Should one derive risk difference from the odds ratio?

[R_cubed]

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Does diabetes modify the effect of treatment on mortality? The authors say no, but is that really true?

I read the article; the authors constructed an example where (by assumption) treatment benefit was independent of disease status, but the naive use of the odds ratio as an effect measure suggested otherwise.

The argument against the odds ratio (AFAICT) is that it overestimates the effect when the outcome of interest is more prevalent in controls.

I don’t see any problems with the logic of their example: caution must be used with OR effect measures. We cannot conclude from an OR based on RCT data that there is any interaction between treatment and a covariate; it could just be a mathematical artifact.

In other articles, Senn and Dr. Harrell have advocated the use of additive scale (such as log OR) as measures of effect, especially for research synthesis/meta-analysis.

This set of slides by Stephen Senn and this paper: Controversies over Randomization also seems relevant (found by looking at Dr. Harrell’s blog posts):

Real world modified

I’m not exactly clear on how one might use this information to improve decision making. Doing a search for “relative risk” on this forum brought up this post:

Problems with NNT

In talking to a patient or in making grand policy decisions, when the likely benefit of a treatment is being considered, it is wise to utilize both relative (e.g., hazard ratio) and absolute treatment effects. For the latter, two classes of effects are the life expectancy scale and absolute risk reduction (ARR). Many clinicians are taught to translate ARR to the number needed to treat to save one life or prevent one clinical event — the NNT. There are many reasons that I dislike the NNT. I t…

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The first problem stems from trying to replace two numbers with one, i.e., instead of reporting the estimated outcome with treatment A and the estimated outcome with treatment B, the physician just reports the difference between the two.

It seems the problems with naive use of OR as effect measures can be avoided, but clinicians would need to use both absolute and relative measures of effect, but I’m not exactly sure how both numbers are related to a create declarative statement of probability for an individual. I’m going to need to read that blog post more carefully.

Back to the initial post: it seems that the debate is a confusion of 2 worthwhile goals: appropriate reporting and analysis for researchers, and appropriate utilization by clinicians. It seems that researches should do the analysis on the OR, but external context is needed by clinicians for proper appliction.