State uncertainty in disease analysis

[ganghis]

Ideally one would solve this dilemma by expressing transition probabilities as a function of continuous time hazard rates (integrating over time; see a recent paper on force-of-infection models by conn, cooch, and caley in j of ornithology). However, there's not currently any bespoken code to help you do this. I might be willing to collaborate on this if you email me offlist (paul.conn@noaa.gov), but that would probably be more of a "long term" project. In the short term, you probably want to go with a time varying transition probability model, or perhaps use the time interval as a covariate on transition probability. There will admittedly be some issues with interpretation of results if multiple transitions can occur between sampling occasions.

[Bill Kendall]

Simone,
Sorry I have not been keeping up with the traffic on the forum. As Jeff, Paul, and Evan have said, MARK has the capability for this kind of model. The paper describing a closed RD version of the model has been accepted in Ecology. If you have already gotten E-SURGE to work for you, great! If not, or if you are interested in direct estimates of prevalence (the proportion of the population that are infected at a given time), then MARK could be helpful here. If you don't have multiple sampling occasions per primary period of interest (i.e., a RD) no worries. You could make it look like a RD analysis by inserting a column of zeroes after every column of real data, tell MARK there are two occasions for every primary period, and make p=0 for each of those dummy sampling occasions.

Soon we will be writing a chapter on these models for the MARK book. In the interim, here are the main points. The extra parameters you deal with in these models, beyond the usual multstate parameters, are pi(s)t = the probability an individual first captured at time t is in state s, given it was not classified to state during time period t.; omega(s)t (state structure) = the probability an individual at time t is in state s, given it is alive and in the population at time t. delta(s|s)t = probability an individual is assigned to state s, given it is in state s and detected. As was mentioned by the others, this model does not permit misclassification, but only state uncertainty. In your detection history you will enter either a code for a state you defined (e.g. I for infected, U for uninfected), if you area sure it is in a given state, or a 'u' (make sure it is lower case) for cases where you are not sure which state it is in. 'u' is NOT a state (i.e., don't try to define it as such in MARK), but an observation, or 'event' as Pradel has described it.

I hope this helps. If you interested in seeing the manuscript, or have additional question, send me an email (William.Kendall@colostate.edu). If you are more comfortable with R-MARK, you should contact Jeff for help.