I'm interested in updating predictions from survival models, in cases where you have time dependent covariates that are a) continuous and b)change in continuous time.
For example, you want to predict a patient's probability of dying before time T, and you want to continuously update your prediction as their blood pressure, weight, etc. changes.
I'm assuming there must be a Bayesian approach for this use case; any package that has implemented this would be massively helpful.
The papers I have seen that explicitly incorporate time dependent covariates usually deal with one or two major events per patient, such as a heart transplant. The data will be left and right censored for each major event, but this is not reasonable for covariates that are constantly changing. I believe this approach comes from longitudinal studies where observation is very infrequent. We now have health data that changes constantly, so we want to change our predictions as well.
Edit This paper describes the same problem set I'm approaching, from a more theoretical standpoint: http://arxiv-web3.library.cornell.edu/pdf/1306.6479v1.pdf Implementing joint models in the wild is quite cumbersome. There has to be a more practical approach, even if it sacrifices some of the theoretical guarantees.