I have data from a study that followed 100 children from birth until their 2nd birthday. Weekly stool samples were examined for presence of a virus and parents were asked whether the child had suffered diarrhea since the last visit.
Samples positive to the virus were not always linked to diarrhea and diarrhea often occurred in the absence of the virus of interest.
We are interested in estimating parameters that would characterize the following:
- Duration of viral infection
- Duration of diarrhea
- Frequency of diarrhea
- How all of the above depends on the specific variant of the virus
Intuitively, I feel I should be modelling a base diarrhea/infection rate and a change of diarrhea rate/duration based on presence of infection. However, I’m not sure how to get started. Incorporating the measurement uncertainty given the week intervals is also one of my goals, though I suspect this should be trivial compared to setting up the rest of the model.
I would appreciate any recommendations on how to approach this analysis. Perhaps there’s a common name for the implied model setup, a textbook or paper showing how to implement it? I am familiar with Stan and R in case it matters.