The impact of alcohol and illicit substance use on the pharmacokinetics of first-line TB drugs.

BACKGROUND: In South Africa, an estimated 11% of the population have high alcohol use, a major risk factor for TB. Alcohol and other substance use are also associated with poor treatment response, with a potential mechanism being altered TB drug pharmacokinetics. OBJECTIVES: To investigate the impact of alcohol and illicit substance use on the pharmacokinetics of first-line TB drugs in participants with pulmonary TB. METHODS: We prospectively enrolled participants ≥15 years old, without HIV, and initiating drug-susceptible TB treatment in Worcester, South Africa. Alcohol use was measured via self-report and blood biomarkers. Other illicit substances were captured through a urine drug test. Plasma samples were drawn 1 month into treatment pre-dose, and 1.5, 3, 5 and 8 h post-dose. Non-linear mixed-effects modelling was used to describe the pharmacokinetics of rifampicin, isoniazid, pyrazinamide and ethambutol. Alcohol and drug use were tested as covariates. RESULTS: The study included 104 participants, of whom 70% were male, with a median age of 37 years (IQR 27-48). Alcohol use was high, with 42% and 28% of participants having moderate and high alcohol use, respectively. Rifampicin and isoniazid had slightly lower pharmacokinetics compared with previous reports, whereas pyrazinamide and ethambutol were consistent. No significant alcohol use effect was detected, other than 13% higher ethambutol clearance in participants with high alcohol use. Methaqualone use reduced rifampicin bioavailability by 19%. CONCLUSION: No clinically relevant effect of alcohol use was observed on the pharmacokinetics of first-line TB drugs, suggesting that poor treatment outcome is unlikely due to pharmacokinetic alterations. That methaqualone reduced rifampicin means dose adjustment may be beneficial.

Test characteristics for combining non-invasive liver fibrosis staging modalities in individuals with Hepatitis C virus.

Non-invasive methods have largely replaced biopsy to identify advanced fibrosis in hepatitis C virus (HCV). Guidelines vary regarding testing strategy to balance accuracy, costs and loss to follow-up. Although individual test characteristics are well-described, data comparing the accuracy of using two tests together are limited. We calculated combined test characteristics to determine the utility of combined strategies. This study synthesizes empirical data from fibrosis staging trials and the literature to estimate test characteristics for Fibrosis-4 (FIB4), APRI or a commercial serum panel (FibroSure®), followed by transient elastography (TE) or FibroSure®. We simulated two testing strategies: (1) second test only for those with intermediate first test results (staged approach), and (2) second test for all. We summarized empiric data with multinomial distributions and used this to estimate test characteristics of each strategy on a simulated population of 10,000 individuals with 4.2% cirrhosis prevalence. Negative predictive value (NPV) for cirrhosis from a single test ranged from 98.2% (95% CB 97.6-98.8%) for FIB-4 to 99.4% (95% CB 99.0-99.8%) for TE. Using a staged approach with TE second, sensitivity for cirrhosis rose to 93.3-96.9%, NPV to 99.7-99.8%, while PPV dropped to <32%. Using TE as a second test for all minimally changed estimated test characteristics compared with the staged approach. Combining two non-invasive fibrosis tests barely improves NPV and decreases or does not change PPV compared with a single test, challenging the utility of serial testing modalities. These calculated combined test characteristics can inform best methods to identify advanced fibrosis in various populations.

Looking under the lamp-post: quantifying the performance of contact tracing in the United States during the SARS-CoV-2 pandemic.

