Investigating Heterogeneity in Pneumococcal Transmission

Randomization for the susceptibility effect of an infectious disease intervention

Randomized trials of infectious disease interventions, such as vaccines, often focus on groups of connected or potentially interacting individuals. When the pathogen of interest is transmissible between study subjects, interference may occur: individual infection outcomes may depend on treatments received by others. Epidemiologists have defined the primary parameter of interest-called the "susceptibility effect"-as a contrast in infection risk under treatment versus no treatment, while holding exposure to infectiousness constant. A related quantity-the "direct effect"-is defined as an unconditional contrast between the infection risk under treatment versus no treatment. The purpose of this paper is to show that under a widely recommended randomization design, the direct effect may fail to recover the sign of the true susceptibility effect of the intervention in a randomized trial when outcomes are contagious. The analytical approach uses structural features of infectious disease transmission to define the susceptibility effect. A new probabilistic coupling argument reveals stochastic dominance relations between potential infection outcomes under different treatment allocations. The results suggest that estimating the direct effect under randomization may provide misleading conclusions about the effect of an intervention-such as a vaccine-when outcomes are contagious. Investigators who estimate the direct effect may wrongly conclude an intervention that protects treated individuals from infection is harmful, or that a harmful treatment is beneficial.

Reconstruction of the Transmission Chain of COVID-19 Outbreak in Beijing's Xinfadi Market, China

Objectives

The aim of the study was to reconstruct the complete transmission chain of the COVID-19 outbreak in Beijing's Xinfadi Market using data from epidemiological investigations, which contributes to reflecting transmission dynamics and transmission risk factors.

Methods

We set up a transmission model, and the model parameters are estimated from the survey data via Markov chain Monte Carlo sampling. Bayesian data augmentation approaches are used to account for uncertainty in the source of infection, unobserved onset, and infection dates.

Results

The rate of transmission of COVID-19 within households is 9.2%. Older people are more susceptible to infection. The accuracy of our reconstructed transmission chain was 67.26%. In the gathering place of this outbreak, the Beef and Mutton Trading Hall of Xinfadi market, most of the transmission occurs within 20 m, only 19.61% of the transmission occurs over a wider area (>20 m), with an overall average transmission distance of 13.00 m. The deepest transmission generation is 9. In this outbreak, there were 2 abnormally high transmission events.

Conclusions

The statistical method of reconstruction of transmission trees from incomplete epidemic data provides a valuable tool to help understand the complex transmission factors and provides a practical guideline for investigating the characteristics of the development of epidemics and the formulation of control measures.

Transmission Modeling with Regression Adjustment for Analyzing Household-based Studies of Infectious Disease: Application to Tuberculosis

BACKGROUND

Household contacts of people infected with a transmissible disease may be at risk due to this proximate exposure, or from other unobserved sources. Understanding variation in infection risk is essential for targeting interventions.

METHODS

We develop an analytical approach to estimate household and exogenous forces of infection, while accounting for individual-level characteristics that affect susceptibility to disease and transmissibility. We apply this approach to a cohort study conducted in Lima, Peru, of 18,544 subjects in 4,500 households with at least one active tuberculosis (TB) case and compare the results to those obtained by Poisson and logistic regression.

RESULTS

HIV-coinfected (susceptibility hazard ratio [SHR] = 3.80, 1.56-9.29), child (SHR = 1.72, 1.32-2.23), and teenage (SHR = 2.00, 1.49-2.68) household contacts of TB cases experience a higher hazard of TB than do adult contacts. Isoniazid preventive therapy (SHR = 0.30, 0.21-0.42) and Bacillus Calmette-Guérin (BCG) vaccination (SHR = 0.66, 0.51-0.86) reduce the risk of disease among household contacts. TB cases without microbiological confirmation exert a smaller hazard of TB among their close contacts compared with smear- or culture-positive cases (excess hazard ratio = 0.88, 0.82-0.93 for HIV- cases and 0.82, 0.57-0.94 for HIV+ cases). The extra household force of infection results in 0.01 (95% confidence interval [CI] = 0.004, 0.028) TB cases per susceptible household contact per year and the rate of transmission between a microbiologically confirmed TB case and susceptible household contact at 0.08 (95% CI = 0.045, 0.129) TB cases per pair per year.

CONCLUSIONS

Accounting for exposure to infected household contacts permits estimation of risk factors for disease susceptibility and transmissibility and comparison of within-household and exogenous forces of infection.

