This article develops an approximate N-mixture model for infectious disease counts that accounts for under-reporting as well as spatial dependence induced by person-to-person spread of disease. We employ the model to estimate actual case counts in Oregon of chlamydia, an easily-treated but usually asymptomatic sexually transmitted disease. We describe a combined parametric bootstrap to account for uncertainty in parameter estimates as well as sampling variability in actual case counts. A simulation study illustrates that our method performs well in many scenarios when the model is correctly specified, and also gives reasonable results when the model is misspecified, and no spatial dependence exists.
AbellanJJ, RichardsonS and BestN (2008) Use of space-time models to investigate the stability of patterns of disease. Environmental Health Perspectives, 116, 1111–19.
2.
BrintzB,FuentesC and MadsenL (2018) An asymptotic approximation to the N-mixture model for the estimation of disease prevalence. Biometrics, 74, 1512–18.
3.
DailD and MadsenL (2011) Models for estimating abundance from repeated counts of an open metapopulation. Biometrics, 67, 577–87.
4.
GibbonsCL, MangenM-JJ, PlaßD HavelaarAH, BrookeRJ, KramarzP,PetersonKL, StuurmanAL, CassiniA,FevreEM and KretzschmarMEE (2014). Measuring underreporting and under-ascertainment in infectious disease datasets: A comparison of methods. BMC Public Health, 14, 147.
5.
MardiaKV and MarshallR (1984) Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika, 71, 135–46.
6.
Oregon Health Authority (2017). Oregon STD statistics. URL http://www.oregon.gov/oha/PH/DiseasesConditions/CommunicableDisease/DiseaseSurveil(last accessed 1 August 2017).
7.
OstfeldRS, GlassGE, and KeesingF (2005) Spatial epidemiology: An emerging (or re-emerging) discipline. Trends in Ecology & Evolution, 20, 328–36.
8.
R Core Team (2016) R: A Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing. URL https://www.R-project.org/9lastaccessed 18 May 2021).
9.
RossmanS,YackulicCB, SaundersSP, ReidJ,DavisR and ZipkinEF (2016) Dynamic N-occupancy models: Estimating demographic rates and local abundance from detection-nondetection data. Ecology, 97, 3300–3307.
10.
RoyleJA (2004) N-mixture models for estimating population size from spatially replicated counts. Biometrics, 60, 108–15.
11.
ZhaoQ, RoyleJA and BoomerGS (2017). Spatially explicit dynamic N-mixture models. Population Ecology, 59, 293–300.
