CHESS, Kerkstraat 27, 1742, Ternat, Belgium

Health Economics, GlaxoSmithKline Vaccines, 2301 Renaissance Boulevard, RN 0220, King of Prussia, PA, 19406, USA

EAH-Consulting, Heimbacher Str. 19, 52428, Juelich, Germany

Abstract

Background

Indirect herd effect from vaccination of children offers potential for improving the effectiveness of influenza prevention in the remaining unvaccinated population. Static models used in cost-effectiveness analyses cannot dynamically capture herd effects. The objective of this study was to develop a methodology to allow herd effect associated with vaccinating children against seasonal influenza to be incorporated into static models evaluating the cost-effectiveness of influenza vaccination.

Methods

Two previously published linear equations for approximation of herd effects in general were compared with the results of a structured literature review undertaken using PubMed searches to identify data on herd effects specific to influenza vaccination. A linear function was fitted to point estimates from the literature using the sum of squared residuals.

Results

The literature review identified 21 publications on 20 studies for inclusion. Six studies provided data on a mathematical relationship between effective vaccine coverage in subgroups and reduction of influenza infection in a larger unvaccinated population. These supported a linear relationship when effective vaccine coverage in a subgroup population was between 20% and 80%. Three studies evaluating herd effect at a community level, specifically induced by vaccinating children, provided point estimates for fitting linear equations. The fitted linear equation for herd protection in the target population for vaccination (children) was slightly less conservative than a previously published equation for herd effects in general. The fitted linear equation for herd protection in the non-target population was considerably less conservative than the previously published equation.

Conclusions

This method of approximating herd effect requires simple adjustments to the annual baseline risk of influenza in static models: (1) for the age group targeted by the childhood vaccination strategy (i.e. children); and (2) for other age groups not targeted (e.g. adults and/or elderly). Two approximations provide a linear relationship between effective coverage and reduction in the risk of infection. The first is a conservative approximation, recommended as a base-case for cost-effectiveness evaluations. The second, fitted to data extracted from a structured literature review, provides a less conservative estimate of herd effect, recommended for sensitivity analyses.

Background

Influenza is an acute viral infection. While self-limiting in most people, it can result in serious illness or death in certain high-risk groups, such as elderly people (aged 65 years or more), young children (aged 2 years or less), or people with chronic medical conditions. The clinical and economic burden of influenza is substantial. In the United Kingdom (UK), influenza has been estimated to account for 779,000 to 1,164,000 general practitioner (GP) consultations, 19,000 to 31,200 hospital admissions and 18,500 to 24,800 deaths annually

Vaccination is the most effective way to prevent influenza infection

Herd effect may thus be an important component of the public health effects of influenza vaccination. Economic evaluations of influenza vaccination that take account of herd effect will be needed by healthcare decision-makers appraising influenza vaccination programmes, in order to capture fully the direct and indirect benefit of childhood vaccination. Static models are most often used to evaluate the cost-effectiveness of mass vaccination against seasonal influenza, whereas dynamic models are most often used to evaluate the impact of vaccination on transmission and disease incidence. However, static cohort models cannot dynamically capture the effect of vaccination on transmission and therefore fail to account for herd effect

If herd effect is included in static models, most use a fixed input parameter derived from empirical data, such as the reduced incidence in susceptible individuals at a specific, pre-defined vaccination coverage

The objective of the current study was to develop an approximation to capture the herd effect induced by annual vaccination of children against influenza at varying coverage levels. This approximation can be incorporated into cohort models to permit the consideration of indirect benefits for the community achieved by annual vaccination of children, without the need to rely on dynamic modelling processes.

Methods

Definitions

Throughout this manuscript, the following definitions apply:

Linear approximation of herd effect

Bauch et al. (2009)

Derived from Equation 2 (known R_{0})

R_{0} = basic reproduction number (average number of secondary infectious persons resulting from the introduction of an infectious person into a totally susceptible population).

