Propensity Score in the Face of Interference: Discussion of.

Rosenbaum and Rubin's (1983) propensity score revolutionized the field of causal inference and has emerged as a standard tool when researchers reason about cause-and-effect relationship across many disciplines. This discussion centers around the key "no interference" assumption in Rosenbaum and Rubin's original development of the propensity score and reviews some recent advances in extending the propensity score to studies involving dependent happenings.

Multimodeling approach to evaluating the efficacy of layering pharmaceutical and nonpharmaceutical interventions for influenza pandemics.

When an influenza pandemic emerges, temporary school closures and antiviral treatment may slow virus spread, reduce the overall disease burden, and provide time for vaccine development, distribution, and administration while keeping a larger portion of the general population infection free. The impact of such measures will depend on the transmissibility and severity of the virus and the timing and extent of their implementation. To provide robust assessments of layered pandemic intervention strategies, the Centers for Disease Control and Prevention (CDC) funded a network of academic groups to build a framework for the development and comparison of multiple pandemic influenza models. Research teams from Columbia University, Imperial College London/Princeton University, Northeastern University, the University of Texas at Austin/Yale University, and the University of Virginia independently modeled three prescribed sets of pandemic influenza scenarios developed collaboratively by the CDC and network members. Results provided by the groups were aggregated into a mean-based ensemble. The ensemble and most component models agreed on the ranking of the most and least effective intervention strategies by impact but not on the magnitude of those impacts. In the scenarios evaluated, vaccination alone, due to the time needed for development, approval, and deployment, would not be expected to substantially reduce the numbers of illnesses, hospitalizations, and deaths that would occur. Only strategies that included early implementation of school closure were found to substantially mitigate early spread and allow time for vaccines to be developed and administered, especially under a highly transmissible pandemic scenario.

Incidence of SARS-CoV-2 infection and associated risk factors among staff and residents at homeless shelters in King County, Washington: an active surveillance study.

Homeless shelter residents and staff may be at higher risk of SARS-CoV-2 infection. However, SARS-CoV-2 infection estimates in this population have been reliant on cross-sectional or outbreak investigation data. We conducted routine surveillance and outbreak testing in 23 homeless shelters in King County, Washington, to estimate the occurrence of laboratory-confirmed SARS-CoV-2 infection and risk factors during 1 January 2020-31 May 2021. Symptom surveys and nasal swabs were collected for SARS-CoV-2 testing by RT-PCR for residents aged ≥3 months and staff. We collected 12,915 specimens from 2,930 unique participants. We identified 4.74 (95% CI 4.00-5.58) SARS-CoV-2 infections per 100 individuals (residents: 4.96, 95% CI 4.12-5.91; staff: 3.86, 95% CI 2.43-5.79). Most infections were asymptomatic at the time of detection (74%) and detected during routine surveillance (73%). Outbreak testing yielded higher test positivity than routine surveillance (2.7% versus 0.9%). Among those infected, residents were less likely to report symptoms than staff. Participants who were vaccinated against seasonal influenza and were current smokers had lower odds of having an infection detected. Active surveillance that includes SARS-CoV-2 testing of all persons is essential in ascertaining the true burden of SARS-CoV-2 infections among residents and staff of congregate settings.

Association between pertussis vaccination coverage and other sociodemographic factors and pertussis incidence using surveillance data.

Routine vaccination with pertussis vaccines has been successful in driving down pertussis mortality and morbidity globally. Despite high vaccination coverage, countries such as Australia, USA, and UK have experienced increase in pertussis activity over the last few decades. This may be due to local pockets of low vaccination coverage that result in persistence of pertussis in the population and occasionally lead to large outbreaks. The objective of this study was to characterize the association between pertussis vaccination coverage and sociodemographic factors and pertussis incidence at the school district level in King County, Washington, USA. We used monthly pertussis incidence data for all ages reported to the Public Health Seattle and King County between January 1, 2010 and December 31, 2017 to obtain school district level pertussis incidence. We obtained immunization data from the Washington State Immunization Information System to estimate school-district level vaccination coverage as proportion of 19-35 month old children fully vaccinated with ≥4 doses of the Diphtheria-Tetanus-acellular-Pertussis (DTaP) vaccine in a school district. We used two methods to quantify the effects of vaccination coverage on pertussis incidence: an ecological vaccine model and an endemic-epidemic model. Even though the effect of vaccination is modeled differently in the two approaches, both models can be used to estimate the association between vaccination coverage and pertussis incidence. Using the ecological vaccine model, we estimated the vaccine effectiveness of 4 doses of Diphtheria-Tetanus-acellular-Pertussis vaccine to be 83% (95% credible interval: 63%, 95%). In the endemic-epidemic model, under-vaccination was statistically significantly associated with epidemic risk of pertussis (adjusted Relative Risk, aRR: 2.76; 95% confidence interval: 1.44, 16.6). Household size and median income were statistically significantly associated with endemic pertussis risk. The endemic-epidemic model suffers from ecological bias, whereas the ecological vaccine model provides less biased and more interpretable estimates of epidemiological parameters, such as DTaP vaccine effectiveness, for each school district.

