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I have a question regarding the odds ratio. A paper that I submitted was sent back for revision after peer review. However, one of the authors asked a question that has left me quite confused.

In this research, I reported the Adjusted Odds Ratios, 95% Confidence Interval, and P-value for a Logistic Regression Generalized Estimation Equation (Binomial) including more than two million people. Even though I provided the odds ratio as a metric of effect size, one reviewer commented that he could not find the effect size results of the table including >2,000,000 people.

Am I off here? Is the odds ratio not a measure of effect size? I am having trouble understanding what the reviewer is requesting me to do.

Any help at all would be greatly appreciated!

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There are different things people call effect sizes, and what they understand by the term may depend on the scientific discipline or the background. I first encountered the term in psychology, where the most common understanding is Cohen's $d$, or $\eta^2$.

Wikipedia has a decent overview, and we also have an tag. Wikipedia specifically mentions ORs as an example of effect sizes:

In relative effect sizes, two groups are directly compared with each other, as in odds ratios and relative risks.

I would recommend that you read through the Wikipedia page and add to your paper any other measures of effect size that make sense to you and for your analysis. In the cover letter to your resubmission, explain what you did and request that the reviewer note explicitly what kind of effect size they would like to see, in case what you did is not enough for them. You could hint that you already had ORs, perhaps like this:

In terms of effect size, we added additional measures X and Y to the adjusted odds ratios already in Table Z. If the reviewer would like to see other measures, we would appreciate to know specifically which ones they think would be most useful to the manuscript.

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