeated measures over 10 time points that are not evenly spaced.

The SAS Proc Mixed code I have used is below, which I believe fits a random coefficients model with a covariance structure of AR(1) over time.  I understand this to give me correlated rats specific intercepts and slopes.

The problem I have is in the interpretation. I think the easiest trhing to do would be to compare the slopes of each of the drug treatment groups vs the Room temperature groups and determine if the pairwise differences in slopes are significant.  How would I do this?  Initially I thought the solutions statement would give this under  the 3 way interaction, but I suspect the slopes are all in relation to the default level (highest level of group) level.  So does this mean I may obtain pairwise differences by changing the default for group level within each group and RT.  So presently Group 4 is the default level so the slopes that I see under solutions of fixed effects are all in relation to this level?

How else may I obtain the pairwise comparisions, hopefully without writing a weeks worth of contrasts Which I don't know how to do, but am willing if someone is will to explain one or two examples.

Thanks in advance for your help.  Let me know if you need more details from the SAS output I would be more than happy to email a Word document of the output.

Alex.

*****SAS Code*****

*** Random coeficients Model ***;
*** Baseline used as covariate ***;
*** Analysis conducted on value (absolute temp)***; 
Proc mixed data=scottr.combine_2 method=ml;
class ratnum group RT timecls;
model value = group|RT|time /solution ddfm=satterth;
random int /sub=ratnum(group*RT);
repeated timecls / sub=ratnum(group*RT) type=AR(1);
title1 "Random coefficients Model";
title2 "AR(1) Covariance pattern";
Title3 "Two between subject factors: Group and RT";
Title4 "The analysis was conducted on Value";
Footnote1 "Group = Drug group 1=saline, 2=ICI 2.5 mg, 3=5 mg 4 =10 mg";
Footnote2 "RT = Temp of Room, 1= Room Temp, 2= 0°C, 3=35°C";
run;
quit;

***  Output from Test of fixed effects  *****

Type 3 Tests of Fixed Effects
                     Num   Den
Effect               DF    DF     F Value        Pr > F
group                3    90.9     0.94           0.4227
RT                   2    90.9     427.91         <.0001
group*RT             6    90.9     1.05           0.4006
time                 1    530      0.00           0.9714
time*group           3    530      7.26           <.0001
time*RT              2    530      75.83          <.0001
time*group*RT        6    530      4.19           0.0004

****  Example of the solutions output for the 3 way interaction ***

Solution for Fixed Effects
                            Temp
              Treatment     of Standard
Effect        Group        Room                Estimate Error DF t Value Pr > |t|
time*group*RT 1             1                  0.001429 0.000941 530 1.52 0.1294
time*group*RT 1             2                  0.003510 0.000812 530 4.32 <.0001
time*group*RT 1             3                  0 . . . .
time*group*RT 2             1                  -0.00027 0.001028 530 -0.26 0.7914
time*group*RT 2             2                  0.002380 0.000826 530 2.88 0.0041
time*group*RT 2             3                  0 . . . .
time*group*RT 3             1                  0.000583 0.000918 530 0.64 0.5256
time*group*RT 3             2                  0.001020 0.000801 530 1.27 0.2034
time*group*RT 3             3                  0 . . . .
time*group*RT 4             1                  0 . . . .
time*group*RT 4             2                  0 . . . .
time*group*RT 4             3                  0 . . . .


Best regards,

Alex.


Alex Gray
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