Dear list members,
 
I would be very grateful for any advice on fitting a model for a cross-over design please excuse my lengthy post. 

I am currently trying to analyze a transient treatment effect (treatment vs. placebo) in a cross-over experiment (2 sessions) in two groups (old, young subjects) with repeated measurements for both treatment conditions (before treatment=baseline, post, post45, post90) in multiple outcome variables separately (2 physiological and 4 behavioral,  all of which metric). 

Points of interest are whether there is an effect of treatment 
in both/either of the groups
in one/more outcome variables
and if an inter-correlation between potential changes in physiological and behavioral outcome exists.

Problems I am trying to deal with:
Although a carry-over of direct treatment effect seems unlikely (sufficient wash-out phase in-between two conditions/sessions), a possible change (improvement) in response rate from 1st to 2nd session irrespective of treatment, i.e. rather "period effect", cannot be ruled out
Is it sufficient to fit a random intercept to tackle this problem? OR  is it necessary to use baseline adjusted outcome? Is there any OTHER option?
Fitting the model (example attached), I am using  separate models for each outcome, correlation structure corAR1, random INTERCEPT, and random SLOPE (time point of repeated measurements).
I sit necessary to specify the random effects for grouping factors, i.e. for treatment and/or agegroup? ~time point|ID OR |treatment/~time pointID?, and in case of the latter, fitting factor treatment also as fixed?
The first time point is baseline, i.e. before onset of treatment effect, and the last time point of measurement is expected to already reflect wash-out of treatment. I read some advice on coding time for repeated measurements but need some help with what might be the most appropriate/accepted way to do it:
time  as continuous variable (in minutes relative to treatment onset, here: time_point: -15, 20, 45, 90)
time point as categorical or ordered?
does it make sense to analyze all time points as categorical in a first step, to see whether there is a significant "treatment*time" interaction  for specified time points, and then in a second step to analyze slope from baseline to respective time point, i.e. code time as continuous?
Is there a reasonable way of quantifying a possible treatment effect in order to analyze relation of potential effects on outcome, i.e. effect on physiological outcome associated with effect on behavioral outcome? 
I  tried to find more detailed advice ( eg. Dı́az-Uriarte, R. (2002). Incorrect analysis of crossover trials in animal behaviour research. Animal Behaviour, 63(4), 815–822. doi:10.1006/anbe.2001.1950) and would appreciate any further recommendations. 

Thank you very much in advance!
kirstin

---
data.frame':	5760 obs. of  21 variables:
 $ ID  [=subject level]       : Factor w/ 20 levels "OMI_01","OMI_02",..: 11 11 11 11 11 11 11 11 11 11 ...
 $ agegroup   : Factor w/ 2 levels "OLD     ","YOUNG   ": 2 2 2 2 2 2 2 2 2 2 ...
 $ session    : num  1 1 1 1 1 1 1 1 1 1 ...
 $ stim.cond [=treatment]: Factor w/ 2 levels "sham","tDCS": 1 1 1 1 1 1 1 1 1 1 ...
 $ timepoint  : Factor w/ 4 levels "BL ","P  ","P45",..: 1 1 1 1 1 1 1 1 1 1 ...
 $ time_point : num  -15 -15 -15 -15 -15 -15 -15 -15 -15 -15 ...
 $ outcome : num  NA 2.887 0.963 4.006 2.06 ...
[....]


example for model, BIC comparison favors the corAR1 correlation structure:

summary(mR0x_corAR <- lme(outcome~factor(agegroup)*factor(timepoint)*factor(treatment),data=tDCSrest, random=~1|ID, correlation = corAR1(), na.action=na.exclude,method="REML"))

Linear mixed-effects model fit by REML
 Data: tDCSrest 
       AIC      BIC    logLik
  5827.065 5936.875 -2894.533

Random effects:
 Formula: ~1 | ID
        (Intercept)  Residual
StdDev:   0.7819433 0.8284249

