Estimation of the direct and indirect effects of vaccination

Quantifying indirect and direct vaccination effects arising in the SIR model

Vaccination campaigns have both direct and indirect effects that act to control an infectious disease as it spreads through a population. Indirect effects arise when vaccinated individuals block disease transmission in any infection chain they are part of, and this in turn can benefit both vaccinated and unvaccinated individuals. Indirect effects are difficult to quantify in practice but, in this article, working with the susceptible-infected-recovered (SIR) model, they are analytically calculated in important cases, through pivoting on the final size formula for epidemics. Their relationship to herd immunity is also clarified. The analysis allows us to identify the important distinction between quantifying the indirect effects of vaccination at the 'population level' versus the 'per capita' level, which often results in radically different conclusions. As an example, our analysis unpacks why the population-level indirect effect can appear significantly larger than its per capita analogue. In addition, we consider a recently proposed epidemiological non-pharmaceutical intervention (by the means of recovered individuals) used over the COVID-19 pandemic, referred to as 'shielding', and study its impact on our mathematical analysis. The shielding scheme is extended to take advantage of vaccination including imperfect vaccination.

Testing Whether Higher Contact Among the Vaccinated Can Be a Mechanism for Observed Negative Vaccine Effectiveness

Evidence from early observational studies suggested negative vaccine effectiveness (${V}_{Eff}$) for the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) Omicron variant. Since true ${V}_{Eff}$ is unlikely to be negative, we explored how differences in contact among vaccinated persons (e.g., potentially from the implementation of vaccine mandates) could lead to observed negative ${V}_{Eff}$. Using a susceptible-exposed-infectious-recovered (SEIR) transmission model, we examined how vaccinated-contact heterogeneity, defined as an increase in the contact rate only between vaccinated individuals, interacted with 2 mechanisms of vaccine efficacy: vaccine efficacy against susceptibility ($V{E}_S$) and vaccine efficacy against infectiousness ($V{E}_I$), to produce underestimated and in some cases, negative measurements of ${V}_{Eff}$. We found that vaccinated-contact heterogeneity led to negative estimates when $V{E}_I$, and especially $V{E}_S$, were low. Moreover, we determined that when contact heterogeneity was very high, ${V}_{Eff}$ could still be underestimated given relatively high vaccine efficacies (0.7), although its effect on ${V}_{Eff}$ was strongly reduced. We also found that this contact heterogeneity mechanism generated a signature temporal pattern: The largest underestimates and negative measurements of ${V}_{Eff}$ occurred during epidemic growth. Overall, our research illustrates how vaccinated-contact heterogeneity could have feasibly produced negative measurements during the Omicron period and highlights its general ability to bias observational studies of ${V}_{Eff}$.

Vaccine and vaccination as a part of human life: In view of COVID-19

Background

Vaccination created a great breakthrough toward the improvement to the global health. The development of vaccines and their use made a substantial decrease and control in infectious diseases. The abundance and emergence of new vaccines has facilitated targeting populations to alleviate and eliminate contagious pathogens from their innate reservoir. However, along with the infections like malaria and HIV, effective immunization remains obscure and imparts a great challenge to science.

Purpose and scope

The novel Corona virus SARS‐CoV‐2 is the reason for the 2019 COVID‐19 pandemic in the human global population, in the first half of 2019. The need for establishing a protected and compelling COVID‐19 immunization is a global prerequisite to end this pandemic.

Summary and conclusion

The different vaccine technologies like inactivation, attenuation, nucleic acid, viral vector, subunit, and viral particle based techniques are employed to develop a safe and highly efficient vaccine. The progress in vaccine development for SARS‐CoV2 is much faster in the history of science. Even though there exist of lot of limitations, continuous efforts has put forward so as to develop highly competent and effective vaccine for many human and animal linked diseases due to its unlimited prospective. This review article focuses on the historical outlook and the development of the vaccine as it is a crucial area of research where the life of the human is saved from various potential diseases.

