Estimating patterns and drivers of infection prevalence and intensity when detection is imperfect and sampling error occurs

1. Epidemiological studies are crucial for understanding the distribution and dynamics of emerging infectious diseases. To accurately assess infection states in wild populations, researchers need to account for observational uncertainty. We focus on two sources of uncertainty when estimating epidemiological parameters: nondetection of infection in sampled individuals and sampling error when quantifying infection intensity for infected individuals. 2. We developed new analytical methods to simultaneously estimate prevalence and the distribution of infection intensities based on repeated sampling of individuals in the wild. The methods are an extension of those used for occupancy estimation and address both sources of observation error. At the same time, we account for heterogeneity in detection probability that results from individual variation in infection intensity. 3. We use two estimation approaches to account for detection. The first is to use the complete likelihood in a hierarchical Bayesian model and fit using Markov chain Monte Carlo sampling. The second is to estimate the detection relationship using a markrecapture abundance estimator and use those results to calculate weighted estimates for prevalence and mean infection intensities. 4. We use data from a field survey of Batrachochytrium dendrobatidis in Illinois amphibians to test these methods. We show that detection probability using quantitative PCR is strongly related to infection intensity, measured in zoospore equivalents. Sites in the study varied greatly in estimated prevalence and to a lesser extent in mean infection intensities of infected individuals. We did not find evidence of a relationship of snout-vent-length to infection intensity or prevalence. Naive estimates of prevalence that do not account for detection were less than estimates for either of our methods, which yielded similar prevalence values for most sites. 5. Uncertainty when assessing disease state is a characteristic of most diagnostic tests. The estimators presented here account for this uncertainty and thus can improve accuracy when assessing the relationship of ecological factors to prevalence and infection intensity.