Estimating the impact of COVID-19 vaccine inequities: a modeling study.

Access to COVID-19 vaccines on the global scale has been drastically hindered by structural socio-economic disparities. Here, we develop a data-driven, age-stratified epidemic model to evaluate the effects of COVID-19 vaccine inequities in twenty lower middle and low income countries (LMIC) selected from all WHO regions. We investigate and quantify the potential effects of higher or earlier doses availability. In doing so, we focus on the crucial initial months of vaccine distribution and administration, exploring counterfactual scenarios where we assume the same per capita daily vaccination rate reported in selected high income countries. We estimate that more than 50% of deaths (min-max range: [54-94%]) that occurred in the analyzed countries could have been averted. We further consider scenarios where LMIC had similarly early access to vaccine doses as high income countries. Even without increasing the number of doses, we estimate an important fraction of deaths (min-max range: [6-50%]) could have been averted. In the absence of the availability of high-income countries, the model suggests that additional non-pharmaceutical interventions inducing a considerable relative decrease of transmissibility (min-max range: [15-70%]) would have been required to offset the lack of vaccines. Overall, our results quantify the negative impacts of vaccine inequities and underscore the need for intensified global efforts devoted to provide faster access to vaccine programs in low and lower-middle-income countries.

Rapid review and meta-analysis of serial intervals for SARS-CoV-2 Delta and Omicron variants.

BACKGROUND: The serial interval is the period of time between symptom onset in the primary case and symptom onset in the secondary case. Understanding the serial interval is important for determining transmission dynamics of infectious diseases like COVID-19, including the reproduction number and secondary attack rates, which could influence control measures. Early meta-analyses of COVID-19 reported serial intervals of 5.2 days (95% CI: 4.9-5.5) for the original wild-type variant and 5.2 days (95% CI: 4.87-5.47) for Alpha variant. The serial interval has been shown to decrease over the course of an epidemic for other respiratory diseases, which may be due to accumulating viral mutations and implementation of more effective nonpharmaceutical interventions. We therefore aggregated the literature to estimate serial intervals for Delta and Omicron variants. METHODS: This study followed Preferred Reporting Items for Systematic Reviews and Meta-analyses guidelines. A systematic literature search was conducted of PubMed, Scopus, Cochrane Library, ScienceDirect, and preprint server medRxiv for articles published from April 4, 2021, through May 23, 2023. Search terms were: ("serial interval" or "generation time"), ("Omicron" or "Delta"), and ("SARS-CoV-2" or "COVID-19"). Meta-analyses were done for Delta and Omicron variants using a restricted maximum-likelihood estimator model with a random effect for each study. Pooled average estimates and 95% confidence intervals (95% CI) are reported. RESULTS: There were 46,648 primary/secondary case pairs included for the meta-analysis of Delta and 18,324 for Omicron. Mean serial interval for included studies ranged from 2.3-5.8 days for Delta and 2.1-4.8 days for Omicron. The pooled mean serial interval for Delta was 3.9 days (95% CI: 3.4-4.3) (20 studies) and Omicron was 3.2 days (95% CI: 2.9-3.5) (20 studies). Mean estimated serial interval for BA.1 was 3.3 days (95% CI: 2.8-3.7) (11 studies), BA.2 was 2.9 days (95% CI: 2.7-3.1) (six studies), and BA.5 was 2.3 days (95% CI: 1.6-3.1) (three studies). CONCLUSIONS: Serial interval estimates for Delta and Omicron were shorter than ancestral SARS-CoV-2 variants. More recent Omicron subvariants had even shorter serial intervals suggesting serial intervals may be shortening over time. This suggests more rapid transmission from one generation of cases to the next, consistent with the observed faster growth dynamic of these variants compared to their ancestors. Additional changes to the serial interval may occur as SARS-CoV-2 continues to circulate and evolve. Changes to population immunity (due to infection and/or vaccination) may further modify it.