Effects of the rotavirus vaccine program across age groups in the United States: analysis of national claims data, 2001-2016

BACKGROUND

The direct effectiveness of infant rotavirus vaccination implemented in 2006 in the United States has been evaluated extensively, however, understanding of population-level vaccine effectiveness (VE) is still incomplete.

METHODS

We analyzed time series data on rotavirus gastroenteritis (RVGE) and all-cause acute gastroenteritis (AGE) hospitalization rates in the United States from the MarketScan® Research Databases for July 2001-June 2016. Individuals were grouped into ages 0-4, 5-9, 10-14, 15-24, 25-44, and 45-64 years. Negative binomial regression models were fitted to monthly RVGE and AGE data to estimate the direct, indirect, overall, and total VE.

RESULTS

A total of 9211 RVGE and 726,528 AGE hospitalizations were analyzed. Children 0-4 years of age had the largest declines in RVGE hospitalizations with direct VE of 87% (95% CI: 83, 90%). Substantial indirect effects were observed across age groups and generally declined in each older group. Overall VE against RVGE hospitalizations for all ages combined was 69% (95% CI: 62, 76%). Total VE was highest among young children; a vaccinated child in the post-vaccine era has a 95% reduced risk of RVGE hospitalization compared to a child in the pre-vaccine era. We observed higher direct VE in odd post-vaccine years and an opposite pattern for indirect VE.

CONCLUSIONS

Vaccine benefits extended to unvaccinated individuals in all age groups, suggesting infants are important drivers of disease transmission across the population. Imperfect disease classification and changing disease incidence may lead to bias in observed direct VE.

TRIAL REGISTRATION

Not applicable.

Estimating the Population-Level Effectiveness of Vaccination Programs in the Netherlands

BACKGROUND

There are few estimates of the effectiveness of long-standing vaccination programs in developed countries. To fill this gap, we investigate the direct and indirect effectiveness of childhood vaccination programs on mortality at the population level in the Netherlands.

METHODS

We focused on three communicable infectious diseases, diphtheria, pertussis, and poliomyelitis, for which we expect both direct and indirect effects. As a negative control, we used tetanus, a noncommunicable infectious disease for which only direct effects are anticipated. Mortality data from 1903 to 2012 were obtained from Statistics Netherlands. Vaccination coverage data were obtained from various official reports. For the birth cohorts 1903 through 1975, all-cause and cause-specific childhood mortality burden was estimated using restricted mean lifetime survival methods, and a model was used to describe the prevaccination decline in burden. By projecting model results into the vaccination era, we obtained the expected burden without vaccination. Program effectiveness was estimated as the difference between observed and expected mortality burden.

RESULTS

Each vaccination program showed a high overall effectiveness, increasing to nearly 100% within 10 birth cohorts. For diphtheria, 14.9% (95% uncertainty interval [UI] = 12.3%, 17.6%) of mortality burden averted by vaccination was due to indirect protection. For pertussis, this was 32.1% (95% UI = 31.3%, 32.8%). No indirect effects were observed for poliomyelitis or tetanus with -2.4% (UI = -16.7%, 7.1%) and 0.6% (UI = -17.9%, 10.7%), respectively.

CONCLUSION

Vaccination programs for diphtheria and pertussis showed substantial indirect effects, providing evidence for herd protection.

Cost-effectiveness analysis of universal influenza vaccination: Application of the susceptible-infectious-complication-recovery model

OBJECTIVES

Despite the fact that vaccination is an effective primary prevention strategy for the containment of influenza outbreaks, health policymakers have shown great concern over the enormous costs involved in universal immunization, particularly when resources are limited.

METHODS

A two-arm cost-effectiveness analysis (CEA) was conducted that took into account the aspect of herd immunity. The analysis used a study cohort of 100000 residents with a demographic make-up identical to that of the underlying population in Taipei County, Taiwan, during the epidemic influenza season of 2001-2002. The parameters embedded in the dynamic process of infection were estimated through the application of the newly proposed susceptible-infection-complication-recovery (SICR) model to the empirical data, in order to compute the number of deaths and complications averted due to universal vaccination compared to no vaccination. Incremental cost-effectiveness ratios (ICERs) and the cost-effectiveness acceptability curve (CEAC) given maximum amount of willingness-to-pay (WTP) were calculated to delineate the results of the two-arm CEA.

