[R-sig-ME] Advise on mixed effect model for a longitudinal study (with lme4)

[wphantomfr]

Dear list members,

I currently trying to apply mixed effects models to a longitudinal 
studies with a treatment period.

The study is :
Several evaluation of a participants characteristic (let's call it DV) 
at different times (in week) : 0 (1 evaluaition), 1 , 3, 6, 8 10.

We have 3 different groups of participants (randomized controlled study) 
: a control group without treatment and groupA and groupB which received 
a different treatment.

The treatment is applied to the groupA & B during weeks 2-5 therefore :
     - evaluations at w0 and w1 are "baseline measures" (pre-treatment)
     - evaluation at w3 is during treatment
     - evaluation at w6 is post treatment
     - evaluation at w8 & w10 are follow-up evaluation.



After reading a lot on mixed effects model I arrived to the following 
model (using lme4 package):

best_model<-lmer(DV ~ (time+I(time^2))*GROUP 
+(1+(time+I(time^2))|SUBJECT),data=brut)

It includes a quadratic effect of time (continuous variable) and both 
intercept and "slopes" (not a good word for the quadratic par) of the 
effects of time (both linear and quadratic) are estimated for the random 
effects of SUBJECT.

This model seems to be the best compared to models including only parts 
of these terms (model comparison with anova ). The summary report of the 
model is pasted at the end of this message


My hypothesis are :
     - that I should see a superior effect of time in group A & B (if 
the treatment increases DV, I should have a positive coeficient for time 
and a negative coeficient for time^2)
     - that the effect of time may be superior in group B compared to 
group A
     - I would also like to see if one of the treatment have a more 
long-term effect (sustained effect in the foloup evaluations)

     I'm not sure how to test/answer my questions from my model.




My guesses :
- the fact that GROUPA et GROUPB have low t-values is a sign that my 
groups are quite similar at the begining of the study
- The coeficient of time:GROUP(A & B) and I(time^2):group(A&B) are in 
line with my hypothesis
- I don't know how, in this context, I can answer to the question of 
long-term effects...


My questions :

Am I totally wrong ?

How to best assess my hypothesis ?

Any more advises ?


Thanks in advance




Here is the model report :


summary(bestM)
Linear mixed model fit by REML
t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
Formula: DV ~ (time + I(time^2)) * GROUP + (1 + (time + I(time^2)) 
|      SUBJECT)
    Data: brut

REML criterion at convergence: -458.9

Scaled residuals:
     Min      1Q  Median      3Q     Max
-3.1714 -0.3972  0.0660  0.4385  2.7059

Random effects:
  Groups   Name        Variance  Std.Dev. Corr
  SUBJECT  (Intercept) 6.201e-02 0.24902
           time        2.042e-03 0.04519  -0.45
           I(time^2)   1.162e-05 0.00341   0.41 -0.95
  Residual             1.314e-02 0.11462
Number of obs: 710, groups:  CODE, 117

Fixed effects:
                          Estimate Std. Error         df t value Pr(>|t|)
(Intercept)             1.858e-01  4.557e-02  1.140e+02   4.078 8.44e-05 ***
time                    1.960e-03  1.159e-02  1.138e+02   0.169  0.86599
I(time^2)               2.149e-04  1.032e-03  1.137e+02   0.208  0.83547
GROUPA                     -2.006e-02  6.198e-02  1.140e+02  -0.324  
0.74681
GROUPB                    -2.898e-02  6.094e-02  1.138e+02  -0.476  0.63531
time:GROUPA                3.837e-02  1.576e-02  1.138e+02   2.435  
0.01645 *
time:GROUPB                4.212e-02  1.546e-02  1.120e+02   2.724  
0.00748 **
I(time^2):GROUPA        -2.749e-03  1.404e-03  1.137e+02  -1.957  0.05277 .
I(time^2):GROUPB          -3.222e-03  1.377e-03  1.113e+02  -2.340  
0.02108 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
              (Intr) time   I(t^2) GROUPA GROUPB t:GROUPA t:GROUPB 
I(^2):GROUPA
time         -0.467
I(time^2)     0.379 -0.951
GROUPA          -0.735  0.343 -0.279
GROUPB       -0.748  0.349 -0.283  0.550
t:GROUPA      0.343 -0.735  0.699 -0.467 -0.257
t:GROUPB      0.350 -0.749  0.712 -0.257 -0.467  0.551
I(^2):GROUPA -0.279  0.699 -0.735  0.379  0.208 -0.951   -0.524
I(^2):GROUPB -0.284  0.713 -0.750  0.209  0.379 -0.524   -0.951    0.551


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