Covariate-constrained randomization with cluster selection and substitution.

BACKGROUND: An ongoing cluster-randomized trial for the prevention of arboviral diseases utilizes covariate-constrained randomization to balance two treatment arms across four specified covariates and geographic sector. Each cluster is within a census tract of the city of Mérida, Mexico, and there were 133 eligible tracts from which to select 50. As some selected clusters may have been subsequently found unsuitable in the field, we desired a strategy to substitute new clusters while maintaining covariate balance. METHODS: We developed an algorithm that successfully identified a subset of clusters that maximized the average minimum pairwise distance between clusters in order to reduce contamination and balanced the specified covariates both before and after substitutions were made. SIMULATIONS: Simulations were performed to explore some limitations of this algorithm. The number of selected clusters and eligible clusters were varied along with the method of selecting the final allocation pattern. CONCLUSION: The algorithm is presented here as a series of optional steps that can be added to the standard covariate-constrained randomization process in order to achieve spatial dispersion, cluster subsampling, and cluster substitution. Simulation results indicate that these extensions can be used without loss of statistical validity, given a sufficient number of clusters included in the trial.

Methods for Assessing Spillover in Network-Based Studies of HIV/AIDS Prevention among People Who Use Drugs.

Human Immunodeficiency Virus (HIV) interventions among people who use drugs (PWUD) often have spillover, also known as interference or dissemination, which occurs when one participant's exposure affects another participant's outcome. PWUD are often members of networks defined by social, sexual, and drug-use partnerships and their receipt of interventions can affect other members in their network. For example, HIV interventions with possible spillover include educational training about HIV risk reduction, pre-exposure prophylaxis, or treatment as prevention. In turn, intervention effects frequently depend on the network structure, and intervention coverage levels and spillover can occur even if not measured in a study, possibly resulting in an underestimation of intervention effects. Recent methodological approaches were developed to assess spillover in the context of network-based studies. This tutorial provides an overview of different study designs for network-based studies and related methodological approaches for assessing spillover in each design. We also provide an overview of other important methodological issues in network studies, including causal influence in networks and missing data. Finally, we highlight applications of different designs and methods from studies of PWUD and conclude with an illustrative example from the Transmission Reduction Intervention Project (TRIP) in Athens, Greece.

Finding influential subjects in a network using a causal framework.

Researchers across a wide array of disciplines are interested in finding the most influential subjects in a network. In a network setting, intervention effects and health outcomes can spill over from one node to another through network ties, and influential subjects are expected to have a greater impact than others. For this reason, network research in public health has attempted to maximize health and behavioral changes by intervening on a subset of influential subjects. Although influence is often defined only implicitly in most of the literature, the operative notion of influence is inherently causal in many cases: influential subjects are those we should intervene on to achieve the greatest overall effect across the entire network. In this work, we define a causal notion of influence using potential outcomes. We review existing influence measures, such as node centrality, that largely rely on the particular features of the network structure and/or on certain diffusion models that predict the pattern of information or diseases spreads through network ties. We provide simulation studies to demonstrate when popular centrality measures can agree with our causal measure of influence. As an illustrative example, we apply several popular centrality measures to the HIV risk network in the Transmission Reduction Intervention Project and demonstrate the assumptions under which each centrality can represent the causal influence of each participant in the study.

Evaluating the Mediating Role of Recall of Intervention Knowledge in the Relationship Between a Peer-Driven Intervention and HIV Risk Behaviors Among People Who Inject Drugs.

