Survival analysis with rare events I want to model survival using Cox regression using R. I have a binary outcome (yes/no) with low prevalence so I would like to apply a correction such as Firth's correction – is this appropriate? I was planning to use the coxphf command although the Help file states this is generally used for non-convergence. My standard Cox model does converge but I am just wondering if I should apply any correction due to the small number of cases… Any suggestion?

With rare events, problems can occur with convergence if there are no events for some particular combinations of predictor values. So, on that account, you don't need a correction if your model is converging.
You might, however, consider some type of penalization if you have a large number of predictors relative to the number of events. Then rare events can lead to a problem of overfitting. A usual rule of thumb is to have at least 10-20 events per predictor in the model (including extra levels of multi-level categorical variables and interaction terms). If you are at danger of overfitting because of a low event/predictor ratio, Firth's correction might be used in such circumstances, but ridge regression is probably a more typical and generally familiar penalization method for this type of study.
