Gaussian process nowcasting: application to COVID-19 mortality reporting

Updating observations of a signal due to the delays in the measurement process is a common problem in signal processing, with prominent examples in a wide range of fields. An important example of this problem is the nowcasting of COVID-19 mortality: given a stream of reported counts of daily deaths, can we correct for the delays in reporting to paint an accurate picture of the present, with uncertainty? Without this correction, raw data will often mislead by suggesting an improving situation. We present a flexible approach using a latent Gaussian process that is capable of describing the changing auto-correlation structure present in the reporting time-delay surface. This approach also yields robust estimates of uncertainty for the estimated nowcasted numbers of deaths. We test assumptions in model specification such as the choice of kernel or hyper priors, and evaluate model performance on a challenging real dataset from Brazil. Our experiments show that Gaussian process nowcasting performs favourably against both comparable methods, and against a small sample of expert human predictions. Our approach has substantial practical utility in disease modelling -- by applying our approach to COVID-19 mortality data from Brazil, where reporting delays are large, we can make informative predictions on important epidemiological quantities such as the current effective reproduction number

Report 46: Factors driving extensive spatial and temporal fluctuations in COVID-19 fatality rates in Brazilian hospitals.

The SARS-CoV-2 Gamma variant spread rapidly across Brazil, causing substantial infection and death waves. We use individual-level patient records following hospitalisation with suspected or confirmed COVID-19 to document the extensive shocks in hospital fatality rates that followed Gamma's spread across 14 state capitals, and in which more than half of hospitalised patients died over sustained time periods. We show that extensive fluctuations in COVID-19 in-hospital fatality rates also existed prior to Gamma's detection, and were largely transient after Gamma's detection, subsiding with hospital demand. Using a Bayesian fatality rate model, we find that the geographic and temporal fluctuations in Brazil's COVID-19 in-hospital fatality rates are primarily associated with geographic inequities and shortages in healthcare capacity. We project that approximately half of Brazil's COVID-19 deaths in hospitals could have been avoided without pre-pandemic geographic inequities and without pandemic healthcare pressure. Our results suggest that investments in healthcare resources, healthcare optimization, and pandemic preparedness are critical to minimize population wide mortality and morbidity caused by highly transmissible and deadly pathogens such as SARS-CoV-2, especially in low- and middle-income countries. NOTE: The following manuscript has appeared as 'Report 46 - Factors driving extensive spatial and temporal fluctuations in COVID-19 fatality rates in Brazilian hospitals' at https://spiral.imperial.ac.uk:8443/handle/10044/1/91875 . ONE SENTENCE SUMMARY: COVID-19 in-hospital fatality rates fluctuate dramatically in Brazil, and these fluctuations are primarily associated with geographic inequities and shortages in healthcare capacity

Author correction: spatial and temporal fluctuations in COVID-19 fatality rates in Brazilian hospitals

Correction to: Nature Medicine https://doi.org/10.1038/s41591-022-01807-1, published online 10 May 2022

