Journal of the Royal Statistical Society Series A-Statistics in Society最新文献

I congratulate: Parag, Thompson, and Donnelly; Jewell and Lewnard; and Coffeng and de Vlas on their papers which highlight both the benefits and potential pitfalls associated with statistics such as the doubling time $�T_d$ and the basic reproductive number $�R_0$ during the COVID-19 pandemic. As is appropriate for a methodological meeting, these papers focus on the choice of statistics themselves rather than the specific data sets on which estimates are based. In this brief comment, I would like to also highlight opportunities for innovative study design and mention specifically the value of accurate measures of infection prevalence.

During a pandemic, when the value of epidemiological information is much higher than at other times, there is an opportunity to gather novel population data which would otherwise be deemed too expensive. In the UK, there are a number of examples of community surveys, including the Office for National Statistics Coronavirus Infection Survey (Pouwels et al., 2021), Virus Watch (Hayward et al., 2020) and the REal-time Assessment of Community Transmission (REACT) (Riley et al., 2020). REACT is a program of studies separated into REACT-1 (Riley et al., 2021) that collects self-administered nose and throat swabs (Riley et al., 2021) and REACT-2 that collects self-administered lateral-flow antibody tests (Ward et al., 2021).

Incidence and growth-rate estimates based on routine surveillance are subject to changes in the propensity of individuals to seek tests and in the ability of the system to supply those test (Omori et al., 2020). Community surveys can help to overcome these issues. For example, in recruiting participants randomly from those registered for healthcare in England, the REACT-1 design attempts to reduce the impact of temporal variation when making growth rate estimates (Riley et al., 2021).

In addition to growth rates, population surveys of infection provide estimates of prevalence at national and regional scales that can be easily understood as measures of individual risk: measured swab-positivity is easily translated into odds of infection. While doubling times and reproduction numbers are valuable as indicators of future changes in risk, it could be argued that their prominence in official UK government communications in the UK has led to their value in assessing current levels of risk being overestimated.

When disaggregation of national estimates in several domains or areas is required, direct survey estimators, which use only the domain-specific survey data, are usually design-unbiased even under complex survey designs (at least approximately) and require no model assumptions. Nevertheless, they are appropriate only for domains or areas with sufficiently large sample size. For example, when estimating poverty in a domain with a small sample size (small area), the volatility of a direct estimator might make that area seems like very poor in one period and very rich in the next one. Small area (or indirect) estimators have been developed in order to avoid such undesired instability. Small area estimators borrow strength from the other areas so as to improve the precision and therefore obtain much more stable estimators. However, the usual model-based assumptions, which include some kind of area homogeneity, may not hold in real applications. A more flexible model based on multivariate mixtures of normal distributions that generalises the usual nested error linear regression model is proposed for estimation of general parameters in small areas. This flexibility makes the model adaptable to more general situations, where there may be areas with a different behaviour from the other ones, making the model less restrictive (hence, more close to nonparametric) and more robust to outlying areas. An expectation-maximisation (E-M) method is designed for fitting the proposed mixture model. Under the proposed mixture model, two different new predictors of general small area indicators are proposed. A parametric bootstrap method is used to estimate the mean squared errors of the proposed predictors. Small sample properties of the new predictors and of the bootstrap procedure are analysed by simulation studies and the new methodology is illustrated with an application to poverty mapping in Palestine.

This study presents an initial framework describing factors that could affect respondents' decisions to link their survey data with their public Twitter data. It also investigates two types of factors, those related to the individual and to the design of the consent request. Individual-level factors include respondents' attitudes towards helpful behaviours, privacy concerns and social media engagement patterns. The design factor focuses on the position of the consent request within the interview. These investigations were conducted using data that was collected from a web survey on a sample of Twitter users selected from an adult online probability panel in the United States. The sample was randomly divided into two groups, those who received the consent to link request at the beginning of the survey, and others who received the request towards the end of the survey. Privacy concerns, measures of social media engagement and consent request placement were all found to be related to consent to link. The findings have important implications for designing future studies that aim at linking social media data with survey data.

I congratulate Pellis and colleagues, and Dunbar and Held on their excellent papers describing a variety of mechanistic models of SARS-Cov-2 transmission, and more generally on their work to support policy formulation during the COVID-19 pandemic. Both papers address the difficulties of predicting and then evaluating the impact if non-pharmaceutical interventions (NPIs) against the transmission of severe respiratory pathogens. These are likely to remain key ongoing challenges for the analytical science of pandemic preparedness, with high demand from policy makers for accurate estimates of the epidemiological benefits of NPIs. Here, I would like to make one related methodological point.

