I’d convert your
“Do the statistics on the (additive) log odds scale, but convert baseline risks to the probability scale”
to something more like
“Do the modeling on the log odds (logit) scale, but convert the final results to the probability scale.”
because we shouldn’t want to limit the logit model to additive or linear (for example “machine-learning” logit models may become arbitrarily nonadditive and nonlinear). The use of the logit link is strictly a technical move to ensure proper range restriction of risks, variation independence of parameters, well-behaved fitting algorithms, and optimal calibration.
I think the problem is that some statisticians seem to think the very desirable technical advantages of the logit link lead to some broader causal or utilitarian argument for using odds ratios as final measures, which is simply a mistake. My impression is that, having seen some statisticians messing up causal inference with idiocies like significance (p<0.05) selection of confounders back in the 1970s, epidemiologic culture became more skeptical of statistical culture than did clinical culture. Some epidemiologists recognized then that not only should we discard “significance” but we should separate choice of the smoothing model from final summarization; the latter should be dictated by the utilities and goals of the context, nonparametrically, not by the statistical model. Here are a few of my writings on the topic since 1979:
Greenland S. Summarization, smoothing, and inference. Scand J Soc Med 1993;21:227–232.
Greenland S. Smoothing observational data: a philosophy and implementation for the health sciences. Int Stat Rev 2006;74:31–46.
As usual if you want to look them over and can’t access them online, e-mail me and I’ll send you a PDF. See also p. 438-442 in Ch. 21 of Modern Epidemiology 3rd ed. 2008.