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paul-buerkner / brms

brms R package for Bayesian generalized multivariate non-linear multilevel models using Stan
https://paul-buerkner.github.io/brms/
GNU General Public License v2.0
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Copulas #444

Open harrelfe opened 6 years ago

harrelfe commented 6 years ago

Paul I see that you list general multivariate models as an area for future development in brms. In randomized clinical trials there is a significant need for multivariate modeling of mixtures of univariate outcomes, including binary, ordinal, continuous, and time-to-event outcomes. Multivariate copulas seem to be the best way to go because researchers wish to get the usual marginal interpretation of treatment effect for each of the component outcomes. This paper by Costa and Drury is excellent, relating to a bivariate situation - a continuous outcome and a binary outcome joined with a copula. They even go so far as to allow the copula dependence parameter to vary by treatment, as in the placebo group the two responses can be decoupled (that would be a feature for the more distant future). I hope you’ll consider implementing copulas, at least ones with dependence parameters with specified priors but the parameter not varying with treatment. Thanks for considering!

statwonk commented 5 years ago

I've found myself in this area and I've been brushing up on copulas and collecting some prior art,

paul-buerkner commented 5 years ago

Thanks! I will take a look.

paul-buerkner commented 5 years ago

A note to myself. Copulas of discrete responses should be rather straight forward as the density can just be constructed as the difference of the cumulative distribution function evaluated at two adjacent response values.