There may be benefits in making the null hypotheses in mechanistic modelling studies of NPIs more explicit and more general. For example, models usually contain an underlying basic rate of transmissibility per unit time per infected individual, often denoted $��\beta �$. The parameter $��\beta �$ is used to calculate the risk of infection per susceptible and is modified by other parameters to reflect differences in infectiousness, susceptibility and mixing (Keeling & Rohani, 2011). For example, when schools are closed, it may be assumed that mixing patterns for children change on that day and that the efficacy of school closures can be estimated by fitting a version of the model to incidence data which includes a free parameter describing the strength of change in mixing. However, this type of calculation is implicitly making the strong assumption that a step change on the day of the intervention is a good explanation for the overall pattern of changing transmissibility at that time, which may not be the case. It may be useful to explicitly represented $��\beta �$ as a smooth function of time in an alternative model, as is common practice for similar parameters in other analytical frameworks (Wood, 2017), so that typical measures of parsimony can be used to assess the information contained in specific model fits when strong assumptions are made about the timing of interventions.

We are very grateful for the interesting and constructive comments about the papers discussed in this meeting. We will address the points pertaining to our paper.

Professor Gibson and Professor Nason stress that our model does not have NPIs or other information as covariates. We agree that ideally, one would like to do this. However, this conflicts with another goal of our model—to provide estimates on a very regular basis. Given the rapid decision-making and implementation of new measures, that varied substantially across the United Kingdom, often without exact precedent, it would have meant frequent adjustment of the model and collection and verification of, for example, NPIs for almost 400 areas on a daily basis, making it almost an implausible task without substantial time-commitment.

Professor Gibson also remarks that our paper does not show prior-predictive checks to validate the model—we have omitted more detailed model checks due to space constraints. Our R package Epidemia has a full suite to do model checks and we have used them to verify and tune our models. We do agree with Professor Gibson that individual-based models can be more useful than aggregate models. However, constraints around data availability and compute time makes running individual models on daily basis an unattainable task. Our main objective behind the framework was to have something that can be updated on an almost daily basis, so we opted for simplicity.

Professor Nason raises the point that there are instances of our estimates of $��{�R�}_{�t�}�$ projections are not overlapping with estimates of $��{�R�}_{�t�}�$ by Teh et al. in the same time period and how health officials should react to this. As Professor Nason, points out, it is not surprising that with models with different assumptions, sometimes conflicting estimates arise. This may actually be an advantage. If it is well understood how models differ this gives a more varied understanding of the epidemic in these places—for example, one model which relies more on spatial correlation would assume that a local outbreak will start spreading whereas another model with less s

The spatio-temporal pattern of Covid-19 infections, as for most infectious disease epidemics, is highly heterogenous as a consequence of local variations in risk factors and exposures. Consequently, the widely quoted national-level estimates of reproduction numbers are of limited value in guiding local interventions and monitoring their effectiveness. It is crucial for national and local policy-makers, and for health protection teams, that accurate, well-calibrated and timely predictions of Covid-19 incidences and transmission rates are available at fine spatial scales. Obtaining such estimates is challenging, not least due to the prevalence of asymptomatic Covid-19 transmissions, as well as difficulties of obtaining high-resolution and high-frequency data. In addition, low case counts at a local level further confounds the inference for Covid-19 transmission rates, adding unwelcome uncertainty.

In this paper we develop a hierarchical Bayesian method for inference of transmission rates at fine spatial scales. Our model incorporates both temporal and spatial dependencies of local transmission rates in order to share statistical strength and reduce uncertainty. It also incorporates information about population flows to model potential transmissions across local areas. A simple approach to posterior simulation quickly becomes computationally infeasible, which is problematic if the system is required to provide timely predictions. We describe how to make posterior simulation for the model efficient, so that we are able to provide daily updates on epidemic developments.

The results can be found at our web site https://localcovid.info, which is updated daily to display estimated instantaneous reproduction numbers and predicted case counts for the next weeks, across local authorities in Great Britain. The codebase updating the web site can be found at https://github.com/oxcsml/Rmap. We hope that our methodology and web site will be of interest to researchers, policy-makers and the public alike, to help identify upcoming local outbreaks and to aid in the containment of Covid-19 through both public health measures and personal decisions taken by the general public.

Our model is applied to publicly available daily counts of positive test results reported under the combined Pillars 1 (NHS and PHE) and 2 (commercial partners) of the UK's Covid-19 testing strategy.1 The data are available for 312 lower-tier local authorities (LTLAs) in England, 14 NHS Health Boards in Scotland (each covering multiple local authorities) and 22 unitary local authorities in Wales, for a total of $��n�=�348�$ local areas. The data are daily counts of lab-confirmed (PCR swab) cases presented by specimen d