Correlation Structure: AR(1)
 Formula: ~1 | ID 
 Parameter estimate(s):
      Phi 
0.3094027 
Fixed effects: outcome ~ factor(agegroup) * factor(timepoint) * factor(stim.cond) 
                                                                            Value Std.Error   DF   t-value p-value
(Intercept)                                                              3.656386 0.2625337 2373 13.927301  0.0000
factor(agegroup)young                                                   -0.530390 0.3710212   18 -1.429540  0.1700
factor(timepoint)P                                                      -0.420957 0.1222664 2373 -3.442950  0.0006
factor(timepoint)P45                                                    -0.120908 0.1265935 2373 -0.955090  0.3396
factor(timepoint)P90                                                    -0.291501 0.1252295 2373 -2.327736  0.0200
factor(stim.cond)sham                                                   -0.253259 0.1292979 2373 -1.958726  0.0503
factor(agegroup)young:factor(timepoint)P                                 0.508492 0.1733311 2373  2.933646  0.0034
factor(agegroup)young:factor(timepoint)P45                               0.372538 0.1768388 2373  2.106652  0.0353
factor(agegroup)young:factor(timepoint)P90                               0.380923 0.1760245 2373  2.164036  0.0306
factor(agegroup)young:factor(stim.cond)sham                              0.284941 0.1792027 2373  1.590047  0.1120
factor(timepoint)P  :factor(stim.cond)sham                               0.587820 0.1777151 2373  3.307656  0.0010
factor(timepoint)P45:factor(stim.cond)sham                               0.050355 0.1824015 2373  0.276066  0.7825
factor(timepoint)P90:factor(stim.cond)sham                               0.430209 0.1832581 2373  2.347559  0.0190
factor(agegroup)young:factor(timepoint)P  :factor(stim.cond)sham        -0.785629 0.2482133 2373 -3.165136  0.0016
factor(agegroup)young:factor(timepoint)P45:factor(stim.cond)sham        -0.383033 0.2539655 2373 -1.508210  0.1316
factor(agegroup)young:factor(timepoint)P90:factor(stim.cond)sham        -0.478725 0.2549540 2373 -1.877691  0.0605
 Correlation: 
                                                                        (Intr) fctr() fct()P fc()P45 fc()P90 fct(.) fc():()P
factor(agegroup)young                                                   -0.708                                              
factor(timepoint)P                                                      -0.233  0.165                                       
factor(timepoint)P45                                                    -0.234  0.165  0.503                                
factor(timepoint)P90                                                    -0.237  0.167  0.489  0.510                         
factor(stim.cond)sham                                                   -0.229  0.162  0.474  0.476   0.480                 
factor(agegroup)young:factor(timepoint)P                                 0.164 -0.230 -0.705 -0.355  -0.345  -0.334         
factor(agegroup)young:factor(timepoint)P45                               0.167 -0.234 -0.360 -0.716  -0.365  -0.341  0.501  
factor(agegroup)young:factor(timepoint)P90                               0.168 -0.235 -0.348 -0.363  -0.711  -0.342  0.485  
factor(agegroup)young:factor(stim.cond)sham                              0.165 -0.231 -0.342 -0.344  -0.347  -0.722  0.476  
factor(timepoint)P  :factor(stim.cond)sham                               0.160 -0.113 -0.688 -0.346  -0.337  -0.690  0.485  
factor(timepoint)P45:factor(stim.cond)sham                               0.162 -0.115 -0.350 -0.695  -0.355  -0.699  0.247
factor(timepoint)P90:factor(stim.cond)sham                               0.168 -0.119 -0.347 -0.362  -0.696  -0.708  0.245
factor(agegroup)young:factor(timepoint)P  :factor(stim.cond)sham        -0.115  0.160  0.493  0.248   0.241   0.494 -0.698  
factor(agegroup)young:factor(timepoint)P45:factor(stim.cond)sham        -0.117  0.163  0.251  0.499   0.255   0.502 -0.350  
factor(agegroup)young:factor(timepoint)P90:factor(stim.cond)sham        -0.121  0.169  0.250  0.260   0.501   0.509 -0.347  
                                                                        fc():()P45 fc():()P90 f():(. f()P:( f()P45: f()P90:
factor(agegroup)young                                                                                                      
factor(timepoint)P                                                                                                         
factor(timepoint)P45                                                                                                       
factor(timepoint)P90                                                                                                       
factor(stim.cond)sham                                                                                                      
factor(agegroup)young:factor(timepoint)P                                                                                   
factor(agegroup)young:factor(timepoint)P45                                                                                 
factor(agegroup)young:factor(timepoint)P90                               0.513                                             
factor(agegroup)young:factor(stim.cond)sham                              0.485      0.487                                  
factor(timepoint)P  :factor(stim.cond)sham                               0.248      0.240      0.498                       
factor(timepoint)P45:factor(stim.cond)sham                               0.497      0.252      0.505  0.508                
factor(timepoint)P90:factor(stim.cond)sham                               0.259      0.495      0.511  0.496  0.521         
factor(agegroup)young:factor(timepoint)P  :factor(stim.cond)sham        -0.350     -0.338     -0.689 -0.716 -0.364  -0.355 
factor(agegroup)young:factor(timepoint)P45:factor(stim.cond)sham        -0.697     -0.358     -0.700 -0.365 -0.718  -0.374 
factor(agegroup)young:factor(timepoint)P90:factor(stim.cond)sham        -0.367     -0.704     -0.711 -0.357 -0.375  -0.719 
                                                                        f():(: f():()P45:
factor(agegroup)young                                                                    
factor(timepoint)P                                                                       
factor(timepoint)P45                                                                     
factor(timepoint)P90                                                                     
factor(stim.cond)sham                                                                    
factor(agegroup)young:factor(timepoint)P                                                 
factor(agegroup)young:factor(timepoint)P45                                               
factor(agegroup)young:factor(timepoint)P90                                               
factor(agegroup)young:factor(stim.cond)sham                                              
factor(timepoint)P  :factor(stim.cond)sham                                               
factor(timepoint)P45:factor(stim.cond)sham                                               
factor(timepoint)P90:factor(stim.cond)sham                                               
factor(agegroup)young:factor(timepoint)P  :factor(stim.cond)sham                         
factor(agegroup)young:factor(timepoint)P45:factor(stim.cond)sham         0.506           
factor(agegroup)young:factor(timepoint)P90:factor(stim.cond)sham         0.494  0.520    

Standardized Within-Group Residuals:
         Min           Q1          Med           Q3          Max 
-3.613364210 -0.622035919 -0.001779787  0.637882645  4.410916182 

Number of Observations: 2407
Number of Groups: 20 


 anova(mR0x_corAR)
                                                     					numDF denDF  F-value p-value
(Intercept)                                              				1  2373 353.1295  <.0001
factor(agegroup)                                         			1    18   0.6113  0.4445
factor(timepoint)                                        			3  2373   0.6737  0.5681
factor(stim.cond)                                        			1  2373   1.1819  0.2771
factor(agegroup):factor(timepoint)                       		3  2373   0.8459  0.4686
factor(agegroup):factor(stim.cond)                       		1  2373   1.7029  0.1920
factor(timepoint):factor(stim.cond)                      		3  2373   3.3753  0.0177
factor(agegroup):factor(timepoint):factor(stim.cond)   3  2373   3.4048  0.0170



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