Repeated Measures Correlation Question

[Ben Jam]

Hello all!

Beginner stats student here. I was hoping to gain some insight from the board in how to approach my dataset. I would like to assess the correlation (or lack thereof) between dose of opioid administered and respective pain score (Score 1-10) for multiple entries.

id time tr y
1 1 3.5 4
1 2 7.0 2
1 3 4.0 5
2 1 3.0 6
2 2 6.0 2
2 3 4.0 4
3 1 2.0 8
3 2 3.0 6
3 3 6.0 1

I figured a repeated measure anova would be appropriate to assess between-subject and within-subject effects however, my inter-patient effect for tr (mg dose) is not uniform. Am I overthinking this or is there another approach?

Thanks!

[Roman Mostazir]

You need a mixed effect model with time X tr interactation. See -help mixed- for proper understanding of the model. Use post-model command 'margins' to explore the dose and time related change in 'y' (see -help margins-). Using your data above a brief purely mechanistic example is given below :

input id time tr y
1 1 3.5 4
1 2 7.0 2
1 3 4.0 5
2 1 3.0 6
2 2 6.0 2
2 3 4.0 4
3 1 2.0 8
3 2 3.0 6
3 3 6.0 1
end

xtset id time //declare dataset to be repeated time

mixed y i.time##c.tr ||id: //run the mixed effect model with random intercepts

//model output:

Performing EM optimization:

Performing gradient-based optimization:

Iteration 0:   log likelihood = -4.4678507  
Iteration 1:   log likelihood = -4.4006586  
Iteration 2:   log likelihood = -4.4005921  
Iteration 3:   log likelihood = -4.4005921  

Computing standard errors:

Mixed-effects ML regression                     Number of obs     =          9
Group variable: id                              Number of groups  =          3

                                                Obs per group:
                                                              min =          3
                                                              avg =        3.0
                                                              max =          3

                                                Wald chi2(5)      =     257.93
Log likelihood = -4.4005921                     Prob > chi2       =     0.0000

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        time |
          2  |  -4.208791   1.298437    -3.24   0.001     -6.75368   -1.663902
          3  |  -1.785714   1.564085    -1.14   0.254    -4.851265    1.279837
             |
          tr |  -2.571429   .3652917    -7.04   0.000    -3.287387    -1.85547
             |
   time#c.tr |
          2  |   1.494505   .3891026     3.84   0.000     .7318785    2.257132
          3  |   .8214286   .4379693     1.88   0.061    -.0369755    1.679833
             |
       _cons |   13.28571   1.059766    12.54   0.000     11.20861    15.36282
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Identity                 |
                  var(_cons) |   1.35e-22   3.89e-21      4.28e-47    426.1588
-----------------------------+------------------------------------------------
               var(Residual) |   .1556777   .0733886      .0617957     .392188
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 0.00          Prob >= chibar2 = 1.0000


//Use of post-model command margins to explore the relationship

margins time, at(tr=(2/6))
marginsplot,