Peer-driven interventions can be effective in reducing HIV injection risk behaviors among people who inject drugs (PWID). We employed a causal mediation framework to examine the mediating role of recall of intervention knowledge in the relationship between a peer-driven intervention and subsequent self-reported HIV injection-related risk behavior among PWID in the HIV Prevention Trials Network (HPTN) 037 study. For each intervention network, the index participant received training at baseline to become a peer educator, while non-index participants and all participants in the control networks received only HIV testing and counseling; recall of intervention knowledge was measured at the 6-month visit for each participant, and each participant was followed to ascertain HIV injection-related risk behaviors at the 12-month visit. We used inverse probability weighting to fit marginal structural models to estimate the total effect (TE) and controlled direct effect (CDE) of the intervention on the outcome. The proportion eliminated (PE) by intervening to remove mediation by the recall of intervention knowledge was computed. There were 385 participants (47% in intervention networks) included in the analysis. The TE and CDE risk ratios for the intervention were 0.47 [95% confidence interval (CI): 0.28, 0.78] and 0.73 (95% CI: 0.26, 2.06) and the PE was 49%. Compared to participants in the control networks, the peer-driven intervention reduced the risk of HIV injection-related risk behavior by 53%. The mediating role of recall of intervention knowledge accounted for less than 50% of the total effect of the intervention, suggesting that other potential causal pathways between the intervention and the outcome, such as motivation and skill, self-efficacy, social norms and behavior modeling, should be considered in future studies.

Hypothesis testing and sample size considerations for the test-negative design.

The test-negative design (TND) is an observational study design to evaluate vaccine effectiveness (VE) that enrolls individuals receiving diagnostic testing for a target disease as part of routine care. VE is estimated as one minus the adjusted odds ratio of testing positive versus negative comparing vaccinated and unvaccinated patients. Although the TND is related to case-control studies, it is distinct in that the ratio of test-positive cases to test-negative controls is not typically pre-specified. For both types of studies, sparse cells are common when vaccines are highly effective. We consider the implications of these features on power for the TND. We use simulation studies to explore three hypothesis-testing procedures and associated sample size calculations for case-control and TND studies. These tests, all based on a simple logistic regression model, are a standard Wald test, a continuity-corrected Wald test, and a score test. The Wald test performs poorly in both case-control and TND when VE is high because the number of vaccinated test-positive cases can be low or zero. Continuity corrections help to stabilize the variance but induce bias. We observe superior performance with the score test as the variance is pooled under the null hypothesis of no group differences. We recommend using a score-based approach to design and analyze both case-control and TND. We propose a modification to the TND score sample size to account for additional variability in the ratio of controls over cases. This work expands our understanding of the data mechanisms of the TND.

Estimating Causal Effects of HIV Prevention Interventions with Interference in Network-based Studies among People Who Inject Drugs.

Evaluating causal effects in the presence of interference is challenging in network-based studies of hard-to-reach populations. Like many such populations, people who inject drugs (PWID) are embedded in social networks and often exert influence on others in their network. In our setting, the study design is observational with a non-randomized network-based HIV prevention intervention. Information is available on each participant and their connections that confer possible HIV risk through injection and sexual behaviors. We considered two inverse probability weighted (IPW) estimators to quantify the population-level spillover effects of non-randomized interventions on subsequent health outcomes. We demonstrated that these two IPW estimators are consistent, asymptotically normal, and derived a closed-form estimator for the asymptotic variance, while allowing for overlapping interference sets (groups of individuals in which the interference is assumed possible). A simulation study was conducted to evaluate the finite-sample performance of the estimators. We analyzed data from the Transmission Reduction Intervention Project, which ascertained a network of PWID and their contacts in Athens, Greece, from 2013 to 2015. We evaluated the effects of community alerts on subsequent HIV risk behavior in this observed network, where the connections or links between participants were defined by using substances or having unprotected sex together. In the study, community alerts were distributed to inform people of recent HIV infections among individuals in close proximity in the observed network. The estimates of the risk differences for spillover using either IPW estimator demonstrated a protective effect. The results suggest that HIV risk behavior could be mitigated by exposure to a community alert when an increased risk of HIV is detected in the network.

Estimating the impact of COVID-19 vaccine allocation inequities: a modeling study.

Access to COVID-19 vaccines on the global scale has been drastically impacted by structural socio-economic inequities. Here, we develop a data-driven, age-stratified epidemic model to evaluate the effects of COVID-19 vaccine inequities in twenty lower middle and low income countries (LMIC) sampled from all WHO regions. We focus on the first critical months of vaccine distribution and administration, exploring counterfactual scenarios where we assume the same per capita daily vaccination rate reported in selected high income countries. We estimate that, in this high vaccine availability scenario, more than 50% of deaths (min-max range: [56% - 99%]) that occurred in the analyzed countries could have been averted. We further consider a scenario where LMIC had similarly early access to vaccine doses as high income countries; even without increasing the number of doses, we estimate an important fraction of deaths (min-max range: [7% - 73%]) could have been averted. In the absence of equitable allocation, the model suggests that considerable additional non-pharmaceutical interventions would have been required to offset the lack of vaccines (min-max range: [15% - 75%]). Overall, our results quantify the negative impacts of vaccines inequities and call for amplified global efforts to provide better access to vaccine programs in low and lower middle income countries.