RESULTS

The incremental costs involved in the vaccinated group as compared to the unvaccinated group were $1195 to reduce one additional complication and $805 to avert one additional death, allowing for herd immunity. The corresponding figures were higher for the results without considering herd immunity. Given the ceiling ratio of WTP equal to $10000 (approximately two-thirds of GDP), the probability of the vaccination being cost-effective for averting death was 100% and for averting complications was 96.7%.

CONCLUSIONS

Universal vaccination against seasonal influenza was found to be very cost-effective, particularly when herd immunity is considered. The probability of being cost-effective was almost certain given the maximum amount of WTP within two-thirds of the GDP.

Vaccination Programs for Endemic Infections: Modelling Real versus Apparent Impacts of Vaccine and Infection Characteristics

Vaccine effect, as measured in clinical trials, may not accurately reflect population-level impact. Furthermore, little is known about how sensitive apparent or real vaccine impacts are to factors such as the risk of re-infection or the mechanism of protection. We present a dynamic compartmental model to simulate vaccination for endemic infections. Several measures of effectiveness are calculated to compare the real and apparent impact of vaccination, and assess the effect of a range of infection and vaccine characteristics on these measures. Although broadly correlated, measures of real and apparent vaccine effectiveness can differ widely. Vaccine impact is markedly underestimated when primary infection provides partial natural immunity, when coverage is high and when post-vaccination infectiousness is reduced. Despite equivalent efficacy, 'all or nothing' vaccines are more effective than 'leaky' vaccines, particularly in settings with high risk of re-infection and transmissibility. Latent periods result in greater real impacts when risk of re-infection is high, but this effect diminishes if partial natural immunity is assumed. Assessments of population-level vaccine effects against endemic infections from clinical trials may be significantly biased, and vaccine and infection characteristics should be considered when modelling outcomes of vaccination programs, as their impact may be dramatic.

Overview of Serological Techniques for Influenza Vaccine Evaluation: Past, Present and Future

Serological techniques commonly used to quantify influenza-specific antibodies include the Haemagglutination Inhibition (HI), Single Radial Haemolysis (SRH) and Virus Neutralization (VN) assays. HI and SRH are established and reproducible techniques, whereas VN is more demanding. Every new influenza vaccine needs to fulfil the strict criteria issued by the European Medicines Agency (EMA) in order to be licensed. These criteria currently apply exclusively to SRH and HI assays and refer to two different target groups-healthy adults and the elderly, but other vaccine recipient age groups have not been considered (i.e., children). The purpose of this timely review is to highlight the current scenario on correlates of protection concerning influenza vaccines and underline the need to revise the criteria and assays currently in use. In addition to SRH and HI assays, the technical advantages provided by other techniques such as the VN assay, pseudotype-based neutralization assay, neuraminidase and cell-mediated immunity assays need to be considered and regulated via EMA criteria, considering the many significant advantages that they could offer for the development of effective vaccines.

Distinguishing vaccine efficacy and effectiveness

BACKGROUND

Mathematical models of disease transmission and vaccination typically assume that protective vaccine efficacy (i.e. the relative reduction in the transmission rate among vaccinated individuals) is equivalent to direct effectiveness of vaccine. This assumption has not been evaluated.

METHODS

We used dynamic epidemiological models of influenza and measles vaccines to evaluate the common measures of vaccine effectiveness in terms of both the protection of individuals and disease control within populations. We determined how vaccine-mediated reductions in attack rates translate into vaccine efficacy as well as into the common population measures of 'direct', 'indirect', 'total', and 'overall' effects of vaccination with examples of compartmental models of influenza and measles vaccination.