The RR of infection can be described as decreasing linearly with increasing effective coverage. The slope of the line (or the value of effective coverage at which a RR of zero is achieved, i.e. the elimination threshold) is dependent on the value of R_{0}: the lower the R_{0}, the steeper the decrease in RR, i.e. the higher the impact of herd effect (the second figure in Bauch et al. (2009)
_{0} and the magnitude of herd effect can be found in Bauch et al. (2009)

Derived from Equation 3 (unknown R_{0})

This equation is only dependent on effective coverage, and is the most conservative approach for estimating the relationship between effective coverage and the RR of infection, since it does not account for any incremental herd immunity induced by R_{0} approaching 1 (the second figure in Bauch et al. (2009)

Although Bauch et al. (2009)

Structured literature review with a focus on seasonal influenza

A structured literature review was performed with a specific focus on herd effect induced by vaccination against seasonal influenza. The objectives of this review were: to validate whether a linear relationship between effective coverage in a subpopulation and RR of symptomatic influenza infection in the non-vaccinated population forms a valid approximation for herd effect; and to identify point estimates of this relationship, expressed as RR as a function of effective coverage in children. Methods of analysis, i.e. keywords, limitations, inclusion criteria, as well as the data extraction sheet, were defined

Database search

Free-text PubMed searches were conducted using the following search terms, limited to English-language publications in humans with abstracts available:

1. influenza

2. herd immunity OR herd protection OR herd effect

3. population protection OR community protection

4. community vaccination OR community disease transmission

5. 1 AND (2 OR 3 OR 4)

No time limits were applied. The last search was run on 3 August 2011.

Other searches

Relevant references cited in articles identified through the database search, as well as literature identified from other sources, were included. Literature identified through other sources was clearly stated as such, as these may be subject to search bias.

Eligibility criteria

Articles were included if they met the following pre-defined criteria:

1. Clinical study or observational study or review or modelling or health economic study;

2. Inclusion of a subpopulation for mass vaccination;

3. Reporting of one of the following outcomes (either directly reported, or reported outcomes allowing a recalculation to obtain these data):

a. A relationship (mathematical function) between varying degrees of vaccine coverage and efficacy in subgroup populations (not restricted to children) and the reduction of influenza transmission (i.e. reduction in probability of infection) in a larger unvaccinated population;

b. Point estimates of the reduction of influenza infection in the unvaccinated population after vaccination of children, which allow for a fitting of the mathematical function to published data (as defined under (a)).

Titles and abstracts were scanned, and the full text of publications meeting the eligibility criteria or requiring further evaluation was reviewed. Publications meeting the eligibility criteria after evaluation of the full text were included in the full data extraction process.

Data extraction

The data extraction sheet was pre-defined and only minor changes, mainly to improve clarity, were applied after the start of review. Data extraction was conducted by one reviewer and reassessed by an independent reviewer (included studies only). Any discrepancies, which were only minor and non-substantial, were resolved by discussion between the two reviewers.

Outcomes considered and additional analyses

The main outcomes and additional analyses from the publications included in the literature review were as follows:

• Vaccination coverage and direct effectiveness of vaccination in subgroup population;

Additional analysis (if not reported): calculation of effective coverage in subpopulation, based on vaccination coverage in subpopulation and effectiveness expressed as a reduction in the probability of infection in vaccinated individuals;

• Indirect effectiveness in unvaccinated individuals after vaccination of subpopulations;

Additional analysis (if not reported): calculation of the reduction in probability of infection in the unvaccinated population, based on the probability of infection in the absence (or baseline level) of effective coverage in subpopulations, and the probability of infection in the presence of increased effective coverage in subpopulations;

• Relationship (mathematical function and point estimates) between different levels of effective coverage in subpopulation and indirect effectiveness in unvaccinated individuals after vaccination of subpopulation;

Additional analysis (if not reported): calculated relationship (mathematical function) between different levels of effective coverage in subpopulation and changes in RR in unvaccinated population.