Identification of causal intervention effects under contagion

Defining and identifying causal intervention effects for transmissible infectious disease outcomes is challenging because a treatment - such as a vaccine - given to one individual may affect the infection outcomes of others. Epidemiologists have proposed causal estimands to quantify effects of interventions under contagion using a two-person partnership model. These simple conceptual models have helped researchers develop causal estimands relevant to clinical evaluation of vaccine effects. However, many of these partnership models are formulated under structural assumptions that preclude realistic infectious disease transmission dynamics, limiting their conceptual usefulness in defining and identifying causal treatment effects in empirical intervention trials. In this paper, we propose causal intervention effects in two-person partnerships under arbitrary infectious disease transmission dynamics, and give nonparametric identification results showing how effects can be estimated in empirical trials using time-to-infection or binary outcome data. The key insight is that contagion is a causal phenomenon that induces conditional independencies on infection outcomes that can be exploited for the identification of clinically meaningful causal estimands. These new estimands are compared to existing quantities, and results are illustrated using a realistic simulation of an HIV vaccine trial.

Geographically dependent individual-level models for infectious diseases transmission

Infectious disease models can be of great use for understanding the underlying mechanisms that influence the spread of diseases and predicting future disease progression. Modeling has been increasingly used to evaluate the potential impact of different control measures and to guide public health policy decisions. In recent years, there has been rapid progress in developing spatio-temporal modeling of infectious diseases and an example of such recent developments is the discrete-time individual-level models (ILMs). These models are well developed and provide a common framework for modeling many disease systems; however, they assume the probability of disease transmission between two individuals depends only on their spatial separation and not on their spatial locations. In cases where spatial location itself is important for understanding the spread of emerging infectious diseases and identifying their causes, it would be beneficial to incorporate the effect of spatial location in the model. In this study, we thus generalize the ILMs to a new class of geographically dependent ILMs, to allow for the evaluation of the effect of spatially varying risk factors (e.g., education, social deprivation, environmental), as well as unobserved spatial structure, upon the transmission of infectious disease. Specifically, we consider a conditional autoregressive (CAR) model to capture the effects of unobserved spatially structured latent covariates or measurement error. This results in flexible infectious disease models that can be used for formulating etiological hypotheses and identifying geographical regions of unusually high risk to formulate preventive action. The reliability of these models is investigated on a combination of simulated epidemic data and Alberta seasonal influenza outbreak data ($2009$). This new class of models is fitted to data within a Bayesian statistical framework using Markov chain Monte Carlo methods.

Improving early epidemiological assessment of emerging Aedes-transmitted epidemics using historical data

Model-based epidemiological assessment is useful to support decision-making at the beginning of an emerging Aedes-transmitted outbreak. However, early forecasts are generally unreliable as little information is available in the first few incidence data points. Here, we show how past Aedes-transmitted epidemics help improve these predictions. The approach was applied to the 2015-2017 Zika virus epidemics in three islands of the French West Indies, with historical data including other Aedes-transmitted diseases (chikungunya and Zika) in the same and other locations. Hierarchical models were used to build informative a priori distributions on the reproduction ratio and the reporting rates. The accuracy and sharpness of forecasts improved substantially when these a priori distributions were used in models for prediction. For example, early forecasts of final epidemic size obtained without historical information were 3.3 times too high on average (range: 0.2 to 5.8) with respect to the eventual size, but were far closer (1.1 times the real value on average, range: 0.4 to 1.5) using information on past CHIKV epidemics in the same places. Likewise, the 97.5% upper bound for maximal incidence was 15.3 times (range: 2.0 to 63.1) the actual peak incidence, and became much sharper at 2.4 times (range: 1.3 to 3.9) the actual peak incidence with informative a priori distributions. Improvements were more limited for the date of peak incidence and the total duration of the epidemic. The framework can adapt to all forecasting models at the early stages of emerging Aedes-transmitted outbreaks.

A simple approach to measure transmissibility and forecast incidence

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Our simple approach relies on very few parameters and minimal assumptions

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Subjective choice of best training period improved forecasts

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Despites its simplicity, our model forecasted well under a range scenarios.

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This approach can be a natural 'null model' for comparison with methods.