RESULTS

We found that the typical parameterization of vaccine efficacy using direct effectiveness of vaccine can lead to the underestimation of the impact of vaccine. Such underestimation occurs when the vaccine is assumed to offer partial protection to every vaccinated person, and becomes worse when the level of vaccine coverage is low. Nevertheless, estimates of 'total', 'indirect' and 'overall' effectiveness increase with vaccination coverage in the population. Furthermore, we show how the measures of vaccine efficacy and vaccine effectiveness can be correctly calculated.

CONCLUSIONS

Typical parameterization of vaccine efficacy in mathematical models may underestimate the actual protective effect of the vaccine, resulting in discordance between the actual effects of vaccination at the population level and predictions made by models. This work shows how models can be correctly parameterized from clinical trial data.

Bayesian inference for causal mediation effects using principal stratification with dichotomous mediators and outcomes

Most investigations in the social and health sciences aim to understand the directional or causal relationship between a treatment or risk factor and outcome. Given the multitude of pathways through which the treatment or risk factor may affect the outcome, there is also an interest in decomposing the effect of a treatment of risk factor into "direct" and "mediated" effects. For example, child's socioeconomic status (risk factor) may have a direct effect on the risk of death (outcome) and an effect that may be mediated through the adulthood socioeconomic status (mediator). Building on the potential outcome framework for causal inference, we develop a Bayesian approach for estimating direct and mediated effects in the context of a dichotomous mediator and dichotomous outcome, which is challenging as many parameters cannot be fully identified. We first define principal strata corresponding to the joint distribution of the observed and counterfactual values of the mediator, and define associate, dissociative, and mediated effects as functions of the differences in the mean outcome under differing treatment assignments within the principal strata. We then develop the likelihood properties and calculate nonparametric bounds of these causal effects assuming randomized treatment assignment. Because likelihood theory is not well developed for nonidentifiable parameters, we consider a Bayesian approach that allows the direct and mediated effects to be expressed in terms of the posterior distribution of the population parameters of interest. This range can be reduced by making further assumptions about the parameters that can be encoded in prior distribution assumptions. We perform sensitivity analyses by using several prior distributions that make weaker assumptions than monotonicity or the exclusion restriction. We consider an application that explores the mediating effects of adult poverty on the relationship between childhood poverty and risk of death.

Two Critical Issues in Quantitative Modeling of Communicable Diseases: Inference of Unobservables and Dependent Happening

In this chapter, we discuss two critical issues which must be remembered whenever we examine epidemiologic data of directly transmitted infectious diseases. Firstly, we would like the readers to recognize the difference between observable and unobservable events in infectious disease epidemiology. Since both infection event and acquisition of infectiousness are generally not directly observable, the total number of infected individuals could not be counted at a point of time, unless very rigorous contact tracing and microbiological examinations were performed. Directly observable intrinsic parameters, such as the incubation period and serial interval, play key roles in translating observable to unobservable information. Secondly, the concept of dependent happening must be remembered to identify a risk of an infectious disease or to assess vaccine efficacy. Observation of a single infected individual is not independent of observing other individuals. A simple solution for dependent happening is to employ the transmission probability which is conditioned on an exposure to infection.

Environmental determinants of infectious disease: a framework for tracking causal links and guiding public health research

BACKGROUND

Discoveries that emerging and re-emerging pathogens have their origin in environmental change has created an urgent need to understand how these environmental changes impact disease burden. In this article we present a framework that provides a context from which to examine the relationship between environmental changes and disease transmission and a structure from which to unite disparate pieces of information from a variety of disciplines.

METHODS

The framework integrates three interrelated characteristics of environment-disease relationships: a) Environmental change manifests in a complex web of ecologic and social factors that may ultimately impact disease; these factors are represented as those more distally related and those more proximally related to disease. b) Transmission dynamics of infectious pathogens mediate the effects that environmental changes have on disease. c) Disease burden is the outcome of the interplay between environmental change and the transmission cycle of a pathogen.

RESULTS

To put this framework into operation, we present a matrix formulation as a means to define important elements of this system and to summarize what is known and unknown about the these elements and their relationships. The framework explicitly expresses the problem at a systems level that goes beyond the traditional risk factor analysis used in public health, and the matrix provides a means to explicitly express the coupling of different system components.