Function fitting process

The linear function calculated from Equation 3 in Bauch et al. (2009)

In a second approach, a linear function was fitted to the point estimates identified through the structured literature review as best predictors of the functional relationship between effective coverage in children and RR of infection in the unvaccinated remainder of the population. Theoretically, the linear function calculated from Equation 2 in Bauch et al. (2009)
_{0} would then be the fitting parameter. However, Equation 2 in Bauch et al. (2009)
_{0} as a result of the fitting process would be of no epidemiological meaning.

Therefore, a simple linear function of the form

Results

Structured literature review

Figure

Flow diagram for the literature review.

**Flow diagram for the literature review.**

Studies included

A total of 21 publications were included, two of which

**Study**

**Source**

**Type of study**

**Outcomes reported as relevant for model population***

* Outcomes assessed as not useful for the current study are given in parentheses.

Clover et al. (1991)

Other searches

Trial

Point estimates

Elveback et al. (1976)

Other searches

Model

Mathematical function deducible

(Point estimates)

Esposito et al. (2003)

Other searches

Trial

Point estimates

Ghendon et al. (2006)

Database

Trial

Point estimates

Glezen et al. (2010)

Database

Trial

(Point estimates)

Gruber et al. (1990)

Other searches

Trial

Point estimates

Halloran et al. (2002)

Database

Model

Mathematical function deducible

Point estimates

Hurwitz et al. (2000)

Other searches

Trial

Point estimates

Lemaitre et al. (2009)

Database

Trial

(Mathematical function)

Loeb et al. (2010)

Database

Trial

Point estimates

Milne et al. (2010)

Database

Model

(Mathematical function)

Monto et al. (1969)

Database

Trial (both articles reporting the same trial)

Point estimates

Monto et al. (1970)

Other searches

Piedra et al. (2007)

Database

Trial

(Point estimates)

Piedra et al. (2005)

Database

Trial

(Point estimates)

Pradas-Velasco et al. (2008)

Database

Model

Additional information on the mathematical function

Principi et al. (2003)

Other searches

Trial

Point estimates

Rudenko et al. (1993)

Other searches

Trial

Mathematical function

Point estimates

Van den Dool et al. (2008)

Database

Model

Mathematical function

Vynnycky et al. (2008)

Database

Model

Point estimates

Weycker et al. (2005)

Database

Model

Mathematical function deducible

(Point estimates)

Studies reporting data useful for the estimation of a mathematical function

The first aim of the literature review was to identify studies that allowed us to test whether a linear relationship between varying degrees of effective coverage in subgroup populations and the reduction of risk of influenza infection in a larger unvaccinated population was a plausible assumption for annual seasonal influenza vaccination. Eight studies identified in the review reported a mathematical function, allowed the recalculation of data and creation of a graph, or provided other data relevant to this aim. Of these, two were not further considered because the function could not be solely attributed to indirect effects

Of the remaining six studies, two provided a graphical illustration

**Additional details of published studies.**

Click here for file

Graphical relationships between vaccine coverage and herd effect in published studies

**Graphical relationships between vaccine coverage and herd effect in published studies.** Relationship between effective vaccine coverage in subpopulation and relative risk of influenza infection in the population analysed for herd effect. Based on data from five studies

Overall, the studies reporting data useful for estimating mathematical functions suggested that within an effective coverage range (vaccine efficacy combined with coverage) of 20% to 80% of the subgroup targeted for vaccination, there was evidence for a linear relationship between effective coverage and RR. For very low effective coverage levels (<20%), literature did not reveal a mathematical function for the relationship between effective coverage and relative risk. However, findings indicate that herd effect is relevant even with very low levels of coverage and can be even greater than direct effect

Studies reporting point estimates

The second aim of the literature review was to identify point estimates for the reduction of influenza infection in the unvaccinated population after vaccination of children, which can be used to populate the linear mathematical function defined from literature. A total of 16 articles on 15 studies reported point estimates or allowed the recalculation of point estimates on the reduction of influenza incidence in the unvaccinated population after vaccination of children. The herd effect was evaluated either at the community level (8 studies

Of the studies evaluating herd effect at a community level, five were considered unsuitable for estimation of point estimates. Three studies

Table

**A. Effective coverage in children**

**0.0%**

**21.00%**

**35.00%**

**45.65%**

**49.00%**

**60.00%**

**62.30%**

**Proportion of children in the total population, for estimating B.**

**25.78% **

**25.78% **

**35.70% **

**25.78% **

**21.08% **

**25.78% **

**B. Change in effective coverage in entire population (induced by varying levels of effective coverage in children)**

**0.0%**

**5.41%**

**9.02%**

**16.30%**

**12.63%**

**12.65%**

**16.06%**

Point estimates for relationship between relative risk of infection in unvaccinated population as a function of (A) effective coverage in children, and (B) change in effective vaccine coverage in entire population induced by varying levels of effective coverage in children, and the corresponding RR estimates from the fitted general linear equations.

*_{
unvaccinated children
} = 1–1.2031*

**_{
other age groups
} = 1–4.6656*(_{
children
}.

**Study and population analysed**

Vynnycky et al. (2008)

1.00

0.44

Influenza A, 15–44 years, minimum

Vynnycky et al. (2008)

1.00

0.05

Influenza A, 15–44 years, maximum

Loeb et al. (2010)

1.00

0.39

Entire (unvaccinated) population

Halloran et al. (2002)

1.00

0.80

0.59

0.42

0.29

Unvaccinated children

Halloran et al. (2002)

1.00

0.77

0.58

0.41

0.28

Adults

**RR estimates from fitted general linear equation**

A. In unvaccinated remainder of children *

1.00

0.75

0.58

0.45

0.41

0.28

0.25

B. In other age groups **

1.00

0.75

0.58

0.24

0.41

0.41

0.25

Eight studies provided information on herd effects in subpopulations after vaccination of children. Seven studies (8 publications) evaluated herd effect in household or family members

Point estimates from studies evaluating herd effect in a subpopulation in published studies

**Point estimates from studies evaluating herd effect in a subpopulation in published studies.** Single data points show point estimates of relative risk (RR) of influenza infection in subpopulation analysed for herd effect plotted against effective vaccine coverage in children. Point estimates from studies evaluating herd effects at a community level are shown as lines (derived by connecting lines through the point where RR = 1.0 and effective coverage = 0%) for comparison.

Therefore, the studies evaluating herd effect at a community level were considered to provide better point estimates than the studies on herd effects in subpopulations, both because of methodological limitations in the subpopulation studies and the questionable ability to generalise their results to herd effects in the entire population. The minimum and maximum values from the study by Vynnycky et al. (2008)

Estimating RR in the unvaccinated remainder of the age group targeted by childhood vaccination, as a function of effective coverage in that age group

The point estimates identified by the structured literature review as the best predictors of herd effect in the age group targeted by childhood vaccination are shown in Table

Linear relationships between effective vaccine coverage and herd effect

**Linear relationships between effective vaccine coverage and herd effect.** Point estimates identified from the literature review and linear relationships (derived from Equation 3 in Bauch et al. (2009)
**A**) effective coverage in children, and (**B**) change in effective vaccine coverage in entire population induced by varying levels of effective coverage in children.

Figure

These findings indicate that for this age group there are two possible approximations for estimating the indirect effect on the annual risk of infection that could be included in a static model. The approach derived from Equation 3 of Bauch et al. (2009)

The approach derived from the linear equation fitted to the data from the literature review provides a slightly less conservative estimate of herd effect:

With this equation, RR = 0 when effective coverage in children is higher than −1 / (− 1.2031), or 83.1%.