Outbreaks of novel pathogens such as SARS, pandemic influenza and Ebola require substantial investments in reactive interventions, with consequent implementation plans sometimes revised on a weekly basis. Therefore, short-term forecasts of incidence are often of high priority. In light of the recent Ebola epidemic in West Africa, a forecasting exercise was convened by a network of infectious disease modellers. The challenge was to forecast unseen “future” simulated data for four different scenarios at five different time points. In a similar method to that used during the recent Ebola epidemic, we estimated current levels of transmissibility, over variable time-windows chosen in an ad hoc way. Current estimated transmissibility was then used to forecast near-future incidence. We performed well within the challenge and often produced accurate forecasts. A retrospective analysis showed that our subjective method for deciding on the window of time with which to estimate transmissibility often resulted in the optimal choice. However, when near-future trends deviated substantially from exponential patterns, the accuracy of our forecasts was reduced. This exercise highlights the urgent need for infectious disease modellers to develop more robust descriptions of processes – other than the widespread depletion of susceptible individuals – that produce non-exponential patterns of incidence.

How social structures, space, and behaviors shape the spread of infectious diseases using chikungunya as a case study

Whether an individual becomes infected in an infectious disease outbreak depends on many interconnected risk factors, which may relate to characteristics of the individual (e.g., age, sex), his or her close relatives (e.g., household members), or the wider community. Studies monitoring individuals in households or schools have helped elucidate the determinants of transmission in small social structures due to advances in statistical modeling; but such an approach has so far largely failed to consider individuals in the wider context they live in. Here, we used an outbreak of chikungunya in a rural community in Bangladesh as a case study to obtain a more comprehensive characterization of risk factors in disease spread. We developed Bayesian data augmentation approaches to account for uncertainty in the source of infection, recall uncertainty, and unobserved infection dates. We found that the probability of chikungunya transmission was 12% [95% credible interval (CI): 8-17%] between household members but dropped to 0.3% for those living 50 m away (95% CI: 0.2-0.5%). Overall, the mean transmission distance was 95 m (95% CI: 77-113 m). Females were 1.5 times more likely to become infected than males (95% CI: 1.2-1.8), which was virtually identical to the relative risk of being at home estimated from an independent human movement study in the country. Reported daily use of antimosquito coils had no detectable impact on transmission. This study shows how the complex interplay between the characteristics of an individual and his or her close and wider environment contributes to the shaping of infectious disease epidemics.

Unraveling the drivers of MERS-CoV transmission

With more than 1,700 laboratory-confirmed infections, Middle East respiratory syndrome coronavirus (MERS-CoV) remains a significant threat for public health. However, the lack of detailed data on modes of transmission from the animal reservoir and between humans means that the drivers of MERS-CoV epidemics remain poorly characterized. Here, we develop a statistical framework to provide a comprehensive analysis of the transmission patterns underlying the 681 MERS-CoV cases detected in the Kingdom of Saudi Arabia (KSA) between January 2013 and July 2014. We assess how infections from the animal reservoir, the different levels of mixing, and heterogeneities in transmission have contributed to the buildup of MERS-CoV epidemics in KSA. We estimate that 12% [95% credible interval (CI): 9%, 15%] of cases were infected from the reservoir, the rest via human-to-human transmission in clusters (60%; CI: 57%, 63%), within (23%; CI: 20%, 27%), or between (5%; CI: 2%, 8%) regions. The reproduction number at the start of a cluster was 0.45 (CI: 0.33, 0.58) on average, but with large SD (0.53; CI: 0.35, 0.78). It was >1 in 12% (CI: 6%, 18%) of clusters but fell by approximately one-half (47% CI: 34%, 63%) its original value after 10 cases on average. The ongoing exposure of humans to MERS-CoV from the reservoir is of major concern, given the continued risk of substantial outbreaks in health care systems. The approach we present allows the study of infectious disease transmission when data linking cases to each other remain limited and uncertain.

Local and regional spread of chikungunya fever in the Americas

Chikungunya fever (CHIKV), a viral disease transmitted by mosquitoes, is currently affecting several areas in the Caribbean. The vector is found in the Americas from southern Florida to Brazil, and the Caribbean is a highly connected region in terms of population movements. There is therefore a significant risk for the epidemic to quickly expand to a wide area in the Americas. Here, we describe the spread of CHIKV in the first three areas to report cases and between areas in the region. Local transmission of CHIKV in the Caribbean is very effective, the mean number of cases generated by a human case ranging from two to four. There is a strong spatial signature in the regional epidemic, with the risk of transmission between areas estimated to be inversely proportional to the distance rather than driven by air transportation. So far, this simple distance-based model has successfully predicted observed patterns of spread. The spatial structure allows ranking areas according to their risk of invasion. This characterisation may help national and international agencies to optimise resource allocation for monitoring and control and encourage areas with elevated risks to act.

