A primer on inference and prediction with epidemic renewal models and sequential Monte Carlo (2503.18875v2)

Abstract: Renewal models are widely used in statistical epidemiology as semi-mechanistic models of disease transmission. While primarily used for estimating the instantaneous reproduction number, they can also be used for generating projections, estimating elimination probabilities, modelling the effect of interventions, and more. We demonstrate how simple sequential Monte Carlo methods (also known as particle filters) can be used to perform inference on these models. Our goal is to acquaint a reader who has a working knowledge of statistical inference with these methods and models and to provide a practical guide to their implementation. We focus on these methods' flexibility and their ability to handle multiple statistical and other biases simultaneously. We leverage this flexibility to unify existing methods for estimating the instantaneous reproduction number and generating projections. A companion website SMC and epidemic renewal models provides additional worked examples, self-contained code to reproduce the examples presented here, and additional materials.

Overview of "A Primer on Inference and Prediction with Epidemic Renewal Models and Sequential Monte Carlo"

The paper "A Primer on Inference and Prediction with Epidemic Renewal Models and Sequential Monte Carlo" authored by Nicholas Steyn, Kris V. Parag, Robin N. Thompson, and Christl A. Donnelly, offers an in-depth exposition on using renewal models in statistical epidemiology, complemented by sequential Monte Carlo (SMC) methods for performing robust inference and prediction tasks. The focus of this paper is to not only estimate instantaneous reproduction numbers but also to broaden the application of renewal models for tasks like projecting future incidences, estimating probabilities of disease elimination, and evaluating interventions.

Renewal Models and Their Applications:

Renewal models are established as semi-mechanistic tools that relate past disease incidences to current ones, primarily to estimate the instantaneous reproduction number, $R_t$. However, the authors extend their utility to generating projections and modeling the effects of interventions—their flexibility is emphasized in handling data biases and statistical inconsistencies. The paper unifies methods for estimating $R_t$ with a comprehensive introduction to SMC methodologies that allows for greater adaptability in real-world scenarios.

Sequential Monte Carlo (SMC) Methods:

The authors advocate for simple particle filters as SMC methods to perform inference. SMC methods, otherwise referred to as particle filters, are used to fit hidden-state models to observed data. By simulating from these models, states at every timestep are inferred, enabling robust simulation-based inference. The application of SMC here provides a means of handling multiple biases within data seamlessly, unifying several epidemiological estimation tasks under a singular methodological roof. The authors detail the fixed-lag smoothing approach for particle filters to retain computational efficiency while reducing degeneracy.

Empirical Studies and Case Scenarios:

Through empirical applications utilizing real COVID-19 data from New Zealand, the paper showcases the flexibility of SMC methods in dynamic epidemiological settings. Three model scenarios were crafted to demonstrate the versatility maneuvers around common epidemiological concerns such as reporting lag, imported cases, and probabilities of disease elimination. Each scenario tested the impact of model assumptions and parameter choices on the inference drawn, advocating for interactive and adaptable modeling processes that adjust as per the demands of incoming data streams.

Model Comparisons and Performance Metrics:

Evaluation of different modeling approaches underlines the importance of adaptable methodologies, such as those using prior knowledge or incorporating additional data, like wastewater samples, when available. The authors also compare various forecasting models, illustrating the readiness of SMC to improve upon traditional models through their noted accuracy in short-term projections—a key decision-making tool. Metrics like root mean square error (RMSE) and the continuous ranked probability score (CRPS) are employed to evaluate and compare model performance quantitatively.

Theoretical Implications and Future Directions:

The paper underlines SMC methods' capacity to evaluate probabilistic forecasts under varying epidemic conditions effectively. This flexibility offers a noteworthy advancement over more rigid techniques, which are often plagued by assumptions that may not hold in rapidly changing epidemic situations. Moreover, the document provides speculative discussion on potential future developments in AI and statistical practices, envisaging integration with real-time policy-making platforms that can heed swiftly changing information.

In essence, this primer provides both a conceptual foundation and practical guide for adopting SMC methods in epidemic modeling, underscoring the critical need for flexibility, adaptability, and robustness in dealing with the inherent complexities of real-world epidemiological data. The comprehensive expository nature of the paper aids in equipping researchers with the requisite knowledge to tailor and apply advanced statistical methodologies adeptly across various pandemic scenarios.