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In this paper, we develop an extension of compartmental epidemiological models which is suitable for COVID-19. The model presented in this paper comprises seven compartments in the progression of the disease. This model, named as the SINTRUE (S usceptible, I nfected and pre-symptomatic, Infected and Symptomatic but N ot Tested, T ested Positive, Recorded R ecovered, U nrecorded Recovered, and E xpired) model. The proposed model incorporates transmission due to asymptomatic carriers and captures the spread of the disease due to the movement of people to/from different administrative boundaries within a country. In addition, the model allows estimating the number of undocumented infections in the population and the number of unrecorded recoveries. The associated parameters in the model can help architect the public health policy and operational management of the pandemic. The results show that the testing rate of the asymptomatic patients is a crucial parameter to fight against the pandemic. The model is also shown to have a better predictive capability than the other epidemiological models. [ABSTRACT FROM AUTHOR]

At the break of a pandemic, the protective efficacy of therapeutic interventions needs rapid evaluation. An experimental approach to the problem will not always be appropriate. An alternative route are observational studies, whether based on regional health service data or hospital records. In this paper, we discuss the use of methods of causal inference for the analysis of such data, with special reference to causal questions that may arise in a pandemic. We apply the methods by using the aid of a directed acyclic graph (DAG) representation of the problem, to encode our causal assumptions and to logically connect the scientific questions. We illustrate the usefulness of DAGs in the context of a controversy over the effects of renin aldosterone system inhibitors (RASIs) in hypertensive individuals at risk of (or affected by) severe acute respiratory syndrome coronavirus 2 disease. We consider questions concerning the existence and the directions of those effects, their underlying mechanisms, and the possible dependence of the effects on context variables. This paper describes the cognitive steps that led to a DAG representation of the problem, based on background knowledge and evidence from past studies, and the use of the DAG to analyze our hospital data and assess the interpretive limits of the results. Our study contributed to subverting early opinions about RASIs, by suggesting that these drugs may indeed protect the older hypertensive Covid-19 patients from the consequences of the disease. Mechanistic interaction methods revealed that the benefit may be greater (in a sense to be made clear) in the older stratum of the population. [ABSTRACT FROM AUTHOR]

Cure models are a class of time-to-event models where a proportion of individuals will never experience the event of interest. The lifetimes of these so-called cured individuals are always censored. It is usually assumed that one never knows which censored observation is cured and which is uncured, so the cure status is unknown for censored times. In this paper, we develop a method to estimate the probability of cure in the mixture cure model when some censored individuals are known to be cured. A cure probability estimator that incorporates the cure status information is introduced. This estimator is shown to be strongly consistent and asymptotically normally distributed. Two alternative estimators are also presented. The first one considers a competing risks approach with two types of competing events, the event of interest and the cure. The second alternative estimator is based on the fact that the probability of cure can be written as the conditional mean of the cure status. Hence, nonparametric regression methods can be applied to estimate this conditional mean. However, the cure status remains unknown for some censored individuals. Consequently, the application of regression methods in this context requires handling missing data in the response variable (cure status). Simulations are performed to evaluate the finite sample performance of the estimators, and we apply them to the analysis of two datasets related to survival of breast cancer patients and length of hospital stay of COVID-19 patients requiring intensive care. [ABSTRACT FROM AUTHOR]

In the recent COVID-19 pandemic, a wide range of epidemiological modelling approaches were used to predict the effective reproduction number, R(t), and other COVID-19-related measures such as the daily rate of exponential growth, r(t). These candidate models use different modelling approaches or differing assumptions about spatial or age-mixing, and some capture genuine uncertainty in scientific understanding of disease dynamics. Combining estimates using appropriate statistical methodology from multiple candidate models is important to better understand the variation of these outcome measures to help inform decision-making. In this paper, we combine estimates for specific UK nations/regions using random-effects meta-analyses techniques, utilising the restricted maximum-likelihood (REML) method to estimate the heterogeneity variance parameter, and two approaches to calculate the confidence interval for the combined estimate: the standard Wald-type and the Knapp and Hartung (KNHA) method. As estimates in this setting are derived using model predictions, each with varying degrees of uncertainty, equal-weighting is favoured over the standard inverse-variance weighting to avoid potential up-weighting of models providing estimates with lower levels of uncertainty that are not fully accounting for inherent uncertainties. Both equally-weighted models using REML alone and REML+KNHA approaches were found to provide similar variation for R(t) and r(t), with both approaches providing wider, and therefore more conservative, confidence intervals around the combined estimate compared to the standard inverse-variance weighting approach. Utilising these meta-analysis techniques has allowed for statistically robust combined estimates to be calculated for key COVID-19 outcome measures. This in turn allows timely and informed decision-making based on all available information. [ABSTRACT FROM AUTHOR]