CONCLUSION

This coupling of environmental and disease transmission processes provides a much-needed construct for furthering our understanding of both specific and general relationships between environmental change and infectious disease.

Effect of within-household reinfestation on design sensitivity

The effect of within-household reinfestation on design sensitivity is investigated through statistical modeling of the reinfestation process. When reinfestation is present, household randomization tends to magnify treatment differences when compared with individual randomization or a randomized blocking design in the simple setting of two patients per household. The effect of reinfestation under more general household randomization settings is investigated by determining the relationship between the treatment effect and the number of patients per household. In an actual clinical study of treatment for head lice infestation, household randomization with proper stratification was adopted. The results from the study were consistent with theoretical expectations. This seeming contradiction to the blocking principle demonstrates the need to check whether all conditions are met before applying standard design principles.

Antimicrobial use and antimicrobial resistance: a population perspective

The need to stem the growing problem of antimicrobial resistance has prompted multiple, sometimes conflicting, calls for changes in the use of antimicrobial agents. One source of disagreement concerns the major mechanisms by which antibiotics select resistant strains. For infections like tuberculosis, in which resistance can emerge in treated hosts through mutation, prevention of antimicrobial resistance in individual hosts is a primary method of preventing the spread of resistant organisms in the community. By contrast, for many other important resistant pathogens, such as penicillin-resistant Streptococcus pneumoniae, methicillin-resistant Staphylococcus aureus, and vancomycin-resistant Enterococcus faecium resistance is mediated by the acquisition of genes or gene fragments by horizontal transfer; resistance in the treated host is a relatively rare event. For these organisms, indirect, population-level mechanisms of selection account for the increase in the prevalence of resistance. These mechanisms can operate even when treatment has a modest, or even negative, effect on an individual host's colonization with resistant organisms.

Advances in medical statistics arising from the AIDS epidemic

Many statisticians have contributed to studies of the HIV epidemic and progression to AIDS. They have developed new statistical methodology, where needed, to address HIV-related issues. The transfer of methods from one area to another often involves a substantial delay. This paper points to methods that were developed in the HIV context and have either already found applications in other areas of medical research or have the potential for such applications, with the hope that this will promote a speedier transfer of the research methods. Among the new tools that HIV studies have placed firmly into the pool of statistical methods for medical research are the methods of back-calculation, methods for the analysis of retrospective ascertainment data and methods of analysis for the combined data from clinical trials and associated longitudinal studies. Notions that have been stimulated substantially are use of surrogate endpoints in clinical trials and screening blood products by the use of pooled serum samples. Research activity in many other areas has been boosted substantially through contributions motivated by HIV/AIDS studies. Noteworthy examples are analyses for doubly-censored lifetime data and methods for assessing vaccines for transmissible diseases.

Design and analysis issues in cluster-randomized trials of interventions against infectious diseases

This paper discusses the application of the cluster-randomized trial (CRT) design to evaluate the effectiveness of interventions against infectious diseases. In addition to the usual rationale for this design, there are a number of other advantages that are peculiar to the study of infectious diseases. In particular, CRTs are able to measure the overall effect of an intervention at the population level, capturing both the direct effect of an intervention on an individual's susceptibility to infection, and also the indirect effects due to changes in risks of transmission to other individuals, or to the mass effect or 'herd immunity' resulting from intervening in a large proportion of the population. We briefly review published CRTs of interventions against infectious diseases, most of which have been conducted in the developing countries where such diseases predominate. The focus is on trials in which communities or other large groupings are randomized, and in which impacts on infectious disease incidence or mortality are assessed. We then discuss three issues that are of special relevance to CRTs of infectious diseases. First, issues relating to the definition and size of clusters; secondly, the role of matching or stratification, and the choice of matching factors; and thirdly, the definition of direct and indirect effects of intervention, and methods of assessing these components in a CRT. We conclude by outlining some areas for future research.