Bayesian reconstruction of disease outbreaks by combining epidemiologic and genomic data

Recent years have seen progress in the development of statistically rigorous frameworks to infer outbreak transmission trees ("who infected whom") from epidemiological and genetic data. Making use of pathogen genome sequences in such analyses remains a challenge, however, with a variety of heuristic approaches having been explored to date. We introduce a statistical method exploiting both pathogen sequences and collection dates to unravel the dynamics of densely sampled outbreaks. Our approach identifies likely transmission events and infers dates of infections, unobserved cases and separate introductions of the disease. It also proves useful for inferring numbers of secondary infections and identifying heterogeneous infectivity and super-spreaders. After testing our approach using simulations, we illustrate the method with the analysis of the beginning of the 2003 Singaporean outbreak of Severe Acute Respiratory Syndrome (SARS), providing new insights into the early stage of this epidemic. Our approach is the first tool for disease outbreak reconstruction from genetic data widely available as free software, the R package outbreaker. It is applicable to various densely sampled epidemics, and improves previous approaches by detecting unobserved and imported cases, as well as allowing multiple introductions of the pathogen. Because of its generality, we believe this method will become a tool of choice for the analysis of densely sampled disease outbreaks, and will form a rigorous framework for subsequent methodological developments.

Linking time-varying symptomatology and intensity of infectiousness to patterns of norovirus transmission

BACKGROUND

Norovirus (NoV) transmission may be impacted by changes in symptom intensity. Sudden onset of vomiting, which may cause an initial period of hyper-infectiousness, often marks the beginning of symptoms. This is often followed by: a 1-3 day period of milder symptoms, environmental contamination following vomiting, and post-symptomatic shedding that may result in transmission at progressively lower rates. Existing models have not included time-varying infectiousness, though representing these features could add utility to models of NoV transmission.

METHODS

We address this by comparing the fit of three models (Models 1-3) of NoV infection to household transmission data from a 2009 point-source outbreak of GII.12 norovirus in North Carolina. Model 1 is an SEIR compartmental model, modified to allow Gamma-distributed sojourn times in the latent and infectious classes, where symptomatic cases are uniformly infectious over time. Model 2 assumes infectiousness decays exponentially as a function of time since onset, while Model 3 is discontinuous, with a spike concentrating 50% of transmissibility at onset. We use Bayesian data augmentation techniques to estimate transmission parameters for each model, and compare their goodness of fit using qualitative and quantitative model comparison. We also assess the robustness of our findings to asymptomatic infections.

RESULTS

We find that Model 3 (initial spike in shedding) best explains the household transmission data, using both quantitative and qualitative model comparisons. We also show that these results are robust to the presence of asymptomatic infections.

CONCLUSIONS

Explicitly representing explosive NoV infectiousness at onset should be considered when developing models and interventions to interrupt and prevent outbreaks of norovirus in the community. The methods presented here are generally applicable to the transmission of pathogens that exhibit large variation in transmissibility over an infection.

Methods to infer transmission risk factors in complex outbreak data

Data collected during outbreaks are essential to better understand infectious disease transmission and design effective control strategies. But analysis of such data is challenging owing to the dependency between observations that is typically observed in an outbreak and to missing data. In this paper, we discuss strategies to tackle some of the ongoing challenges in the analysis of outbreak data. We present a relatively generic statistical model for the estimation of transmission risk factors, and discuss algorithms to estimate its parameters for different levels of missing data. We look at the problem of computational times for relatively large datasets and show how they can be reduced by appropriate use of discretization, sufficient statistics and some simple assumptions on the natural history of the disease. We also discuss approaches to integrate parametric model fitting and tree reconstruction methods in coherent statistical analyses. The methods are tested on both real and simulated datasets of large outbreaks in structured populations.

Role of social networks in shaping disease transmission during a community outbreak of 2009 H1N1 pandemic influenza

Evaluating the impact of different social networks on the spread of respiratory diseases has been limited by a lack of detailed data on transmission outside the household setting as well as appropriate statistical methods. Here, from data collected during a H1N1 pandemic (pdm) influenza outbreak that started in an elementary school and spread in a semirural community in Pennsylvania, we quantify how transmission of influenza is affected by social networks. We set up a transmission model for which parameters are estimated from the data via Markov chain Monte Carlo sampling. Sitting next to a case or being the playmate of a case did not significantly increase the risk of infection; but the structuring of the school into classes and grades strongly affected spread. There was evidence that boys were more likely to transmit influenza to other boys than to girls (and vice versa), which mimicked the observed assortative mixing among playmates. We also investigated the presence of abnormally high transmission occurring on specific days of the outbreak. Late closure of the school (i.e., when 27% of students already had symptoms) had no significant impact on spread. School-aged individuals (6-18 y) facilitated the introduction and spread of influenza in households, but only about one in five cases aged >18 y was infected by a school-aged household member. This analysis shows the extent to which clearly defined social networks affect influenza transmission, revealing strong between-place interactions with back-and-forth waves of transmission between the school, the community, and the household.

