Could somebody provide some references on the application of logistic regression for modelling rare events?

So far I've come across three methods with the main references below:

  1. Exact logistic regression (paper)
  2. Firth method (paper)
  3. King and Langche approach (paper)
  • 1
    $\begingroup$ Ordinary maximum likelihood estimation for logistic regression parameters is intended to handle rare events. More care needs to be taken for getting confidence limits and p-values, by using likelihood ratio test methods instead of Wald (standard error-based) methods. What is your worry? $\endgroup$ – Frank Harrell May 26 at 11:08
  • $\begingroup$ @FrankHarrell I was reading at link that 'The problem is that maximum likelihood estimation of the logistic model is well-known to suffer from small-sample bias'. For rare events like the one I'm trying to model (<3%, around 39 cases) I'm worried that MLE would be too biased because of the rarity of the event. $\endgroup$ – alessandro May 26 at 11:22
  • 1
    $\begingroup$ Paul Allison's comments are very useful and on point. I just don't know whether the magnitude of the bias makes it worth doing anything about. And note that if you used a Bayesian logistic model, everything is exact, and it doesn't require changing the model as "exact" logistic regression does in the frequentist setting. $\endgroup$ – Frank Harrell May 26 at 12:12

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