Estimating RR in other age groups, as a function of change in effective coverage in the entire population induced by varying levels of effective coverage in children

Table

The effective coverage in the age groups not being targeted by the childhood vaccination strategy differs among the studies identified as best predictors, since most age groups were partially vaccinated in the base case or control group. As such, the RR values calculated during the literature review correspond to the change in effective coverage in the entire population induced by increasing effective coverage in children. For this reason, this change in effective coverage in the total population was recalculated, based on the age distribution applied in the corresponding studies (Table

Figure

For the age groups not targeted by the childhood vaccination strategy, there are two possible approximations for estimating the indirect effect on the annual risk of infection that could be included in a static model. The approach derived from Equation 3 of Bauch et al. (2009)

where P_{children} is the proportion of children (i.e. the age groups targeted by a childhood vaccination strategy) in the total population.

The approach derived from the linear equation fitted to the data from the literature review provides a more optimistic estimate of herd effect:

With this equation, RR = 0 when the change in effective coverage in the entire population induced by effective coverage in children (effective coverage in children * P_{children}) is higher than −1 / (−4.6656), or 21.4%, or – equivalently – if effective coverage in children is higher than 21.4% / P_{children}.

Discussion

Studies have shown that the potential benefit of vaccinating children against influenza extends to other members of their families, which supports the recommendation to make wider use of influenza vaccine in healthy children of any age in order to reduce the burden of infection on the community. The vaccination of otherwise healthy day-care and school-aged children may significantly reduce indirect influenza-related costs, thus supporting earlier economic modelling analyses of immunization programs

The structured literature review provided evidence to support the hypothesis of a linear relationship between effective coverage and RR within an effective coverage range (vaccine efficacy combined with coverage) of 20% to 80% of the subgroup targeted for vaccination. Point estimates identified from the literature review allowed the fitting of a linear equation of the form y = a + bx for each of two broad age groups, the age group targeted by a childhood vaccination strategy (i.e. children) and the group not targeted by the vaccination strategy (i.e. adults and/or elderly people). In children, the fitted equation was not very different from the slightly more conservative function derived from Equation 3 in Bauch et al. (2009)

Limitations

A non-dynamic approximation such as those presented here cannot replace a fully dynamic modelling approach, and should only be intended for a preliminary assessment of herd effect

Our second linear approximation is only intended for exploratory purposes, since it implicitly assumes a constant basic reproduction number (R_{0}) for seasonal influenza. The potential bias induced by this assumption is likely to be marginal for seasonal influenza, since R_{0} estimates for these epidemics are low and fairly constant

Although the literature review conducted was not systematic, it was structured in a transparent and reproducible manner, with search terms, eligibility criteria and data extraction defined in advance. An independent reviewer checked all included studies and data extracted, in an effort to minimise selection bias. However, the initial screening process included studies that could not be ruled out with certainty, and reasons for exclusion were documented for all studies rejected after full text review. In addition, the inclusion of studies from sources other than the database search (in this review, mainly from reference lists) also bears a risk of selection bias. Most of the studies identified as useful for the main aim of the project were derived from the database search, and the two which came from other sources

The literature review did not reveal a mathematical function for the relationship between the relative risk in unvaccinated and very low (<20%) or very high (>81.1%) effective coverage levels in a subpopulation. However, findings have indicated that herd effect is relevant even with very low levels of coverage and can be even greater than direct effect
_{0}

For very high levels of effective coverage, i.e. very high coverage and vaccine efficacy, a linear function might overestimate the impact of herd effect and a flattening of the curve, i.e. a more exponential function with exponent <1 in age groups others than those considered for mass vaccination might be expected. However, this is a more intuitive conclusion, rather than based on evidence from literature search.