Spillover benefit of pre-exposure prophylaxis for HIV prevention: evaluating the importance of effect modification using an agent-based model.

We developed an agent-based model using a trial emulation approach to quantify effect measure modification of spillover effects of pre-exposure prophylaxis (PrEP) for HIV among men who have sex with men (MSM) in the Atlanta-Sandy Springs-Roswell metropolitan area, Georgia. PrEP may impact not only the individual prescribed, but also their partners and beyond, known as spillover. We simulated a two-stage randomised trial with eligible components (≥3 agents with ≥1 HIV+ agent) first randomised to intervention or control (no PrEP). Within intervention components, agents were randomised to PrEP with coverage of 70%, providing insight into a high PrEP coverage strategy. We evaluated effect modification by component-level characteristics and estimated spillover effects on HIV incidence using an extension of randomisation-based estimators. We observed an attenuation of the spillover effect when agents were in components with a higher prevalence of either drug use or bridging potential (if an agent acts as a mediator between ≥2 connected groups of agents). The estimated spillover effects were larger in magnitude among components with either higher HIV prevalence or greater density (number of existing partnerships compared to all possible partnerships). Consideration of effect modification is important when evaluating the spillover of PrEP among MSM.

A platform trial design for preventive vaccines against Marburg virus and other emerging infectious disease threats.

BACKGROUND: The threat of a possible Marburg virus disease outbreak in Central and Western Africa is growing. While no Marburg virus vaccines are currently available for use, several candidates are in the pipeline. Building on knowledge and experiences in the designs of vaccine efficacy trials against other pathogens, including SARS-CoV-2, we develop designs of randomized Phase 3 vaccine efficacy trials for Marburg virus vaccines. METHODS: A core protocol approach will be used, allowing multiple vaccine candidates to be tested against controls. The primary objective of the trial will be to evaluate the effect of each vaccine on the rate of virologically confirmed Marburg virus disease, although Marburg infection assessed via seroconversion could be the primary objective in some cases. The overall trial design will be a mixture of individually and cluster-randomized designs, with individual randomization done whenever possible. Clusters will consist of either contacts and contacts of contacts of index cases, that is, ring vaccination, or other transmission units. RESULTS: The primary efficacy endpoint will be analysed as a time-to-event outcome. A vaccine will be considered successful if its estimated efficacy is greater than 50% and has sufficient precision to rule out that true efficacy is less than 30%. This will require approximately 150 total endpoints, that is, cases of confirmed Marburg virus disease, per vaccine/comparator combination. Interim analyses will be conducted after 50 and after 100 events. Statistical analysis of the trial will be blended across the different types of designs. Under the assumption of a 6-month attack rate of 1% of the participants in the placebo arm for both the individually and cluster-randomized populations, the most likely sample size is about 20,000 participants per arm. CONCLUSION: This event-driven design takes into the account the potentially sporadic spread of Marburg virus. The proposed trial design may be applicable for other pathogens against which effective vaccines are not yet available.

Quantifying the importance and location of SARS-CoV-2 transmission events in large metropolitan areas.

Detailed characterization of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission across different settings can help design less disruptive interventions. We used real-time, privacy-enhanced mobility data in the New York City, NY and Seattle, WA metropolitan areas to build a detailed agent-based model of SARS-CoV-2 infection to estimate the where, when, and magnitude of transmission events during the pandemic's first wave. We estimate that only 18% of individuals produce most infections (80%), with about 10% of events that can be considered superspreading events (SSEs). Although mass gatherings present an important risk for SSEs, we estimate that the bulk of transmission occurred in smaller events in settings like workplaces, grocery stores, or food venues. The places most important for transmission change during the pandemic and are different across cities, signaling the large underlying behavioral component underneath them. Our modeling complements case studies and epidemiological data and indicates that real-time tracking of transmission events could help evaluate and define targeted mitigation policies.

