Mixed model with covariate?

[Tamas Vegh]

I conducted a clinical trial in which I compared the one-lung ventilation methods used during thoracic surgery.
I ran into a problem while analyzing the data.

1. The patients were divided into two groups: traditional one-lung ventilation (Control Group) and a special type of ventilation (Treatment Group).

2. During a 60-minute ventilation period, blood samples were taken every 5 minutes (that is, 12 times) and the oxygen content (PaO2) was determined.

3. The average PaO2 in the Treatment Group was lower than in the Control Group.

4. However, when analyzing the baseline data, I found that the number of left-sided ventilation was higher in the Treatment Group. This is important because the left lung is smaller than the right, so if you ventilate the left lung while the right lung is being operated on, it has been shown that the oxygen level will be lower than ventilating the right lung at the same settings.

5. My problem is the following:

- how can I prove or exclude that the oxygen level is lower in the Treatment Group not only because the examined ventilation method is not as effective, but also because there was more left-sided ventilation? Is PaO2 lower in the Treatment Group because there was more left OLV?

- what analysis should I perform? I used mixed-effects linear regression first, but I don't know how to incorporate the side of ventilation.

Thank you for your suggestions

[Clyde Schechter]

The most convincing approach would be to separately analyze the left-lung ventilated patients and the right-lung ventilated patients. If in both groups the Treatment group is less oxygenated than the control group, you will have demonstrated the inferiority of the new ventilation method, regardless of which lung is ventilated.

However, your sample size might be too small for that. In that case, you can salvage a part of the lost power that comes from breaking up the data set by including a variable for which lung was ventilated and the interaction of that with the treatment group in your analysis of the (unified) data set. If you are not familiar with Stata's factor-variable notation, read -help fvvarlist- for instructions on the best way to do that.

Nevertheless, you may remain underpowered even for this analysis (and it is already less convincing than separate analyses for each lung). I hate to say it, but this is a problem that would have best been anticipated when the study was being designed, and the sample size should have been set large enough to adequately power separate analyses for each lung. If that did not happen you are left in the unenviable position of trying to statistically patch a flawed study design, with no truly good option. So you may have to settle for the least bad approach you can find.