A comparison of observation models for statistical inference of emerging disease transmission dynamics: Application to SARS-CoV-2

1Parameter estimation is often necessary to inform transmission models of infectious diseases. This estimation requires choosing an observation model that links the model outputs to the observed data. Although potentially consequential, this choice has received little attention in the literature. Here, we aimed to compare eight observation models, including common distributions such as the Poisson, binomial, negative binomial, and normal (equivalent to least-squares estimation). Using Bayesian inference methods, we fit an SIR-like model to daily case reports during the first wave of COVID-19 in Belgium, Finland, Germany, and the UK. We found considerable differences in the log-likelihoods of the observation models, spanning three orders of magnitude between the best and the worst. Compared with the best models, the binomial, Poisson, and normal models received no support due to their rigid variance structures. Additionally, the binomial and Poisson models produced overly narrow prediction and confidence intervals, especially for key parameters such as the basic reproduction number. The other five models--each with a free dispersion parameter scaling the variance to the mean--performed significantly better, with the negative binomial model ranking first in three countries. We conclude that flexible observation models are essential for transmission models to accurately capture all sources of uncertainty.