Marginal Likelihood Inference for Fitting Dynamical Survival Analysis Models to Epidemic Count Data

TL;DR

This paper introduces a computationally efficient likelihood-based method for fitting dynamical survival analysis models to epidemic count data, improving inference in partially observed disease spread scenarios.

Contribution

It develops a closed-form likelihood for discretely observed epidemic data under the DSA framework, enabling flexible and efficient inference for complex epidemic models.

Findings

Parameter estimation is competitive with existing methods.

Method extends to models with individual heterogeneity.

Demonstrated on Ebola and COVID-19 datasets.

Abstract

Stochastic compartmental models are prevalent tools for describing disease spread, but inference under these models is challenging for many types of surveillance data when the marginal likelihood function becomes intractable due to missing information. To address this, we develop a closed-form likelihood for discretely observed incidence count data under the dynamical survival analysis (DSA) paradigm. The method approximates the stochastic population-level hazard by a large population limit while retaining a count-valued stochastic model, and leads to survival analytic inferential strategies that are both computationally efficient and flexible to model generalizations. Through simulation, we show that parameter estimation is competitive with recent exact but computationally expensive likelihood-based methods in partially observed settings. Previous work has shown that the DSA approximation is generalizable, and we show that the inferential developments here also carry over to models featuring individual heterogeneity, such as frailty models. We consider case studies of both Ebola and COVID-19 data on variants of the model, including a network-based epidemic model and a model with distributions over susceptibility, demonstrating its flexibility and practical utility on real, partially observed datasets.