Hi, I am working on a joint model. Many examples I found are to joint a mixed model and a survival model. I am wondering the feasibility to use Stan to integrate ODEs inside a survival model. Anybody has experience on that? Thank you.

I guess â€śjoint modelâ€ť is a very broad category, I am not sure if thereâ€™s a technical basic definition for it, but Iâ€™d say itâ€™s anything with more than one parameter â€“ maybe a better one would be â€śanything that could otherwise be inferred separately, or can be logically separatedâ€ť.

So in principle, yes, Stan can be used for all sorts of joint models, but we would have so see if thereâ€™s anything in your specific model that is not very standard. From what you describe it seems like you would have some sort of multilevel model where ODEs would be used at a lower level to compute some property for a survival model on the level above. I worked on something where survival models went into a dose-response model, so itâ€™s opposite hierarchy and not ODE-based. If you canâ€™t find in the literature examples of the exact (or similar enough) model you are trying to set up, maybe you have to do it yourself from scratch, and when you get to specific issues this is the place to ask.

Thank you. yes, I am going to use ODE as first level; the output of ODE will be used in the survival model. I see from your paper that you worked with virus, do you know anything about the M3 approach for modeling below the limit of quantification observations?

No, I donâ€™t know about it. In this work we used survival as the observable outcome, so there was not detection/quantification of virus for the main analysis. But normally treatment of samples below limit of quantification are assumed to be zero, anything else would be part of a preprocessing scheme for which there should be a justification.

In other work with a similar model we did use viral quantification and there was some criticism because we didnâ€™t remove samples that were around the mean of the (detectable) negative controls. The preprocessing scheme suggested by the group that criticized us was very rough, because it ignored all other negative controls with undetectable titers (which were \sim 95\% of the distribution, so the detectable ones were in over the 95th percentile). Both data sets used were from previously published work, so we didnâ€™t change it, but in any case we ran the same analysis using the cut-off suggested by the critics and showed that the qualitative results they criticized were robust to the change (in fact they were less like what they expected with their scheme).

That was maybe too long, but it took a minute to write so there it is. The point is, maybe try different schemes and see if the results are robust, otherwise you may need strong justification for different pre processing of your data based on the detection limits.

Thank you for all those. I finally modelled the observations under limit of quantification by assuming they are censored data (definition of M3 approach), following this paper â€śWays to Fit a PK Model with Some Data Below the Quantification Limitâ€ť. M3 approach is well accepted in this modeling area.