Statistical inference for epidemic models accounting for population heterogeneity: computational efficiency & model development

点击翻译按钮获取中文摘要

At the beginning of the COVID-19 pandemic, disease modellers very quickly put together fairly complex epidemic models (e.g., incorporating age structure, effect of movement restrictions, etc.) to make forecasts/projections. This was done, as is typical, in what a statistician would consider a fairly ad hoc manner, obtaining estimates for the various parameters (e.g., transmission rates, infectious & incubation periods, mixing rates) from different studies and/or using non-linear least squares estimation. To try and allow for uncertainty in these estimates, hopefully a sensitivity analysis would be carried out. In those circumstances, I do not criticize this approach -- and indeed, my group carried out such work; it was really the only way to get these models up and running quickly. However, from a statistical point of view, such an approach to building models has well known dangers, lacking reliable and rigorous quantification of uncertainty, or the testing of the significance of risk factors, etc., in a statistically coherent framework. A Bayesian approach to building these models would seem ideal. Such an approach allows for the uncertainty quantification regarding parameters and model, incorporation of uncertainty regarding the data, and incorporation of prior knowledge from different sources, all in a structured and transparent way. However, in emerging epidemics and pandemics, disease forecast models are not typically built in this way. Why is this? In the main, it is because the statistical technology (e.g., methodology and software) to fit such models quickly to data (especially if very messy), is not readily available. So, in early 2019, the time taken to code up the required models, and run the computational algorithms used to carry out the Bayesian analysis, would have been prohibitive. Unfortunately, this problem is common across a wide variety of models we might want to fit the data on human, animal and crop disease. My focus here is on so-called `individual-based' or `individual-level' disease models. These models allow for complex heterogeneities in the population, such as spatial location, vaccination status, and mixing between different groups, to be accounted for. They are therefore more realistic than simple `classical' disease models that assume the population is homogeneous, but the computational problems mentioned are even more acute. Thus, the goal of this research program is to develop: 1. individual-level disease model classes which can more realistically mimic real life (e.g., incorporating population behavioural change); 2.  computational technology to fit these models to observed data quickly in a Bayesian framework; and, 3. make such developments more widely available through the development of easy-to-use software. These developments can then be used to further our understanding of infectious diseases, and through this, our ability to control them, helping save lives and alleviating severe economic outcomes.