Bayesian nonparametric methods and applications in statistical network modelling

Bayesian Statistics provide us with a powerful approach to model real-world phenomena and quantify the uncertainty therein by treating unknown factors as random. The Bayesian paradigm prescribes quantifying the prior knowledge about some state of the world, and after having obtained new information updating that knowledge in order to update the prior beliefs and propose posterior knowledge. A central approach to Bayesian Statistics is modelling, i.e. to represent a data generating process using statistical models equipped with some parameters which are to be estimated via Bayesian inference. Bayesian Nonparametric modelling comes with great flexibility as it provides infnitely many parameters. Bayesian Nonparametric models are data adaptive because when given a finite set of data, the size of the finite set of parameters to be used, adapts to the complexity of the observed data. Bayesian Nonparametric models have been used in many applications of machine learning such as density estimation, clustering, latent feature models, survival analysis and function approximation. One of the contributions of this thesis to Bayesian Nonparametrics is the formulation of priors on random graphs to model networks. Our motivation for networks sources from the fact that networks are found in numerous areas of modern society reflecting the patterns of connection across a wide range of physical and social phenomena. Our research focus is on modelling two types of networks; undirected static networks and directed networks with temporal connections. In both cases our objective is to overcome the limitations of the current literature and propose network methodology that captures real-world network properties. Precisely, the property of graph sparsity is particularly important. However, traditional Bayesian network models that assume the desirable property of exchangeability are necessarily not sparse. The first random graph to allow sparsity as well as exchangeability was recently introduced by Caron and Fox [2017] whose framework we follow. Our objective is to propose models with communities in their latent structure, and we therefore propose a generalisation of existing undirected network models with community structure to the sparse regime. Regarding temporal interaction network data, our goal is to capture reciprocation in interactions and therefore define a family of network models that generalises existing classes of reciprocating models to the sparse graph case. The key building blocks of our models as well as for various other popular Bayesian Nonparametric constructions, are infnite-activity completely random measures. The use of these random measures offers flexibility, but is also accompanied by computational complexity. The third objective of this thesis is a methodological and theoretical contribution to Bayesian Nonparametrics consisting of a novel framework to form approximations of infinite-activity completely random measures. By providing finite approximations to these infinite data structures we offer practicality and efficiency. Our constructions can be used to develop efficient posterior inference algorithms and shed light on current Bayesian Nonparametric issues of computational complexity.</p

Exchangeable random measures for sparse and modular graphs with overlapping communities

We propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process and naturally generalizes existing probabilistic models with overlapping block structure to the sparse regime. Our construction builds on vectors of completely random measures and has interpretable parameters, each node being assigned a vector representing its levels of affiliation to some latent communities. We develop methods for efficient simulation of this class of random graphs and for scalable posterior inference. We show that the approach proposed can recover interpretable structure of real world networks and can handle graphs with thousands of nodes and tens of thousands of edges

Unifying incidence and prevalence under a time-varying general branching process

Renewal equations are a popular approach used in modelling the number of new infections, i.e., incidence, in an outbreak. We develop a stochastic model of an outbreak based on a time-varying variant of the Crump–Mode–Jagers branching process. This model accommodates a time-varying reproduction number and a time-varying distribution for the generation interval. We then derive renewal-like integral equations for incidence, cumulative incidence and prevalence under this model. We show that the equations for incidence and prevalence are consistent with the so-called back-calculation relationship. We analyse two particular cases of these integral equations, one that arises from a Bellman–Harris process and one that arises from an inhomogeneous Poisson process model of transmission. We also show that the incidence integral equations that arise from both of these specific models agree with the renewal equation used ubiquitously in infectious disease modelling. We present a numerical discretisation scheme to solve these equations, and use this scheme to estimate rates of transmission from serological prevalence of SARS-CoV-2 in the UK and historical incidence data on Influenza, Measles, SARS and Smallpox

Report 44: Recent trends in SARS-CoV-2 variants of concern in England

Since its emergence in Autumn 2020, the SARS-CoV-2 Variant of Concern (VOC) B.1.1.7 rapidly became the dominant lineage across much of Europe. Simultaneously, several other VOCs were identified globally. Unlike B.1.1.7, some of these VOCs possess mutations thought to confer partial immune escape. Understanding when, whether, and how these additional VOCs pose a threat in settings where B.1.1.7 is currently dominant is vital. This is particularly true for England, which has high coverage from vaccines that are likely more protective against B.1.1.7 than some other VOCs. We examine trends in B.1.1.7’s prevalence in London and other English regions using passive-case detection PCR data, cross-sectional community infection surveys, genomic surveillance, and wastewater monitoring. Our results suggest shifts in the composition of SARS-CoV-2 lineages driving transmission in England between March and April 2021. Local transmission of non-B.1.1.7 VOCs may be increasing; this warrants urgent further investigation