Contact tracing forms a crucial part of the public-health toolbox in mitigating and understanding emergent pathogens and nascent disease outbreaks. Contact tracing in the United States was conducted during the pre-Omicron phase of the ongoing COVID-19 pandemic. This tracing relied on voluntary reporting and responses, often using rapid antigen tests due to lack of accessibility to PCR tests. These limitations, combined with SARS-CoV-2's propensity for asymptomatic transmission, raise the question "how reliable was contact tracing for COVID-19 in the United States"? We answered this question using a Markov model to examine the efficiency with which transmission could be detected based on the design and response rates of contact tracing studies in the United States. Our results suggest that contact tracing protocols in the U.S. are unlikely to have identified more than 1.65% (95% uncertainty interval: 1.62-1.68%) of transmission events with PCR testing and 1.00% (95% uncertainty interval 0.98-1.02%) with rapid antigen testing. When considering a more robust contact tracing scenario, based on compliance rates in East Asia with PCR testing, this increases to 62.7% (95% uncertainty interval: 62.6-62.8%). We did not assume presence of asymptomatic transmission or superspreading, making our estimates upper bounds on the actual percentages traced. These findings highlight the limitations in interpretability for studies of SARS-CoV-2 disease spread based on U.S. contact tracing and underscore the vulnerability of the population to future disease outbreaks, for SARS-CoV-2 and other pathogens.

Contribution of Reinfection to Annual Rate of Tuberculosis Infection (ARI) and Incidence of Tuberculosis Disease.

BACKGROUND: Modeling studies have concluded that 60-80% of tuberculosis (TB) infections result from reinfection of previously infected persons. The annual rate of infection (ARI), a standard measure of the risk of TB infection in a community, may not accurately reflect the true risk of infection among previously infected persons. We constructed a model of infection and reinfection with Mycobacterium tuberculosis to explore the predictive accuracy of ARI and its effect on disease incidence. METHODS: We created a deterministic simulation of the progression from TB infection to disease and simulated the prevalence of TB infection at the beginning and end of a theoretical year of infection. We considered 10 disease prevalence scenarios ranging from 100/100 000 to 1000/100 000 in simulations where TB exposure probability was homogeneous across the whole simulated population or heterogeneously stratified into high-risk and low-risk groups. ARI values, rates of progression from infection to disease, and the effect of multiple reinfections were obtained from published studies. RESULTS: With homogeneous exposure risk, observed ARI values produced expected numbers of infections. However, when heterogeneous risk was introduced, observed ARI was seen to underestimate true ARI by 25-58%. Of the cases of TB disease that occurred, 36% were among previously infected persons when prevalence was 100/100 000, increasing to 79% of cases when prevalence was 1000/100 000. CONCLUSIONS: Measured ARI underestimates true ARI as a result of heterogeneous population mixing. The true force of infection in a community may be greater than previously appreciated. Hyperendemic communities likely contribute disproportionally to the global TB disease burden.

Early Introduction and Rise of the Omicron Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) Variant in Highly Vaccinated University Populations.

BACKGROUND: The Omicron variant of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is highly transmissible in vaccinated and unvaccinated populations. The dynamics that govern its establishment and propensity toward fixation (reaching 100% frequency in the SARS-CoV-2 population) in communities remain unknown. Here, we describe the dynamics of Omicron at 3 institutions of higher education (IHEs) in the greater Boston area. METHODS: We use diagnostic and variant-specifying molecular assays and epidemiological analytical approaches to describe the rapid dominance of Omicron following its introduction into 3 IHEs with asymptomatic surveillance programs. RESULTS: We show that the establishment of Omicron at IHEs precedes that of the state and region and that the time to fixation is shorter at IHEs (9.5-12.5 days) than in the state (14.8 days) or region. We show that the trajectory of Omicron fixation among university employees resembles that of students, with a 2- to 3-day delay. Finally, we compare cycle threshold values in Omicron vs Delta variant cases on college campuses and identify lower viral loads among college affiliates who harbor Omicron infections. CONCLUSIONS: We document the rapid takeover of the Omicron variant at IHEs, reaching near-fixation within the span of 9.5-12.5 days despite lower viral loads, on average, than the previously dominant Delta variant. These findings highlight the transmissibility of Omicron, its propensity to rapidly dominate small populations, and the ability of robust asymptomatic surveillance programs to offer early insights into the dynamics of pathogen arrival and spread.

Aspirin and nonaspirin nonsteroidal antiinflammatory drug use and occurrence of colorectal adenoma in Black American women.