The serial interval of an infectious disease, commonly interpreted as the time between the onset of symptoms in sequentially infected individuals within a chain of transmission, is a key epidemiological quantity involved in estimating the reproduction number. The serial interval is closely related to other key quantities, including the incubation period, the generation interval (the time between sequential infections), and time delays between infection and the observations associated with monitoring an outbreak such as confirmed cases, hospital admissions, and deaths. Estimates of these quantities are often based on small data sets from early contact tracing and are subject to considerable uncertainty, which is especially true for early coronavirus disease 2019 data. In this paper, we estimate these key quantities in the context of coronavirus disease 2019 for the UK, including a meta-analysis of early estimates of the serial interval. We estimate distributions for the serial interval with a mean of 5.9 (95% CI 5.2; 6.7) and SD 4.1 (95% CI 3.8; 4.7) days (empirical distribution), the generation interval with a mean of 4.9 (95% CI 4.2; 5.5) and SD 2.0 (95% CI 0.5; 3.2) days (fitted gamma distribution), and the incubation period with a mean 5.2 (95% CI 4.9; 5.5) and SD 5.5 (95% CI 5.1; 5.9) days (fitted log-normal distribution). We quantify the impact of the uncertainty surrounding the serial interval, generation interval, incubation period, and time delays, on the subsequent estimation of the reproduction number, when pragmatic and more formal approaches are taken. These estimates place empirical bounds on the estimates of most relevant model parameters and are expected to contribute to modeling coronavirus disease 2019 transmission. [ABSTRACT FROM AUTHOR]

Excess mortality is an important measure of the scale of the coronavirus-2019 pandemic. It includes both deaths caused directly by the pandemic, and deaths caused by the unintended consequences of containment such as delays to accessing care or postponements of healthcare provision in the population. In 2020 and 2021, in England, multiple groups have produced measures of excess mortality during the pandemic. This paper describes the data and methods used in five different approaches to estimating excess mortality and compares their estimates. The fundamental principles of estimating excess mortality are described, as well as the key commonalities and differences between five approaches. Two of these are based on the date of registration: a quasi-Poisson model with offset and a 5-year average; and three are based on date of occurrence: a Poisson model without offset, the European monitoring of excess mortality model and a synthetic controls model. Comparisons between estimates of excess mortality are made for the period March 2020 through March 2021 and for the two waves of the pandemic that occur within that time-period. Model estimates are strikingly similar during the first wave of the pandemic though larger differences are observed during the second wave. Models that adjusted for reduced circulation of winter infection produced higher estimates of excess compared with those that did not. Models that do not adjust for reduced circulation of winter infection captured the effect of reduced winter illness as a result of mobility restrictions during the period. None of the estimates captured mortality displacement and therefore may underestimate excess at the current time, though the extent to which this has occurred is not yet identified. Models use different approaches to address variation in data availability and stakeholder requirements of the measure. Variation between estimates reflects differences in the date of interest, population denominators and parameters in the model relating to seasonality and trend. [ABSTRACT FROM AUTHOR]

Randomized controlled trials (RCTs) have been widely recognized as the gold standard to infer the treatment effect in clinical research. Recently, there has been growing interest in enhancing and complementing the result in an RCT by integrating real-world evidence from observational studies. The unit information prior (UIP) is a newly proposed technique that can effectively borrow information from multiple historical datasets. We extend this generic approach to synthesize the non-randomized evidence into a current RCT. Not only does the UIP only require summary statistics published from observational studies for ease of implementation, but it also has clear interpretations and can alleviate the potential bias in the real-world evidence via weighting schemes. Extensive numerical experiments show that the UIP can improve the statistical efficiency in estimating the treatment effect for various types of outcome variables. The practical potential of our UIP approach is further illustrated with a real trial of hydroxychloroquine for treating COVID-19 patients. [ABSTRACT FROM AUTHOR]

