I am modeling Hospital Length of Stay. More specifically, I would like to predict the number of days until a patient is discharged given all of the patients clinical factors throughout his/her stay. I would also like to be able to make this prediction at any point in the patients stay -- Yes, you will be here for another 7 days.
These factors might vary over time, for instance blood pressure. I will measure the Y variable in days, this means I will also use a day for the overall granularity of all other aggregation I do. Length of Stay tends to have a very long right tail.
There are a few ways I have thought to approach this problem:
- Survival Analysis seems like a good option here. Since I am interested in the actual survival time, I would need to use an accelerated life model. I have some familiarity with the Survival Package in R and I believe the survreg function can handle this.
- A Nonlinear Training method such as MARS or SVM. To train this model, I would have each day of a patients stay be its own observation. Among the cofactors would be "Time since admission." The Y variable would be "Remaining days to discharge."
- Do these approaches make sense? Which one do you think would work better? Do you have a better suggestion?
- Would the SurvReg function be able to handle time varying covariates such as blood pressure?
- What would be the format of the newdata I need to feed Predict.SurvReg to make a prediction on a brand new patient? Would I need his full history?
- For the nonlinear models, would splitting up each admission in to days violate any assumptions? The observations would certainly not be independent.