Depending on the study, the RR of infection was calculated from either the probability of infection (modelling studies) or the probability of symptomatic influenza (observational studies). Thus, we implicitly assumed that both probabilities are linearly related, so that the RR is identical irrespective of which outcome is considered. It is however important to note that the RR obtained with our approximations refer to the baseline risk of true influenza infections (whether or not symptomatic), and do not reflect the reduction in risk of influenza-like-illness (ILI). Seasonal influenza vaccination is not efficacious against ILI other than true influenza, and hence will only partially reduce transmission of all ILI. As such, the effective coverage estimates to be applied in our linear approximations should be based on vaccine efficacy against true influenza, and not vaccine effectiveness against ILI. And consequently, our approximations can only be applied in cohort models operating on the basis of true influenza and its health and economic consequences.

Our second linear equation fitted to the point estimates in this literature review assumes that individuals in a population mix randomly within and between all age groups, and do not take account of the variety of mixing and contact patterns apparent in real life. The wide range between the minimum and maximum point estimates derived from Vynnycky et al. (2008)

A further limitation is that the approximation of herd effect in age groups not targeted for vaccination does not account for any effective vaccine coverage already present in those age groups. If effective coverage is already substantial in these age groups, a modest increase in effective coverage in the total population induced by vaccinating children might result in a situation where the elimination threshold is exceeded and RR falls to zero. As such, the magnitude of the herd effect reported by the studies identified in this review is dependent on the pre-existing vaccine coverage in the age groups not targeted for vaccination. This could explain why the point estimate derived from the study by Loeb et al. (2010)

For the purpose of this study, point estimates of effective coverage were derived or calculated from vaccine efficacy data reported in the various publications. There is a risk of bias when using data from observational studies since the vaccinated population might also potentially benefit from a reduction in the baseline risk of influenza (indirect effect), where observed vaccine efficacy is in fact the sum of both direct and indirect effects of vaccination. However, the linear fitting in our study was performed against data extracted from three publications in which this risk of bias is not present or negligible: the two modelling studies compared the post-vaccination population against a pre-vaccination population

As a result of these limitations, we would recommend using the more conservative approach (the linear function derived from Equation 3 of Bauch et al. (2009)

Conclusions

This method of approximating herd effect does not rely on dynamic modelling and can be used in static models. It requires simple adjustments to the annual baseline risk of influenza, first for the age group targeted by the childhood vaccination strategy (i.e. children), and second for other age groups not targeted by vaccination (e.g. adults and/or elderly people). We present two approximations that provide a linear relationship between effective coverage and reduction in the risk of infection. The first is a conservative approximation, recommended as base-case for cost-effectiveness evaluations. The second, fitted to data extracted from a structured literature review, provides a less conservative estimate of herd effect and is recommended for use in sensitivity analyses.

Abbreviations

RR: Relative risk; SSR: Sum of squared residuals; WHO: World Health Organization; ILI: Influenza-like-illness.

Competing interests

GM is an employee of GlaxoSmithKline group of companies and holds stock or stock options in GlaxoSmithKline group of companies.

IVV’s and LAVB’s institution received consulting fees from GlaxoSmithKline Biologicals SA for conducting the present study and writing the manuscript outline, and has also received consultancy fees from GlaxoSmithKline Biologicals SA for other projects and for writing manuscript outlines related to these other projects.

BNP received consulting fees for conducting the literature review and fees for writing the manuscript outline from GlaxoSmithKline Biologicals SA in relation to the present study.

Authors’ contributions

IVV, LAVB and GM designed the study, BPN conducted the literature review, IVV was an independent reviewer of the literature review. IVV and LAVB carried out the mathematical analyses and fitting of the linear equations. All authors reviewed and commented on manuscript drafts, and read and approved the final manuscript.

Acknowledgements

The authors thank Maud Boyer (Business and Decision Life Sciences) for publication co-ordination and Carole Nadin for medical writing services on behalf of GlaxoSmithKline Biologicals SA, Rixensart, Belgium. This study, including preparation of the manuscript, was funded by GlaxoSmithKline Biologicals, Wavre, Belgium.

Pre-publication history

The pre-publication history for this paper can be accessed here: