Should one derive risk difference from the odds ratio?

[R_cubed]

@f2harrell

I don’t think for a minute that a default approach will work for all situations/datasets. Data analysis is hard and prior knowledge about data patterns is not frequently available. So we need help. If a particular approach worked best in 8 out of 10 representative datasets I would continue to use it in many cases as a default approach. So what do we mean by “worked best?” Here is the way I think about that. Ignoring nonlinearity for the moment, I would choose 10 moderately large “representative” datasets and four or more link functions such as the identity function (additive risk model), logit (logistic model), log probability (relative risk model), and probit. For each dataset and each link function compute A = likelihood ratio \chi^2 χ2\chi^2 statistic for a model containing all the predictors and all their two-way interactions, and B = the same but omitting all interactions. Compute the ratio B/A, the so-called “adequacy index” in the maximum likelihood chapter of Regression Modeling Strategies. B/A is the relative extent to which interaction terms were needed to explain outcome variation (high values indicating less need for interactions). Display B/A ratios for all datasets and all link functions. See what you learn.

This proposal is very similar to what @Sander wrote in his 1979 paper on logistic regression limitations:

Blockquote
A general paradigm can be derived … The necessity of adding complex terms (eg. product terms) to a multiplicative (additive) statistical model in order to achieve a “good fit” may indicate that the exposures under study do not influence the disease risk through a process following the multiplicative (additive) biological model; the form of the best fitting, parsimonious statistical model may in turn suggest a form of the biological model in action… Results of such generalized model searches may be combined with physiologic observations and data from animal experiments to test old and generate new models…

I also don’t understand this preference for “Marginal” models over conditional ones. Direct reference to the Nelder paper I mentioned above:

Blockquote
An advantage of a random effects model is they allow conditional inferences in addition to marginal inferences.… The conditional model is a basic model, which leads to a specific marginal model.