Perhaps I’m misunderstanding the authors, but despite referencing @Sander in their paper, they recommend OLS on the risk difference, a variable which must be constrained to a finite range, since it is the difference between 2 probabilities. In this post, he agreed with Frank that the logistic is useful in a wide number of scenarios.
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The fitted logistic probabilities can be easily used to compute estimated risks, risk ratios, risk differences, attributable fractions etc. - whatever is called for by the study context. This is not a statistical choice, but one of topic relevance, e.g., if costs are proportional to risks then risks and their differences are more relevant than odds and their ratios.
In the OR vs RR mega-thread, he had this comment:
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You know Frank I agree completely with your response and have said the same thing to colleagues who have misguidedly promoted use of log-linear risk or (worse) linear risk models. In fact I’ve been advocating our shared view on that since the 1970s (although, as I cited earlier, I have encountered exceptions in pair-matched cohorts in which log-linear risk models outperformed logistic models for a common outcome).
Some further criticism of linear models on probabilities: