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

在新冠肺炎大流行之初，疾病建模人员非常迅速地将相当复杂的流行病模型组合在一起(例如，纳入了年龄结构、行动限制的影响等)。作出预测/预测。正如统计学家通常认为的那样，这是以一种相当特别的方式完成的，从不同的研究中获得对各种参数(例如，传播率、传染病和潜伏期、混合率)的估计和/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，希望将进行敏感性分析。在这种情况下，我不会批评这种方法--事实上，我的团队进行了这种工作；这真的是让这些模型快速启动和运行的唯一方法。然而，从统计角度来看，这种建立模型的方法具有众所周知的危险，缺乏可靠和严格的不确定性量化，或在统计上连贯的框架内检验风险因素的重要性等。构建这些模型的贝叶斯方法似乎很理想。这种办法允许量化有关参数和模型的不确定性，纳入有关数据的不确定性，并纳入来自不同来源的先验知识，所有这些都是有条理和透明的。然而，在新出现的流行病和大流行中，疾病预测模型通常不是以这种方式建立的。这是为什么？大体上，这是因为统计技术(例如方法和软件)不容易使这些模型与数据相适应(特别是在非常混乱的情况下)。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，这个问题在各种各样的模型中是常见的，我们可能想要匹配关于人类、动物和作物疾病的数据。这里我的重点是所谓的“以个体为基础”或“个体水平”的疾病模型。这些模型考虑了人群中复杂的异质性，如空间位置、疫苗接种状况和不同群体之间的混合。因此，它们比简单的“经典”疾病模型更现实，后者假设人口是同质的，但所提到的计算问题甚至更尖锐。因此，这项研究计划的目标是：1.开发能够更真实地模拟现实生活的个人级别的疾病模型类(例如，纳入人口行为变化)；2.开发计算技术，使这些模型在贝叶斯框架中快速适应观察数据；以及3.通过开发易于使用的软件使这种开发更广泛地可用。然后，这些发展可以用来促进我们对传染病的了解，并通过这一点，促进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.