Likelihood-based estimation and prediction for a measles outbreak in Samoa

TL;DR

This paper introduces a likelihood-based method for predicting infectious disease outbreaks, specifically applied to the 2019-2020 Samoa measles outbreak, addressing model misspecification and enabling efficient inference and uncertainty quantification.

Contribution

It develops a novel likelihood-based variation of the generalised profiling method that improves prediction accuracy and inference under model misspecification, with applications to real outbreak data.

Findings

Achieved fast and accurate outbreak predictions in Samoa

Provided a new interpretation of model approximation as a stochastic constraint

Enabled identifiability analysis and uncertainty quantification without marginalisation

Abstract

Prediction of the progression of an infectious disease outbreak is important for planning and coordinating a response. Differential equations are often used to model an epidemic outbreak's behaviour but are challenging to parameterise. Furthermore, these models can suffer from misspecification, which biases predictions and parameter estimates. Stochastic models can help with misspecification but are even more expensive to simulate and perform inference with. Here, we develop an explicitly likelihood-based variation of the generalised profiling method as a tool for prediction and inference under model misspecification. Our approach allows us to carry out identifiability analysis and uncertainty quantification using profile likelihood-based methods without the need for marginalisation. We provide justification for this approach by introducing a new interpretation of the model approximation component as a stochastic constraint. This preserves the rationale for using profiling rather than integration to remove nuisance parameters while also providing a link back to stochastic models. We applied an initial version of this method during an outbreak of measles in Samoa in 2019-2020 and found that it achieved relatively fast, accurate predictions. Here we present the most recent version of our method and its application to this measles outbreak, along with additional validation.