I have a question regarding the conversion of cohen's d into odds ratio (OR) and the comparability of results from two different situations. I wonder if the ORs derived from the two situations can both be used in the same meta-analysis. The meta-analysis is interested in the effects of pretreatment predictors on treatment outcome. For conversion, I use the formulas from Borenstein et al.'s "Introduction to Meta-Analysis" (2009).
Situation 1: a study on the treatment of depression reports the means and standard deviations of an outcome measure in two groups of a pretreatment predictor. For example:
- mean(SD) of depression severity at posttreatment in participants with pretreatment comorbid anxiety
- mean(SD) of depression severity at posttreatment in participants without pretreatment comorbid anxiety
Situation 2: a study on the treatment of depression reports the means and standard deviations of the predictor measure in two groups of outcome. For example:
- mean(SD) of pretreatment comorbid anxiety symptomatology in participants free of depression at posttreatment
- mean(SD) of pretreatment comorbid anxiety symptomatology in participants that still have depression at posttreatment.
For both situations, I can compute cohen's d and convert it to OR. However, can these ORs be compared? Or do they represent two opposing directions, i.e. the effect of the predictor on the outcome (= situation 1) and the "effect" of the outcome on the predictor (= situation 2)? Or does the conversion or the nature of odds ratios make these ORs comparable?
Thank you very much for your time!