Evidence suggests that aspirin use reduces the occurrence of colorectal neoplasia. Few studies have investigated the association among Black Americans, who are disproportionately burdened by the disease. We assessed aspirin use in relation to colorectal adenoma among Black women. The Black Women's Health Study is a prospective cohort of self-identified Black American women established in 1995. Participants reported regular aspirin use on baseline and follow-up questionnaires. Beginning in 1999, participants reported undergoing a colonoscopy or sigmoidoscopy, the only procedures through which colorectal adenomas can be diagnosed. Multivariable logistic regression was used to estimate odds ratios (OR) and 95% confidence intervals (CI) for associations between aspirin use and colorectal adenoma among 34 397 women who reported at least 1 colonoscopy or sigmoidoscopy. From 1997 through 2018, 1913 women were diagnosed with an adenoma. Compared to nonaspirin users, regular users had 14% (OR = 0.86, 95% CI: 0.78-0.95) lower odds of adenoma. The odds of adenoma decreased with increasing duration of aspirin use (≥10 years: OR = 0.80, 95% CI: 0.66-0.96). Initiating aspirin at a younger age was associated with a reduced adenoma occurrence (age < 40 years at initiation: OR = 0.69, 95% CI: 0.55-0.86). Regular aspirin use was associated with a decreased odds of colorectal adenoma in our study of Black women. These findings support evidence demonstrating a chemopreventive impact of aspirin on colorectal neoplasia and suggest that aspirin may be a useful prevention strategy among US Black women.

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.

Massachusetts Prevalence of Opioid Use Disorder Estimation Revisited: Comparing a Bayesian Approach to Standard Capture-Recapture Methods.

BACKGROUND: The National Survey on Drug Use and Health (NSDUH) estimated the prevalence of opioid use disorder (OUD) among the civilian, noninstitutionalized people aged 12 years or older in Massachusetts as 1.2% between 2015 and 2017. Accurate estimation of the prevalence of OUD is critical to the success of treatment and resource planning. Various indirect estimation approaches have been used but are subject to data availability and infrastructure-related issues. METHODS: We used 2015 data from the Massachusetts Public Health Data Warehouse (PHD) to compare the results of two approaches to estimating OUD prevalence in the Massachusetts population. First, we used a seven-dataset capture-recapture analysis under log-linear model parameterization, controlling for the source dependence and effects of age, sex, and county through stratification. Second, we applied a benchmark-multiplier method in a Bayesian framework by linking health care claims data to death certificate data assuming an extrapolation of death rates from observed untreated OUD to unobserved OUD. RESULTS: Our estimates for OUD prevalence among Massachusetts residents (aged 18-64 years) were 4.62% (95% CI = 4.59%, 4.64%) in the capture-recapture approach and 4.29% (95% CrI = 3.49%, 5.32%) in the Bayesian model. Both estimates were approximately four times higher than NSDUH estimates. CONCLUSION: The synthesis of our findings suggests that the disease surveillance system misses a large portion of the population with OUD. Our study also suggests that concurrent use of multiple methods improves the justification and facilitates the triangulation and interpretation of the resulting estimates. TRIAL REGISTRATION: ClinicalTrials.gov Identifier: NCT04111939.

Estimation of heterogeneous instantaneous reproduction numbers with application to characterize SARS-CoV-2 transmission in Massachusetts counties.