Epidemiological inference for partially observed epidemics: the example of the 2001 foot and mouth epidemic in Great Britain

This paper develops a statistical framework for a retrospective analysis for well-observed livestock epidemics during which intervention policies may conceal cases, thus potentially biasing naively derived parameter and final size estimates. We apply the methods to the 2001 foot and mouth epidemic (FMD) in Great Britain, during which a large number of farms (about 7500) were pre-emptively culled as part of the control effort without ever being diagnosed as being infected. We infer farm-level infectivity and susceptibility parameters, a distribution for the delay from infection to report, together with a time varying farm infectivity profile for farms. Hidden infections among proactively culled farms were accounted for using a data augmentation approach utilising reversible jump MCMC methods. Simulated epidemics derived using the parameter estimates obtained reproduced the 2001 epidemic well. Our analysis demonstrates that time-varying infectivity profiles fit the 2001 data better than naive assumptions of constant infectiousness. We estimate that around 210 (or 2.8%) of the farms proactively culled in the 2001 epidemic were infected. However, for the parameter estimated obtained, preliminary simulation results indicate that had contiguous culling not been applied in 2001, the epidemic might have been substantially larger.

Likelihood-based estimation of continuous-time epidemic models from time-series data: application to measles transmission in London

We present a new statistical approach to analyse epidemic time-series data. A major difficulty for inference is that (i) the latent transmission process is partially observed and (ii) observed quantities are further aggregated temporally. We develop a data augmentation strategy to tackle these problems and introduce a diffusion process that mimics the susceptible-infectious-removed (SIR) epidemic process, but that is more tractable analytically. While methods based on discrete-time models require epidemic and data collection processes to have similar time scales, our approach, based on a continuous-time model, is free of such constraint. Using simulated data, we found that all parameters of the SIR model, including the generation time, were estimated accurately if the observation interval was less than 2.5 times the generation time of the disease. Previous discrete-time TSIR models have been unable to estimate generation times, given that they assume the generation time is equal to the observation interval. However, we were unable to estimate the generation time of measles accurately from historical data. This indicates that simple models assuming homogenous mixing (even with age structure) of the type which are standard in mathematical epidemiology miss key features of epidemics in large populations.

Practical identifiability of HIV dynamics models

We study the practical identifiability of parameters, i.e., the accuracy of the estimation that can be hoped, in a model of HIV dynamics based on a system of non-linear Ordinary Differential Equations (ODE). This depends on the available information such as the schedule of the measurements, the observed components, and the measurement precision. The number of patients is another way to increase it by introducing an appropriate statistical "population" framework. The impact of each improvement of the experimental condition is not known in advance but it can be evaluated via the Fisher Information Matrix (FIM). If the non-linearity of the biological model, as well as the complex statistical framework makes computation of the FIM challenging, we show that the particular structure of these models enables to compute it as precisely as wanted. In the HIV model, measuring HIV viral load and total CD4+ count were not enough to achieve identifiability of all the parameters involved. However, we show that an appropriate statistical approach together with the availability of additional markers such as infected cells or activated cells should considerably improve the identifiability and thus the usefulness of dynamical models of HIV.

Estimating in real time the efficacy of measures to control emerging communicable diseases

Controlling an emerging communicable disease requires prompt adoption of measures such as quarantine. Assessment of the efficacy of these measures must be rapid as well. In this paper, the authors present a framework to monitor the efficacy of control measures in real time. Bayesian estimation of the reproduction number R (mean number of cases generated by a single infectious person) during an outbreak allows them to judge rapidly whether the epidemic is under control (R < 1). Only counts and time of onset of symptoms, plus tracing information from a subset of cases, are required. Markov chain Monte Carlo and Monte Carlo sampling are used to infer the temporal pattern of R up to the last observation. The operating characteristics of the method are investigated in a simulation study of severe acute respiratory syndrome-like outbreaks. In this particular setting, control measures lacking efficacy (R > or = 1.1) could be detected after 2 weeks in at least 70% of the epidemics, with less than a 5% probability of a wrong conclusion. When control measures are efficacious (R = 0.5), this situation may be evidenced in 68% of the epidemics after 2 weeks and 92% of the epidemics after 3 weeks, with less than a 5% probability of a wrong conclusion.