The impact of prior information on estimates of disease transmissibility using Bayesian tools

Estimation of the generation interval using pairwise relative transmission probabilities

The generation interval (the time between infection of primary and secondary cases) and its often used proxy, the serial interval (the time between symptom onset of primary and secondary cases) are critical parameters in understanding infectious disease dynamics. Because it is difficult to determine who infected whom, these important outbreak characteristics are not well understood for many diseases. We present a novel method for estimating transmission intervals using surveillance or outbreak investigation data that, unlike existing methods, does not require a contact tracing data or pathogen whole genome sequence data on all cases. We start with an expectation maximization algorithm and incorporate relative transmission probabilities with noise reduction. We use simulations to show that our method can accurately estimate the generation interval distribution for diseases with different reproductive numbers, generation intervals, and mutation rates. We then apply our method to routinely collected surveillance data from Massachusetts (2010-2016) to estimate the serial interval of tuberculosis in this setting.

A Comparative Analysis of Statistical Methods to Estimate the Reproduction Number in Emerging Epidemics, With Implications for the Current Coronavirus Disease 2019 (COVID-19) Pandemic

BACKGROUND

As the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic continues its rapid global spread, quantification of local transmission patterns has been, and will continue to be, critical for guiding the pandemic response. Understanding the accuracy and limitations of statistical methods to estimate the basic reproduction number, R0, in the context of emerging epidemics is therefore vital to ensure appropriate interpretation of results and the subsequent implications for control efforts.

METHODS

Using simulated epidemic data, we assess the performance of 7 commonly used statistical methods to estimate R0 as they would be applied in a real-time outbreak analysis scenario: fitting to an increasing number of data points over time and with varying levels of random noise in the data. Method comparison was also conducted on empirical outbreak data, using Zika surveillance data from the 2015-2016 epidemic in Latin America and the Caribbean.

RESULTS

We find that most methods considered here frequently overestimate R0 in the early stages of epidemic growth on simulated data, the magnitude of which decreases when fitted to an increasing number of time points. This trend of decreasing bias over time can easily lead to incorrect conclusions about the course of the epidemic or the need for control efforts.

CONCLUSIONS

We show that true changes in pathogen transmissibility can be difficult to disentangle from changes in methodological accuracy and precision in the early stages of epidemic growth, particularly for data with significant over-dispersion. As localized epidemics of SARS-CoV-2 take hold around the globe, awareness of this trend will be important for appropriately cautious interpretation of results and subsequent guidance for control efforts.

Multi-population stochastic modeling of Ebola in Sierra Leone: Investigation of spatial heterogeneity

A major outbreak of the Ebola virus occurred in 2014 in Sierra Leone. We investigate the spatial heterogeneity of the outbreak among districts in Sierra Leone. The stochastic discrete-time susceptible-exposed-infectious-removed (SEIR) model is used, allowing for probabilistic movements from one compartment to another. Our model accounts for heterogeneity among districts by making use of a hierarchical approach. The transmission rates are considered time-varying. It is investigated whether or not incubation period, infectious period and transmission rates are different among districts. Estimation is done using the Bayesian formalism. The posterior estimates of the effective reproductive number were substantially different across the districts, with pronounced variability in districts with few cases of Ebola. The posterior estimates of the reproductive number at the district level varied between below 1.0 and 4.5, whereas at nationwide level it varied between below 1.0 and 2.5. The posterior estimate of the effective reproductive number reached a value below 1.0 around December. In some districts, the effective reproductive number pointed out for the persistence of the outbreak or for a likely resurgence of new cases of Ebola virus disease (EVD). The posterior estimates have shown to be highly sensitive to prior elicitation, mainly the incubation period and infectious period.

Statistical Estimation of the Reproductive Number From Case Notification Data

The reproductive number, or reproduction number, is a valuable metric in understanding infectious disease dynamics. There is a large body of literature related to its use and estimation. In the last 15 years, there has been tremendous progress in statistically estimating this number using case notification data. These approaches are appealing because they are relevant in an ongoing outbreak (e.g., for assessing the effectiveness of interventions) and do not require substantial modeling expertise to be implemented. In this article, we describe these methods and the extensions that have been developed. We provide insight into the distinct interpretations of the estimators proposed and provide real data examples to illustrate how they are implemented. Finally, we conclude with a discussion of available software and opportunities for future development.

Practical considerations for measuring the effective reproductive number, Rt

Estimation of the effective reproductive number Rt is important for detecting changes in disease transmission over time. During the Coronavirus Disease 2019 (COVID-19) pandemic, policy makers and public health officials are using Rt to assess the effectiveness of interventions and to inform policy. However, estimation of Rt from available data presents several challenges, with critical implications for the interpretation of the course of the pandemic. The purpose of this document is to summarize these challenges, illustrate them with examples from synthetic data, and, where possible, make recommendations. For near real-time estimation of Rt, we recommend the approach of Cori and colleagues, which uses data from before time t and empirical estimates of the distribution of time between infections. Methods that require data from after time t, such as Wallinga and Teunis, are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for retrospective analyses of how individuals infected at different time points contributed to the spread. We advise caution when using methods derived from the approach of Bettencourt and Ribeiro, as the resulting Rt estimates may be biased if the underlying structural assumptions are not met. Two key challenges common to all approaches are accurate specification of the generation interval and reconstruction of the time series of new infections from observations occurring long after the moment of transmission. Naive approaches for dealing with observation delays, such as subtracting delays sampled from a distribution, can introduce bias. We provide suggestions for how to mitigate this and other technical challenges and highlight open problems in Rt estimation.

CR, White LF. Using Cure Models to Estimate the Serial Interval of Tuberculosis With Limited Follow-up

Serial interval (SI), defined as the time between symptom onset in an infector and infectee pair, is commonly used to understand infectious diseases transmission. Slow progression to active disease, as well as the small percentage of individuals who will eventually develop active disease, complicate the estimation of the SI for tuberculosis (TB). In this paper, we showed via simulation studies that when there is credible information on the percentage of those who will develop TB disease following infection, a cure model, first introduced by Boag in 1949, should be used to estimate the SI for TB. This model includes a parameter in the likelihood function to account for the study population being composed of those who will have the event of interest and those who will never have the event. We estimated the SI for TB to be approximately 0.5 years for the United States and Canada (January 2002 to December 2006) and approximately 2.0 years for Brazil (March 2008 to June 2012), which might imply a higher occurrence of reinfection TB in a developing country like Brazil.

Practical considerations for measuring the effective reproductive number, R t

Estimation of the effective reproductive number, R t , is important for detecting changes in disease transmission over time. During the COVID-19 pandemic, policymakers and public health officials are using R t to assess the effectiveness of interventions and to inform policy. However, estimation of R t from available data presents several challenges, with critical implications for the interpretation of the course of the pandemic. The purpose of this document is to summarize these challenges, illustrate them with examples from synthetic data, and, where possible, make recommendations. For near real-time estimation of R t , we recommend the approach of Cori et al. (2013), which uses data from before time t and empirical estimates of the distribution of time between infections. Methods that require data from after time t, such as Wallinga and Teunis (2004), are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for retrospective analyses of how individuals infected at different time points contributed to spread. We advise against using methods derived from Bettencourt and Ribeiro (2008), as the resulting R t estimates may be biased if the underlying structural assumptions are not met. Two key challenges common to all approaches are accurate specification of the generation interval and reconstruction of the time series of new infections from observations occurring long after the moment of transmission. Naive approaches for dealing with observation delays, such as subtracting delays sampled from a distribution, can introduce bias. We provide suggestions for how to mitigate this and other technical challenges and highlight open problems in R t estimation.

Quantifying TB transmission: a systematic review of reproduction number and serial interval estimates for tuberculosis

Tuberculosis (TB) is the leading global infectious cause of death. Understanding TB transmission is critical to creating policies and monitoring the disease with the end goal of TB elimination. To our knowledge, there has been no systematic review of key transmission parameters for TB. We carried out a systematic review of the published literature to identify studies estimating either of the two key TB transmission parameters: the serial interval (SI) and the reproductive number. We identified five publications that estimated the SI and 56 publications that estimated the reproductive number. The SI estimates from four studies were: 0.57, 1.42, 1.44 and 1.65 years; the fifth paper presented age-specific estimates ranging from 20 to 30 years (for infants <1 year old) to <5 years (for adults). The reproductive number estimates ranged from 0.24 in the Netherlands (during 1933-2007) to 4.3 in China in 2012. We found a limited number of publications and many high TB burden settings were not represented. Certain features of TB dynamics, such as slow transmission, complicated parameter estimation, require novel methods. Additional efforts to estimate these parameters for TB are needed so that we can monitor and evaluate interventions designed to achieve TB elimination.

Estimating age-specific reproductive numbers-A comparison of methods

Large outbreaks, such as those caused by influenza, put a strain on resources necessary for their control. In particular, children have been shown to play a key role in influenza transmission during recent outbreaks, and targeted interventions, such as school closures, could positively impact the course of emerging epidemics. As an outbreak is unfolding, it is important to be able to estimate reproductive numbers that incorporate this heterogeneity and to use surveillance data that is routinely collected to more effectively target interventions and obtain an accurate understanding of transmission dynamics. There are a growing number of methods that estimate age-group specific reproductive numbers with limited data that build on methods assuming a homogenously mixing population. In this article, we introduce a new approach that is flexible and improves on many aspects of existing methods. We apply this method to influenza data from two outbreaks, the 2009 H1N1 outbreaks in South Africa and Japan, to estimate age-group specific reproductive numbers and compare it to three other methods that also use existing data from social mixing surveys to quantify contact rates among different age groups. In this exercise, all estimates of the reproductive numbers for children exceeded the critical threshold of one and in most cases exceeded those of adults. We introduce a flexible new method to estimate reproductive numbers that describe heterogeneity in the population.