Know what you don't know: Embracing state uncertainty in disease-structured multistate models

Hidden Markov models (HMMs) are broadly applicable hierarchical models
that derive their utility from separating state processes from observation
processes yielding the data. Multistate models such as mark-recapture and
dynamic multistate occupancy models are examples of HMMs that are
frequently used in ecology. In their early formulations, states, such as
pathogen infection status, were assumed to be perfectly observed without
ambiguity in state assignment. However, state uncertainty is a pervasive
feature of many ecological systems, and multievent models were developed
to explicitly account for it. We developed a novel extended multievent
mark-recapture model that incorporates state uncertainty at multiple
levels of detection. Using a disease-structured example, both
false-negative and false-positive state assignment errors are modeled at
two levels of state assignment---the pathogen sampling process and the
diagnostic process that samples are subjected to. We additionally describe
methods to jointly model infection intensity to integrate heterogeneity in
ecological parameters, such as survival, and the pathogen detection
processes. We provide code to simulate and analyze datasets with various
underlying ecological processes and fit our model to a mark-recapture
dataset of Mixophyes fleayi (Fleay's barred frog) infected with the
amphibian chytrid fungus (Batrachochytrium dendrobatidis, Bd). In our case
study, we found evidence for various state assignment errors: the sampling
protocol performed poorly in detecting Bd, pathogen detection was highly
dependent on infection intensity, and false-positives were non-negligible.
Incorporating state uncertainty yielded significantly higher estimates of
infection prevalence and 4--5 times lower rates of infection state
transitions compared to those obtained from a traditional multistate
model. Our results highlight that incorporating state assignment errors
improves inference on the ecological state process, especially when
sensitivity and specificity of the state assignment processes are low. The
general model structure can be applied to other HMMs, providing a
foundation for modeling state uncertainty in a range of related models. --