Dynamic modelling approaches for the analysis of the cost-effectiveness of seasonal influenza control

KEYWORDS:

• Cost-effectiveness analysis
• dynamic modelling
• seasonal influenza
• vaccination

Influenza is an acute respiratory infection primarily caused by influenza virus types A or B [1]. Next to occasional pandemics, influenza virus causes annual seasonal outbreaks. Globally, these annual influenza epidemics are responsible for approximately 250,000–500,000 deaths and a wide range of other health-related and economic consequences [1–3]. Therefore, control of seasonal influenza through preventive measures such as vaccination has become a major priority for public health authorities.

Mathematical models can be used to estimate the effectiveness and cost-effectiveness of influenza vaccination. Many different mathematical models with varying levels of complexity exist, ranging from simple, static, models to more complex, dynamic, models. Dynamic models allow for the explicit inclusion of transmission of influenza between and within different age groups with potential variation over time, whereas static models do not allow this [4]. For many years, most studies have relied exclusively on static models for modeling seasonal influenza [5]. However, currently, it is increasingly understood that for valid estimates of the cost-effectiveness of infectious diseases’ control, only dynamic models adequately capture changes in the probability of infection over time [5,6]. Use of such dynamic models is also fully in line with recommendations of the International Society of Pharmacoeconomics & Outcomes Research [4]. While we previously reported on the use of dynamic models for estimating the cost-effectiveness of control measures for pandemic influenza [7], this editorial aims to review their use in seasonal influenza control.

A PubMed search was performed in order to select relevant English-language studies on the cost-effectiveness of seasonal influenza vaccination using a dynamic modeling approach and those published before June 2016. This search resulted in 12 studies. For this editorial, we highlight six of these studies which we agreed to be noteworthy in that they reflect various issues of relevance, all from a different perspective. In particular, these six studies address different targeted populations (i.e. children, elderly, and all ages), different countries (i.e. Canada, UK, United States, and Germany), and different vaccine types including inactivated trivalent influenza vaccine (TIV), inactivated quadrivalent influenza vaccine (QIV), and live attenuated influenza vaccine.

A first notable example of our current interest in dynamic modeling of seasonal influenza relates to the article by Thommes et al. [8]. In this article, both the epidemiology and the economic consequences of the switch from TIV to QIV were analyzed for Canada and the United Kingdom. The authors used a compartmental dynamic transmission model from a previous publication [9], with susceptible (S), infected (I), recovered (R), and vaccinated as the explicit compartments, typical for this kind of SIR models. For the age-dependent contact patterns, the contact matrix from Mossong et al. [10] was employed for the UK, and data from the United States were used for Canada [11]. Due to its dynamic structure, the model was able to reproduce the crucial transmission dynamics of seasonal influenza, including indirect effects, strain interaction, waning immunity, and interactions within contact patterns.

Another typical example of a dynamic compartmental model can be found in the article by Crepey et al. [12]. A SIR model was used to study the retrospective impact of QIV on the number of influenza infections in the United States over the years 2003–2013. The model was calibrated using weekly incidence data of influenza in the period of 2000–2013 and accounted for cross-protection of TIV against the second influenza virus B strain not included in the vaccine. The authors found that QIV could have led to a reduction of 661,600 influenza cases per year compared to TIV, which represents approximately twice the number that Reed et al. [13] estimated in the period of 2001–2009 using a static approach. In a separate analysis by de Boer et al. [14], the dynamic model was linked to a health–economic decision model to translate the number of influenza cases prevented into cost-effectiveness outcomes. Indeed, the incremental cost-effectiveness ratio (ICER) was found to be US$27,400, which is threefold lower than the ICER found in a previously published study using a static approach [15].

The above analyses on high-risk populations like the elderly and people with comorbidities used dynamic models to fully reveal the benefits of one vaccination strategy against another. Nonetheless, it may be expected that static models might also have identified corresponding trends in preference for a specific vaccine, although potentially underestimating benefits in terms of cost-effectiveness due to possibly sizeable indirect effects. Notably, in this case involving vaccination of a high-risk population, the potential correspondence between the outcomes of dynamic and static models is related to the fact that the expected benefits of a new vaccination strategy are due to direct – primary – protection of the vaccinated group. However, there are other target groups of interest for influenza vaccination, including pregnant women, health-care workers, and children. Here, dynamic modeling is likely to be the only type of modeling to arrive at valid conclusions on the cost-effectiveness of vaccination, whereas static modeling will probably fail to do so [16]. In particular, over the last decade, various studies have reported that it could be a cost-effective option to extend influenza vaccination to children. Although influenza-related mortality among children is low, hospitalization rates due to seasonal influenza among children are high, and parental work loss is significant with major benefits to be achieved [17]. Additionally, and possibly more importantly, children are responsible for much of the transmission of influenza among their relatives, and, thus, pediatric influenza vaccination may provide indirect benefits through herd protection of vulnerable high-risk groups [18]. Dynamic models are essential here to adequately quantify and valorize these indirect effects.

