[R-sig-ME] lme with interaction: how to decide which treatment is more efficaceous? how to deal with p value column of the lme summary?

[Martina Giovannella]

I am using an lme to check the effect of 3 types of treatment (A,B, C) 
on my variable, over time. I do not expect any effect of treatment A, 
which is a fake treatment.

I have measurement over 5 periods,on 2 sides.

My question is: for each treatment and each period, is my variable 
different from the reference point (treatment A, period 1)?

My model is

             lme(var ~ treatment*period+side,
            method="ML",
            random=list(IDlog=~1), na.action=na.omit,
            data=changes)

This is the anova of the model

     numDF denDF  F-value p-value
     (Intercept)          1   473 79.36094  <.0001
     treatment            2   473  3.49473  0.0311
     period               4   473 12.51296  <.0001
     side                 1   473 12.16210  0.0005
     treatment:period     8   473  2.02865  0.0416

and the summary for fixed effects

     Fixed effects: var ~ treatment * period + hemisphere
                        Value Std.Error  DF   t-value p-value
     (Intercept)         4.622038  3.180983 473  1.453022  0.1469
     treatmentB         -1.376755  3.703398 473 -0.371754  0.7102
     treatmentC         -1.113021  3.703398 473 -0.300540  0.7639
     period2             3.799946  4.168792 473  0.911522  0.3625
     period3             6.124463  4.168792 473  1.469122  0.1425
     period4             4.309267  4.168792 473  1.033697  0.3018
     period5             5.482068  4.168792 473  1.315026  0.1891
     sideright          -4.278672  1.226887 473 -3.487420  0.0005
     treatmentB:period2  4.059350  5.190104 473  0.782133  0.4345
     treatmentC:period2  7.508426  5.190104 473  1.446681  0.1486
     treatmentB:period3  1.965207  5.190104 473  0.378645  0.7051
     treatmentC:period3  5.312525  5.190104 473  1.023587  0.3066
     treatmentB:period4  9.031016  5.190104 473  1.740045  0.0825
     treatmentC:period4  7.819397  5.190104 473  1.506597  0.1326
     treatmentB:period5 13.620365  5.190104 473  2.624295  0.0090
     treatmentC:period5  4.224340  5.215896 473  0.809897  0.4184

The anova states the treatment has an effect, period as well, and there 
is an interaction between treatment and period. Sides are different. 
This is what I expected.

How can I use the p values columns to state for which treatment and 
which period I see a difference from the reference value?

What I would like to retrieve is the numbers I obtain when I test each 
treatment separately. I know how to obtain the mean, what I have to sum 
up in the value column. What about the p values?

Treatment A

     Fixed effects: var ~ period + hemisphere
                     Value Std.Error DF    t-value p-value
     (Intercept)      1.849555  3.768596 94  0.4907810  0.6247
     period2          3.799946  4.174739 94  0.9102236  0.3650
     period3          6.124463  4.174739 94  1.4670291  0.1457
     period4          4.309267  4.174739 94  1.0322244  0.3046
     period5          5.482068  4.174739 94  1.3131524  0.1923
     sideright       -1.142925  2.640337 94 -0.4328710  0.6661

Anova

     numDF denDF  F-value p-value
     (Intercept)     1    94 4.967367  0.0282
     period          4    94 0.654946  0.6248
     side            1    94 0.187377  0.6661

Treatment B

     Fixed effects: var ~ period + hemisphere
                     Value Std.Error  DF   t-value p-value
     (Intercept)      4.674863  2.938724 175  1.590780  0.1135
     period2          7.859296  3.241315 175  2.424724  0.0163
     period3          8.089670  3.241315 175  2.495799  0.0135
     period4         13.340283  3.241315 175  4.115700  0.0001
     period5         19.102433  3.241315 175  5.893420  0.0000
     sideright       -7.137831  2.049988 175 -3.481889  0.0006

Anova

             numDF denDF  F-value p-value
     (Intercept)     1   175 34.37766  <.0001
     period          4   175  9.60042  <.0001
     side            1   175 12.12355   6e-04

Treatment C

     Fixed effects: var ~ period + hemisphere
                     Value Std.Error  DF   t-value p-value
      (Intercept)      2.936039  2.166417 173  1.355251  0.1771
     period2         11.308372  2.392119 173  4.727346  0.0000
     period3         11.436988  2.392119 173  4.781112  0.0000
     period4         12.128664  2.392119 173  5.070260  0.0000
     period5          9.949632  2.428331 173  4.097314  0.0001
     sideright       -3.132715  1.520530 173 -2.060278  0.0409

Anova

            numDF denDF  F-value p-value
     (Intercept)     1   173 58.13208  <.0001
     period          4   173  8.99083  <.0001
     side            1   173  4.24474  0.0409

 From this test it is very clear that for treatment A, var is not bigger 
in any period respect to the reference point, while it is for treatment 
B and C; right side smaller than left.

I want to obtain this information using the first model, with the 3 
treatments.