The reproductive number is an important metric that has been widely used to quantify the infectiousness of communicable diseases. The time-varying instantaneous reproductive number is useful for monitoring the real-time dynamics of a disease to inform policy making for disease control. Local estimation of this metric, for instance at a county or city level, allows for more targeted interventions to curb transmission. However, simultaneous estimation of local reproductive numbers must account for potential sources of heterogeneity in these time-varying quantities-a key element of which is human mobility. We develop a statistical method that incorporates human mobility between multiple regions for estimating region-specific instantaneous reproductive numbers. The model also can account for exogenous cases imported from outside of the regions of interest. We propose two approaches to estimate the reproductive numbers, with mobility data used to adjust incidence in the first approach and to inform a formal priori distribution in the second (Bayesian) approach. Through a simulation study, we show that region-specific reproductive numbers can be well estimated if human mobility is reasonably well approximated by available data. We use this approach to estimate the instantaneous reproductive numbers of COVID-19 for 14 counties in Massachusetts using CDC case report data and the human mobility data collected by SafeGraph. We found that, accounting for mobility, our method produces estimates of reproductive numbers that are distinct across counties. In contrast, independent estimation of county-level reproductive numbers tends to produce similar values, as trends in county case-counts for the state are fairly concordant. These approaches can also be used to estimate any heterogeneity in transmission, for instance, age-dependent instantaneous reproductive number estimates. As people are more mobile and interact frequently in ways that permit transmission, it is important to account for this in the estimation of the reproductive number.

Projected Long-Term Impact of the Coronavirus Disease 2019 (COVID-19) Pandemic on Hepatitis C Outcomes in the United States: A Modeling Study.

BACKGROUND: The coronavirus disease 2019 (COVID-19) pandemic disrupted access to and uptake of hepatitis C virus (HCV) care services in the United States. It is unknown how substantially the pandemic will impact long-term HCV-related outcomes. METHODS: We used a microsimulation to estimate the 10-year impact of COVID-19 disruptions in healthcare delivery on HCV outcomes including identified infections, linkage to care, treatment initiation and completion, cirrhosis, and liver-related death. We modeled hypothetical scenarios consisting of an 18-month pandemic-related disruption in HCV care starting in March 2020 followed by varying returns to pre-pandemic rates of screening, linkage, and treatment through March 2030 and compared them to a counterfactual scenario in which there was no COVID-19 pandemic or disruptions in care. We also performed alternate scenario analyses in which the pandemic disruption lasted for 12 and 24 months. RESULTS: Compared to the "no pandemic" scenario, in the scenario in which there is no return to pre-pandemic levels of HCV care delivery, we estimate 1060 fewer identified cases, 21 additional cases of cirrhosis, and 16 additional liver-related deaths per 100 000 people. Only 3% of identified cases initiate treatment and <1% achieve sustained virologic response (SVR). Compared to "no pandemic," the best-case scenario in which an 18-month care disruption is followed by a return to pre-pandemic levels, we estimated a smaller proportion of infections identified and achieving SVR. CONCLUSIONS: A recommitment to the HCV epidemic in the United States that involves additional resources coupled with aggressive efforts to screen, link, and treat people with HCV is needed to overcome the COVID-19-related disruptions.

What Can Genetic Relatedness Tell Us About Risk Factors for Tuberculosis Transmission?

BACKGROUND: To stop tuberculosis (TB), the leading infectious cause of death globally, we need to better understand transmission risk factors. Although many studies have identified associations between individual-level covariates and pathogen genetic relatedness, few have identified characteristics of transmission pairs or explored how closely covariates associated with genetic relatedness mirror those associated with transmission. METHODS: We simulated a TB-like outbreak with pathogen genetic data and estimated odds ratios (ORs) to correlate each covariate and genetic relatedness. We used a naive Bayes approach to modify the genetic links and nonlinks to resemble the true links and nonlinks more closely and estimated modified ORs with this approach. We compared these two sets of ORs with the true ORs for transmission. Finally, we applied this method to TB data in Hamburg, Germany, and Massachusetts, USA, to find pair-level covariates associated with transmission. RESULTS: Using simulations, we found that associations between covariates and genetic relatedness had the same relative magnitudes and directions as the true associations with transmission, but biased absolute magnitudes. Modifying the genetic links and nonlinks reduced the bias and increased the confidence interval widths, more accurately capturing error. In Hamburg and Massachusetts, pairs were more likely to be probable transmission links if they lived in closer proximity, had a shorter time between observations, or had shared ethnicity, social risk factors, drug resistance, or genotypes. CONCLUSIONS: We developed a method to improve the use of genetic relatedness as a proxy for transmission, and aid in understanding TB transmission dynamics in low-burden settings.