Understanding the patterns of infectious diseases spread in the population is an important element of mitigation and vaccination programs. A major and common characteristic of most infectious diseases is age-related heterogeneity in the transmission, which potentially can affect the dynamics of an epidemic as manifested by the pattern of disease incidence in different age groups. Currently there are no statistical criteria of how to partition the disease incidence data into clusters. We develop the first data-driven methodology for deciding on the best partition of incidence data into age-groups, in a well defined statistical sense. The method employs a top-down hierarchical partitioning algorithm, with a stopping criteria based on multiple hypotheses significance testing controlling the family wise error rate. The type one error and statistical power of the method are tested using simulations. The method is then applied to Covid-19 incidence data in Israel, in order to extract the significant age-group clusters in each wave of the epidemic. [ABSTRACT FROM AUTHOR]

When comparing the risk of a post-infection binary outcome, for example, hospitalisation, for two variants of an infectious pathogen, it is important to adjust for calendar time of infection. Typically, the infection time is unknown and positive test time used as a proxy for it. Positive test time may also be used when assessing how risk of the outcome changes over calendar time. We show that if time from infection to positive test is correlated with the outcome, the risk conditional on positive test time is a function of the trajectory of infection incidence. Hence, a risk ratio adjusted for positive test time can be quite different from the risk ratio adjusted for infection time. We propose a simple sensitivity analysis that indicates how risk ratios adjusted for positive test time and infection time may differ. This involves adjusting for a shifted positive test time, shifted to make the difference between it and infection time uncorrelated with the outcome. We illustrate this method by reanalysing published results on the relative risk of hospitalisation following infection with the Alpha versus pre-existing variants of SARS-CoV-2. Results indicate the relative risk adjusted for infection time may be lower than that adjusted for positive test time. [ABSTRACT FROM AUTHOR]

Scientific advice to the UK government throughout the COVID-19 pandemic has been informed by ensembles of epidemiological models provided by members of the Scientific Pandemic Influenza group on Modelling. Among other applications, the model ensembles have been used to forecast daily incidence, deaths and hospitalizations. The models differ in approach (e.g. deterministic or agent-based) and in assumptions made about the disease and population. These differences capture genuine uncertainty in the understanding of disease dynamics and in the choice of simplifying assumptions underpinning the model. Although analyses of multi-model ensembles can be logistically challenging when time-frames are short, accounting for structural uncertainty can improve accuracy and reduce the risk of over-confidence in predictions. In this study, we compare the performance of various ensemble methods to combine short-term (14-day) COVID-19 forecasts within the context of the pandemic response. We address practical issues around the availability of model predictions and make some initial proposals to address the shortcomings of standard methods in this challenging situation. [ABSTRACT FROM AUTHOR]

We compare two multi-state modelling frameworks that can be used to represent dates of events following hospital admission for people infected during an epidemic. The methods are applied to data from people admitted to hospital with COVID-19, to estimate the probability of admission to intensive care unit, the probability of death in hospital for patients before and after intensive care unit admission, the lengths of stay in hospital, and how all these vary with age and gender. One modelling framework is based on defining transition-specific hazard functions for competing risks. A less commonly used framework defines partially-latent subpopulations who will experience each subsequent event, and uses a mixture model to estimate the probability that an individual will experience each event, and the distribution of the time to the event given that it occurs. We compare the advantages and disadvantages of these two frameworks, in the context of the COVID-19 example. The issues include the interpretation of the model parameters, the computational efficiency of estimating the quantities of interest, implementation in software and assessing goodness of fit. In the example, we find that some groups appear to be at very low risk of some events, in particular intensive care unit admission, and these are best represented by using 'cure-rate' models to define transition-specific hazards. We provide general-purpose software to implement all the models we describe in the flexsurv R package, which allows arbitrarily flexible distributions to be used to represent the cause-specific hazards or times to events. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has brought to the fore the need for policy makers to receive timely and ongoing scientific guidance in response to this recently emerged human infectious disease. Fitting mathematical models of infectious disease transmission to the available epidemiological data provide a key statistical tool for understanding the many quantities of interest that are not explicit in the underlying epidemiological data streams. Of these, the effective reproduction number, R , has taken on special significance in terms of the general understanding of whether the epidemic is under control (R < 1). Unfortunately, none of the epidemiological data streams are designed for modelling, hence assimilating information from multiple (often changing) sources of data is a major challenge that is particularly stark in novel disease outbreaks. Here, focusing on the dynamics of the first wave (March–June 2020), we present in some detail the inference scheme employed for calibrating the Warwick COVID-19 model to the available public health data streams, which span hospitalisations, critical care occupancy, mortality and serological testing. We then perform computational simulations, making use of the acquired parameter posterior distributions, to assess how the accuracy of short-term predictions varied over the time course of the outbreak. To conclude, we compare how refinements to data streams and model structure impact estimates of epidemiological measures, including the estimated growth rate and daily incidence. [ABSTRACT FROM AUTHOR]

