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

在2019冠状病毒病大流行之初，疾病建模者很快就建立了相当复杂的流行病模型（例如，（包括年龄结构、行动限制的影响等）进行预测/预测。这是典型的，统计学家会认为这是一种相当特别的方式，获得各种参数的估计值（例如，传播率、感染和潜伏期、混合率）和/或使用非线性最小二乘估计。为了尝试并考虑到这些估计中的不确定性，希望进行敏感性分析。在这种情况下，我并不批评这种方法--事实上，我的小组进行了这样的工作;这确实是让这些模型快速启动和运行的唯一方法。 然而，从统计学的角度来看，这种建立模型的方法具有众所周知的危险性，缺乏对不确定性的可靠和严格的量化，或者对风险因素的显著性进行测试等，在一个统计连贯的框架内。贝叶斯方法来建立这些模型似乎是理想的。这种方法允许对参数和模型的不确定性进行量化，纳入数据的不确定性，并纳入来自不同来源的先验知识，所有这些都是以结构化和透明的方式进行的。然而，在新出现的流行病和大流行病中，疾病预测模型通常不是以这种方式建立的。这是为什么呢？主要是因为统计技术（例如，方法和软件）来快速地将这种模型拟合到数据（特别是如果非常混乱的话）。因此，在2019年初，编写所需模型并运行用于进行贝叶斯分析的计算算法所需的时间将是令人望而却步的。不幸的是，这个问题在我们可能想要拟合人类，动物和作物疾病数据的各种模型中很常见。 我在这里的重点是所谓的“基于个人”或“个人层面”的疾病模型。这些模型考虑到了群体中复杂的异质性，如空间位置、疫苗接种状态和不同群体之间的混合。因此，它们比简单的假定人口是同质的“经典”疾病模型更为现实，但所提到的计算问题更为尖锐。因此，本研究计划的目标是开发：1。可以更真实地模拟真实的生活的个体水平疾病模型类（例如，纳入人口行为变化）; 2. 计算技术，以适应这些模型，以观察到的数据迅速在贝叶斯框架;和，3。通过开发易于使用的软件，使这些发展更广泛地得到利用。这些发展可以用来进一步了解传染病，并通过这一点，我们控制它们的能力，帮助拯救生命和减轻严重的经济后果。

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.