Variation in Initiation, Engagement, and Retention on Medications for Opioid Use Disorder Based on Health Insurance Plan Design.

BACKGROUND: The association between cost-sharing and receipt of medication for opioid use disorder (MOUD) is unknown. METHODS: We constructed a cohort of 10,513 commercially insured individuals with a new diagnosis of opioid use disorder and information on insurance cost-sharing in a large national deidentified claims database. We examined 4 cost-sharing measures: (1) pharmacy deductible; (2) medical service deductible; (3) pharmacy medication copay; and (4) medical office copay. We measured MOUD (naltrexone, buprenorphine, or methadone) initiation (within 14 d of diagnosis), engagement (second receipt within 34 d of first), and 6-month retention (continuous receipt without 14-d gap). We used multivariable logistic regression to assess the association between cost-sharing and MOUD initiation, engagement, and retention. We calculated total out-of-pocket costs in the 30 days following MOUD initiation for each type of MOUD. RESULTS: Of 10,513 individuals with incident opioid use disorder, 1202 (11%) initiated MOUD, 742 (7%) engaged, and 253 (2%) were retained in MOUD at 6 months. A high ($1000+) medical deductible was associated with a lower odds of initiation compared with no deductible (odds ratio: 0.85, 95% confidence interval: 0.74-0.98). We found no significant associations between other cost-sharing measures for initiation, engagement, or retention. Median initial 30-day out-of-pocket costs ranged from $100 for methadone to $710 for extended-release naltrexone. CONCLUSIONS: Among insurance plan cost-sharing measures, only medical services deductible showed an association with decreased MOUD initiation. Policy and benefit design should consider ways to reduce cost barriers to initiation and retention in MOUD.

Projecting Quarantine Utilization During a Pandemic.

Objectives. To develop an approach to project quarantine needs during an outbreak, particularly for communally housed individuals who interact with outside individuals. Methods. We developed a method that uses basic surveillance data to do short-term projections of future quarantine needs. The development of this method was rigorous, but it is conceptually simple and easy to implement and allows one to anticipate potential superspreading events. We demonstrate how this method can be used with data from the fall 2020 semester of a large urban university in Boston, Massachusetts, that provided quarantine housing for students living on campus in response to the COVID-19 pandemic. Our approach accounted for potentially infectious interactions between individuals living in university housing and those who did not. Results. Our approach was able to accurately project 10-day-ahead quarantine utilization for on-campus students in a large urban university. Our projections were most accurate when we anticipated weekend superspreading events around holidays. Conclusions. We provide an easy-to-use software tool to project quarantine utilization for institutions that can account for mixing with outside populations. This software tool has potential application for universities, corrections facilities, and the military. (Am J Public Health. 2022;112(2):277-283. https://doi.org/10.2105/AJPH.2021.306573).

Bayesian back-calculation and nowcasting for line list data during the COVID-19 pandemic.

Surveillance is critical to mounting an appropriate and effective response to pandemics. However, aggregated case report data suffers from reporting delays and can lead to misleading inferences. Different from aggregated case report data, line list data is a table contains individual features such as dates of symptom onset and reporting for each reported case and a good source for modeling delays. Current methods for modeling reporting delays are not particularly appropriate for line list data, which typically has missing symptom onset dates that are non-ignorable for modeling reporting delays. In this paper, we develop a Bayesian approach that dynamically integrates imputation and estimation for line list data. Specifically, this Bayesian approach can accurately estimate the epidemic curve and instantaneous reproduction numbers, even with most symptom onset dates missing. The Bayesian approach is also robust to deviations from model assumptions, such as changes in the reporting delay distribution or incorrect specification of the maximum reporting delay. We apply the Bayesian approach to COVID-19 line list data in Massachusetts and find the reproduction number estimates correspond more closely to the control measures than the estimates based on the reported curve.

Correction: Practical considerations for measuring the effective reproductive number, Rt.

[This corrects the article DOI: 10.1371/journal.pcbi.1008409.].

