Odds ratios in mixed model, REML

[Anders Grejs]

Dear all,

I have a dataset of samples taken at three consecutive timepoints (scan_nr).

In an effort to estimate whether the change in a sample estimate (E) over time correlates to a specified outcome (outcome_gr, good or bad outcome) a mixed model was fitted to the dataset.

The dataset was split in two groups defined by having either a good or bad outcome.

mixed logsample i.scan_nr#i.outcome_gr || rand_nr: , residuals(un,t(scan_nr)) reml technique(bfgs)
predict res, rstandard
qnorm res, yscale(range(-6 6))  mlab(rand_nr)
qnorm res if res<3 & res>-3, yscale(range(-3 3))
predict fit, fit
scatter res fit, yscale(range(-6 6)) yline(0)
drop res fit
margins scan_nr#outcome_gr, expression(exp(predict(xb)))
marginsplot, title("E in good versus poor outcome groups") ytitle("median sample")

STATA output for the following command: mixed logsample i.scan_nr#i.outcome_gr || rand_nr: , residuals(un,t(scan_nr)) reml technique(bfgs)

Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0: log restricted-likelihood = -126.80478
Iteration 1: log restricted-likelihood = -121.53404 (backed up)
Iteration 2: log restricted-likelihood = -120.91787
Iteration 3: log restricted-likelihood = -119.28295
Iteration 4: log restricted-likelihood = -119.279
Iteration 5: log restricted-likelihood = -117.39115
Iteration 6: log restricted-likelihood = -116.88247
Iteration 7: log restricted-likelihood = -116.32189
Iteration 8: log restricted-likelihood = -115.68504
Iteration 9: log restricted-likelihood = -115.4023
Iteration 10: log restricted-likelihood = -115.17604
Iteration 11: log restricted-likelihood = -114.95332
Iteration 12: log restricted-likelihood = -114.89151
Iteration 13: log restricted-likelihood = -114.8646
Iteration 14: log restricted-likelihood = -114.8577
Iteration 15: log restricted-likelihood = -114.85561
Iteration 16: log restricted-likelihood = -114.85486
Iteration 17: log restricted-likelihood = -114.85484
Iteration 18: log restricted-likelihood = -114.85484


Computing standard errors:

Mixed-effects REML regression Number of obs = 281

Group variable: rand_nr Number of groups = 99

Obs per group:
min = 1
avg = 2.8
max = 3

Wald chi2(5) = 9.56
Log restricted-likelihood = -114.85484 Prob > chi2 = 0.0888

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My questions are:

1. Output: is it in anyway possible to transform the output to odds ratios?
2. Regarding interpretation: 1#bad outcome: there is no evidence against the null-hypothesis (p=0,052), and scan number 1 in the bad outcome group is not significantly different from scan number 1 in the good outcome group. How do I interpret the rest of the following results? Are they all compared with scan number 1 in the good outcome group?

I hope you can help!

Best regards,

Anders and Thomas

[Clyde Schechter]

Odds ratios are used when the dependent variable of the model is discrete; you have modeled an apparently continuous variable (or at least you have treated it as such by using -mixed-), so odds ratios are not derivable from this kind of analysis. Depending on the meaning of your variables and the context, it might be sensible to invert the analysis and make outcome_gr the dependent variable, and move logsample to the other side of the equation and then run this as -melogit- or -meqrlogit- In that situation you could get odds ratios in your results if you specify the -or- option.

With regard to interpreting your -mixed- output, the model is mis-specified, so you should not attempt to interpret it. You should not run a model which includes interaction terms but does not include the constituents of those interactions, except under very special circumstances that, I'm confident, do not apply here. (And when they do apply, Stata will automatically omit them for you anyway.) Your error was in using i.scan_nr#i.outcome_gr: it should have been i.scan_nr##i.outcome_gr.