Point estimator for nomogram in rmsb

data analysis
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1

In the frequentist approach that rms used, it is usually straightforward to use the maximum likelihood (ML) estimator as a point estimator for nomogram - as there is no other choice/everything is Normal in frequentist world so there is no difference whatsoever.

However, in the Bayesian context, there are not just ML estimator: posterior mean, mode, and median, all are point estimators. I think the current approach in rmsb is the marginal posterior mode. However, as pointed out by Florian Hartig the joint mode might not correspond to the marginal one. That makes me wonder if it is really the optimal option.

That said, to minimize the error, shouldn’t we aim for the transformed mean of the mortality risk (i.e. the mean of inv_logit of the log-odd), rather than the MAP/joint Mode?

2

Nomograms from rmsb fits are plotted using the rms package’s nomogram function, which has an argument to allow you to select posterior mode, median, or mean. It is a shame to have to pick one as Bayes wants us to use the whole distribution, and no ordinary nomogram can compute multiple estimates and then pick the posterior mode, median, or mean of those risk estimates. It would be hard to write a new predict method that predicts a whole posterior distribution, and you could make a web app using RShiny that gives you the right output.