Methods for handling missing data in serially sampled sputum specimens for mycobacterial culture conversion calculation.

BACKGROUND: The occurrence and timing of mycobacterial culture conversion is used as a proxy for tuberculosis treatment response. When researchers serially sample sputum during tuberculosis studies, contamination or missed visits leads to missing data points. Traditionally, this is managed by ignoring missing data or simple carry-forward techniques. Statistically advanced multiple imputation methods potentially decrease bias and retain sample size and statistical power. METHODS: We analyzed data from 261 participants who provided weekly sputa for the first 12 weeks of tuberculosis treatment. We compared methods for handling missing data points in a longitudinal study with a time-to-event outcome. Our primary outcome was time to culture conversion, defined as two consecutive weeks with no Mycobacterium tuberculosis growth. Methods used to address missing data included: 1) available case analysis, 2) last observation carried forward, and 3) multiple imputation by fully conditional specification. For each method, we calculated the proportion culture converted and used survival analysis to estimate Kaplan-Meier curves, hazard ratios, and restricted mean survival times. We compared methods based on point estimates, confidence intervals, and conclusions to specific research questions. RESULTS: The three missing data methods lead to differences in the number of participants achieving conversion; 78 (32.8%) participants converted with available case analysis, 154 (64.7%) converted with last observation carried forward, and 184 (77.1%) converted with multiple imputation. Multiple imputation resulted in smaller point estimates than simple approaches with narrower confidence intervals. The adjusted hazard ratio for smear negative participants was 3.4 (95% CI 2.3, 5.1) using multiple imputation compared to 5.2 (95% CI 3.1, 8.7) using last observation carried forward and 5.0 (95% CI 2.4, 10.6) using available case analysis. CONCLUSION: We showed that accounting for missing sputum data through multiple imputation, a statistically valid approach under certain conditions, can lead to different conclusions than naïve methods. Careful consideration for how to handle missing data must be taken and be pre-specified prior to analysis. We used data from a TB study to demonstrate these concepts, however, the methods we described are broadly applicable to longitudinal missing data. We provide valuable statistical guidance and code for researchers to appropriately handle missing data in longitudinal studies.

Estimation of local time-varying reproduction numbers in noisy surveillance data.

A valuable metric in understanding local infectious disease dynamics is the local time-varying reproduction number, i.e. the expected number of secondary local cases caused by each infected individual. Accurate estimation of this quantity requires distinguishing cases arising from local transmission from those imported from elsewhere. Realistically, we can expect identification of cases as local or imported to be imperfect. We study the propagation of such errors in estimation of the local time-varying reproduction number. In addition, we propose a Bayesian framework for estimation of the true local time-varying reproduction number when identification errors exist. And we illustrate the practical performance of our estimator through simulation studies and with outbreaks of COVID-19 in Hong Kong and Victoria, Australia. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Socioeconomic Disparities in Subway Use and COVID-19 Outcomes in New York City.

Using data from New York City from January 2020 to April 2020, we found an estimated 28-day lag between the onset of reduced subway use and the end of the exponential growth period of severe acute respiratory syndrome coronavirus 2 within New York City boroughs. We also conducted a cross-sectional analysis of the associations between human mobility (i.e., subway ridership) on the week of April 11, 2020, sociodemographic factors, and coronavirus disease 2019 (COVID-19) incidence as of April 26, 2020. Areas with lower median income, a greater percentage of individuals who identify as non-White and/or Hispanic/Latino, a greater percentage of essential workers, and a greater percentage of health-care essential workers had more mobility during the pandemic. When adjusted for the percentage of essential workers, these associations did not remain, suggesting essential work drives human movement in these areas. Increased mobility and all sociodemographic variables (except percentage of people older than 75 years old and percentage of health-care essential workers) were associated with a higher rate of COVID-19 cases per 100,000 people, when adjusted for testing effort. Our study demonstrates that the most socially disadvantaged not only are at an increased risk for COVID-19 infection, they lack the privilege to fully engage in social distancing interventions.

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.