Using social contact data to improve the overall effect estimate of a cluster-randomized influenza vaccination program in Senegal.

This study estimates the overall effect of two influenza vaccination programs consecutively administered in a cluster-randomized trial in western Senegal over the course of two influenza seasons from 2009-2011. We apply cutting-edge methodology combining social contact data with infection data to reduce bias in estimation arising from contamination between clusters. Our time-varying estimates reveal a reduction in seasonal influenza from the intervention and a nonsignificant increase in H1N1 pandemic influenza. We estimate an additive change in overall cumulative incidence (which was 6.13% in the control arm) of -0.68 percentage points during Year 1 of the study (95% CI: -2.53, 1.18). When H1N1 pandemic infections were excluded from analysis, the estimated change was -1.45 percentage points and was significant (95% CI, -2.81, -0.08). Because cross-cluster contamination was low (0-3% of contacts for most villages), an estimator assuming no contamination was only slightly attenuated (-0.65 percentage points). These findings are encouraging for studies carefully designed to minimize spillover. Further work is needed to estimate contamination - and its effect on estimation - in a variety of settings.

Household Secondary Attack Rates of SARS-CoV-2 by Variant and Vaccination Status: An Updated Systematic Review and Meta-analysis.

Importance: An overall household secondary attack rate (SAR) of 18.9% (95% CI, 16.2%-22.0%) through June 17, 2021 was previously reported for SARS-CoV-2. Emerging variants of concern and increased vaccination have affected transmission rates. Objective: To evaluate how reported household SARs changed over time and whether SARs varied by viral variant and index case and contact vaccination status. Data Sources: PubMed and medRxiv from June 18, 2021, through March 8, 2022, and reference lists of eligible articles. Preprints were included. Study Selection: Articles with original data reporting the number of infected and total number of household contacts. Search terms included SARS-CoV-2, COVID-19, variant, vaccination, secondary attack rate, secondary infection rate, household, index case, family contacts, close contacts, and family transmission. Data Extraction and Synthesis: The Preferred Reporting Items for Systematic Reviews and Meta-Analyses reporting guideline was followed. Meta-analyses used generalized linear mixed models to obtain SAR estimates and 95% CIs. Main Outcomes and Measures: SAR stratified by covariates according to variant, index case and contact vaccination status, and index case identification period. SARs were used to estimate vaccine effectiveness on the basis of the transmission probability for susceptibility to infection (VES,p), infectiousness given infection (VEI,p), and total vaccine effectiveness (VET,p). Results: Household SARs were higher for 33 studies with midpoints in 2021 to 2022 (37.3%; 95% CI, 32.7% to 42.1%) compared with 63 studies with midpoints through April 2020 (15.5%; 95% CI, 13.2% to 18.2%). Household SARs were 42.7% (95% CI, 35.4% to 50.4%) for Omicron (7 studies), 36.4% (95% CI, 33.4% to 39.5%) for Alpha (11 studies), 29.7% (95% CI, 23.0% to 37.3%) for Delta (16 studies), and 22.5% (95% CI, 18.6% to 26.8%) for Beta (3 studies). For full vaccination, VES,p was 78.6% (95% CI, 76.0% to 80.9%) for Alpha, 56.4% (95% CI, 54.6% to 58.1%) for Delta, and 18.1% (95% CI, -18.3% to 43.3%) for Omicron; VEI,p was 75.3% (95% CI, 69.9% to 79.8%) for Alpha, 21.9% (95% CI, 11.0% to 31.5%) for Delta, and 18.2% (95% CI, 0.6% to 32.6%) for Omicron; and VET,p was 94.7% (95% CI, 93.3% to 95.8%) for Alpha, 64.4% (95% CI, 58.0% to 69.8%) for Delta, and 35.8% (95% CI, 13.0% to 52.6%) for Omicron. Conclusions and Relevance: These results suggest that emerging SARS-CoV-2 variants of concern have increased transmissibility. Full vaccination was associated with reductions in susceptibility and infectiousness, but more so for Alpha than Delta and Omicron. The changes in estimated vaccine effectiveness underscore the challenges of developing effective vaccines concomitant with viral evolution.

Protecting the herd with vaccination.

How much do COVID-19 vaccines reduce transmission? The answer is a moving target.