Three groups comparison - Repeated measurements

#1
Hello everyone

A knee prosthesis is well positioned when the line that goes from the center of the hip to the center of the ankle passes through the middle of the knee (more or less). We have three methods of knee alignment (conventional, navigation or robotic surgery). And we measured the alignment before and after surgery in the x-rays.
So we have the following variables:
  • axis_0: Preoperative alignment.
  • axis_1: Postoperative alignment.
  • error_0: Difference (in absolute value) between the optimum (180 degrees) and the preoperative alignment. [error_0 = abs(180 - axis_0)]
  • error_1: Difference (in absolute value) between the optimum (180 degrees) and the postoperative alignment. [error_1 = abs(180 - axis_1)]
  • error_change: Difference between the postoperative and preoperative error. That is, what has improved the alignment of the knee. [error_change = error_1 – error_0]
We would like to see what method is better to get a better alignment. The trick here is that the postoperative alignment is the main indicator for a good result, but obviously is not the same to start from 179 degrees than from 160.

So we tried several options:

ANALYSIS OPTION 1: LINEAR REGRESSION
Code:
. reg error_change i.group, baselevels

      Source |       SS           df       MS      Number of obs   =       124
-------------+----------------------------------   F(2, 121)       =      4.03
       Model |  169.390993         2  84.6954966   Prob > F        =    0.0202
    Residual |  2542.25035       121  21.0103334   R-squared       =    0.0625
-------------+----------------------------------   Adj R-squared   =    0.0470
       Total |  2711.64134       123  22.0458645   Root MSE        =    4.5837

-------------------------------------------------------------------------------
 error_change |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
        group |
Conventional  |          0  (base)
   Navigated  |   .3461958   1.046932     0.33   0.741    -1.726483    2.418875
     Robotic  |  -2.208407   1.015209    -2.18   0.032     -4.21828   -.1985336
              |
        _cons |  -3.886806   .7639505    -5.09   0.000    -5.399247   -2.374364
-------------------------------------------------------------------------------

. pwcompare group, effects

Pairwise comparisons of marginal linear predictions

Margins      : asbalanced

--------------------------------------------------------------------------------------------
                           |                            Unadjusted           Unadjusted
                           |   Contrast   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
                     group |
Navigated vs Conventional  |   .3461958   1.046932     0.33   0.741    -1.726483    2.418875
  Robotic vs Conventional  |  -2.208407   1.015209    -2.18   0.032     -4.21828   -.1985336
     Robotic vs Navigated  |  -2.554603   .9795282    -2.61   0.010    -4.493837   -.6153684
--------------------------------------------------------------------------------------------
ANALYSIS OPTION 2: REPEATED MEASURES ANOVA
Code:
. anova error_ group / id|group pre_or_post group#pre_or_post, repeat(pre_or_post)

                         Number of obs =        248    R-squared     =  0.7094
                         Root MSE      =    3.24117    Adj R-squared =  0.4069

                  Source | Partial SS         df         MS        F    Prob>F
       ------------------+----------------------------------------------------
                   Model |  3103.7283        126   24.632764      2.34  0.0000
                         |
                   group |  48.500335          2   24.250168      1.77  0.1739
                id|group |   1653.248        121   13.663206 
       ------------------+----------------------------------------------------
             pre_or_post |  1244.8936          1   1244.8936    118.50  0.0000
       group#pre_or_post |  84.695502          2   42.347751      4.03  0.0202
                         |
                Residual |  1271.1252        121   10.505167 
       ------------------+----------------------------------------------------
                   Total |  4374.8535        247   17.711957 


Between-subjects error term:  id|group
                     Levels:  124       (121 df)
     Lowest b.s.e. variable:  id
     Covariance pooled over:  group     (for repeated variable)

Repeated variable: pre_or_post
                                          Huynh-Feldt epsilon        =  1.0167
                                          *Huynh-Feldt epsilon reset to 1.0000
                                          Greenhouse-Geisser epsilon =  1.0000
                                          Box's conservative epsilon =  1.0000

                                            ------------ Prob > F ------------
                  Source |     df      F    Regular    H-F      G-G      Box
       ------------------+----------------------------------------------------
             pre_or_post |      1   118.50   0.0000   0.0000   0.0000   0.0000
       group#pre_or_post |      2     4.03   0.0202   0.0202   0.0202   0.0202
                Residual |    121
       -----------------------------------------------------------------------


. pwmean error_, over(group) mcompare(tukey) effects

Pairwise comparisons of means with equal variances

over         : group

---------------------------
             |    Number of
             |  Comparisons
-------------+-------------
       group |            3
---------------------------

--------------------------------------------------------------------------------------------
                           |                              Tukey                Tukey
                    error_ |   Contrast   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
                     group |
Navigated vs Conventional  |  -.4334943   .6786801    -0.64   0.799    -2.033854    1.166866
  Robotic vs Conventional  |    .610294    .658115     0.93   0.624    -.9415724     2.16216
     Robotic vs Navigated  |   1.043788   .6349849     1.64   0.229    -.4535363    2.541113
--------------------------------------------------------------------------------------------
What is the correct p-value here? 0.0202 as in the first analysis? But why do I get non significant differences in the post hoc analysis?

ANALYSIS OPTION 3: GENERAL LINEAR REPEATED MEASURES MODEL (SPSS)

I am not familiar with SPSS... I don't know if I should use between subjects contrast (p=0,020) or inter-subjects contrast (p=0.174). Post hoc comparisons are not significative (as in the option 2) so I guess that I should use p=0.174... but the graphical representation suggest otherwise.
1654006508175.png ç
Thanks a lot for your help.