The response of many governments to the COVID-19 pandemic has involved measures to control within- and between-household transmission, providing motivation to improve understanding of the absolute and relative risks in these contexts. Here, we perform exploratory, residual-based, and transmission-dynamic household analysis of the Office for National Statistics COVID-19 Infection Survey data from 26 April 2020 to 15 July 2021 in England. This provides evidence for: (i) temporally varying rates of introduction of infection into households broadly following the trajectory of the overall epidemic and vaccination programme; (ii) susceptible-Infectious transmission probabilities of within-household transmission in the 15-35% range; (iii) the emergence of the Alpha and Delta variants, with the former being around 50% more infectious than wildtype and 35% less infectious than Delta within households; (iv) significantly (in the range of 25-300%) more risk of bringing infection into the household for workers in patient-facing roles pre-vaccine; (v) increased risk for secondary school-age children of bringing the infection into the household when schools are open; (vi) increased risk for primary school-age children of bringing the infection into the household when schools were open since the emergence of new variants. [ABSTRACT FROM AUTHOR]

Time-to-event data are right-truncated if only individuals who have experienced the event by a certain time can be included in the sample. For example, we may be interested in estimating the distribution of time from onset of disease symptoms to death and only have data on individuals who have died. This may be the case, for example, at the beginning of an epidemic. Right truncation causes the distribution of times to event in the sample to be biased towards shorter times compared to the population distribution, and appropriate statistical methods should be used to account for this bias. This article is a review of such methods, particularly in the context of an infectious disease epidemic, like COVID-19. We consider methods for estimating the marginal time-to-event distribution, and compare their efficiencies. (Non-)identifiability of the distribution is an important issue with right-truncated data, particularly at the beginning of an epidemic, and this is discussed in detail. We also review methods for estimating the effects of covariates on the time to event. An illustration of the application of many of these methods is provided, using data on individuals who had died with coronavirus disease by 5 April 2020. [ABSTRACT FROM AUTHOR]

Infectious diseases, such as the ongoing COVID-19 pandemic, pose a significant threat to public health globally. Fatality rate serves as a key indicator for the effectiveness of potential treatments or interventions. With limited time and understanding of novel emerging epidemics, comparisons of the fatality rates in real-time among different groups, say, divided by treatment, age, or area, have an important role to play in informing public health strategies. We propose a statistical test for the null hypothesis of equal real-time fatality rates across multiple groups during an ongoing epidemic. An elegant property of the proposed test statistic is that it converges to a Brownian motion under the null hypothesis, which allows one to develop a sequential testing approach for rejecting the null hypothesis at the earliest possible time when statistical evidence accumulates. This property is particularly important as scientists and clinicians are competing with time to identify possible treatments or effective interventions to combat the emerging epidemic. The method is widely applicable as it only requires the cumulative number of confirmed cases, deaths, and recoveries. A large-scale simulation study shows that the finite-sample performance of the proposed test is highly satisfactory. The proposed test is applied to compare the difference in disease severity among Wuhan, Hubei province (exclude Wuhan) and mainland China (exclude Hubei) from February to March 2020. The result suggests that the disease severity is potentially associated with the health care resource availability during the early phase of the COVID-19 pandemic in mainland China. [ABSTRACT FROM AUTHOR]

As the interactions between people increases, the impending menace of COVID-19 outbreaks materializes, and there is an inclination to apply lockdowns. In this context, it is essential to have easy-to-use indicators for people to employ as a reference. The effective reproduction number of confirmed positives, Rt, fulfills such a role. This document proposes a data-driven approach to nowcast Rt based on previous observations' statistical behavior. As more information arrives, the method naturally becomes more precise about the final count of confirmed positives. Our method's strength is that it is based on the self-reported onset of symptoms, in contrast to other methods that use the daily report's count to infer this quantity. We show that our approach may be the foundation for determining useful epidemy tracking indicators. [ABSTRACT FROM AUTHOR]