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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.

Improve this question
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3
  • $\begingroup$ If you are interested in the development or accumulation of the treatment effect over time, it may be best to rename 'period' as 'time', and to encode it as a continuous variable rather than a categorical one. How do you expect the effect to develop? Linearly with time? By $e^{-k t}$ type relaxation back to a healthy state? Including a term in your model appropriate to your conjecture would help you to explore it directly using your model. $\endgroup$
    – David C. Norris
    Commented Mar 17, 2016 at 12:11
  • $\begingroup$ For the moment I would like to stay simple and just test for each period which treatment shows a difference, instead of using time as continuous variable. I have edited the question in order to make it more clear. $\endgroup$
    – Martina
    Commented Mar 21, 2016 at 9:52
  • $\begingroup$ you can perform this analysis using the repeated measures parametric analysis module in invivostat... its a free to use package based on r. www.invivostat.co.uk $\endgroup$
    – simon
    Commented Mar 28, 2016 at 9:28

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