The question as to whether extension of influenza vaccination from conventional target groups (elderly and other traditional risk groups) to children is cost-effective has been analyzed by Pitman et al. for England and Wales, using a dynamic model [19]. The authors used a previously published extended SIR model [4], and, for the age-dependent contact patterns, the results of the POLYMOD (Improving Public Health Policy in Europe through Modelling and Economic Evaluation of Interventions for the Control of Infectious Diseases) study were used [10]. With this model, the economic benefits of influenza vaccination of children were analyzed over a 200-year time horizon. It was argued that the vaccination of children aged 2–18 years could be the most cost-effective policy of those investigated. Indeed, it is expected that this policy will cost roughly £250 per quality-adjusted life year gained, which is obviously below any threshold ever considered for the UK.

Thorrington et al. published another typical example of a dynamic approach for extending influenza vaccination policies to children for the UK [20]. This study also used an extended SIR framework, as well as the POLYMOD study of Mossong et al. [10]. The aim of this study was to determine whether a vaccination program in either primary (age 4–11 years) or secondary (age 11–16 years) schools would be more cost-effective than a single vaccination program across both age groups. The authors came to the same conclusion as that of Pitman et al. [19], namely that a heterogeneous vaccination program stretching across both groups would be the optimal policy, with all three pediatric vaccination strategies investigated (heterogeneous, secondary, and primary schools) being cost-effective.

Obviously, both UK studies strengthen the arguments in favor of pediatric vaccination. In the meantime, the UK has indeed implemented pediatric influenza vaccination. Other countries may follow the example. Damm et al. published a health–economic analysis on pediatric vaccination for Germany in 2015 [21]. The objective of this study was to make a comparison between the health-related and economic consequences of vaccinating healthy children versus vaccinating high-risk groups. A dynamic modeling approach with a 10-year time horizon was used [21,22]. The extension of the vaccination policy to children was estimated to lead to a substantial decrease in morbidity and mortality across all age groups, due to direct and indirect protection. Furthermore, the results indicated potentials for cost savings. This example, and both previous examples from the UK, illustrates how dynamic models are indispensable for analyzing the specific issues related to pediatric influenza vaccination.

In contrast to static models, dynamic models are notoriously ‘data-hungry.’ Reliable data are needed for model parameters involving, for example, duration of protection induced by vaccination or by natural infection and the extent of cross-immunity between different influenza strains and subtypes. In current modeling studies, duration of protection provoked by natural infection is typically set at 6 years for influenza A viruses and 12 years for influenza type B [23]. However, these durations are merely based on assumptions and searches for reasonable inputs to successfully calibrate the model on the observed incidence patterns of influenza. Also little evidence on vaccine-induced protection is available, which for instance has been set equal to the duration of protection of natural infection [4] or been limited to 1 year [12]. Dynamic models have been helpful here in the identification of plausible ranges in the absence of decisive data. Further understanding and specification of such variables will likely have a significant impact on cost-effectiveness outcomes and may guide potential switches to alternative vaccination strategies such as biannual vaccination in the case of a longer duration of vaccine-induced protection.

Another challenge for complex dynamic transmission models is the model validation process. Obviously, the effort of code verification and validation of the model’s input parameters and outcomes will increase with the complexity of the model. In the case of influenza, dynamic models can be calibrated using historical surveillance data in order to find plausible values for input parameters where uncertainty is high [4]. If possible, validation of model outcomes against empirical is desirable, using either data on which the model is based (dependent validation) or data from other sources (independent validation). Finally, more systematic reporting of validation efforts is needed to improve the transparency of the validation process [24].

Summarizing, there are strong arguments for the use of dynamic models for analysis of the cost-effectiveness of seasonal influenza vaccination. First, it is argued that only dynamic models achieve valid, integral, and exact estimates of the savings and health effects of different vaccination strategies. Notably, static models – as opposed to dynamic models – would generally underestimate the benefits (e.g. of the use of QIV versus TIV in vulnerable elderly). Second, it should be realized that only dynamic models have the capacity to analyze those situations where indirect protection potentially represents the main goal (e.g. pediatric vaccination). It can be concluded that dynamic models are needed to reveal the full spectrum of costs and health savings of seasonal influenza vaccination. Indeed, this finding may be extended to all influenza control interventions – including, for example, school closures [25] and approaches to control pandemic influenza [7] – and ideally to the control of infectious diseases in general, whenever the intervention impacts transmission. Timely topics in seasonal influenza vaccination, such as the use of QIV versus TIV in elderly vaccination, higher dosing [26], and pediatric vaccination, therefore need to be addressed with dynamic modeling approaches. ‘Data hungriness’ is a well-known limitation of dynamic models. In this regard, analyzing initial ranges of core variables with dynamic models and comparison with available outcomes may help to limit core variables to smaller plausible ranges. Indeed, dynamic models have the potential to aid future research and policy also in this respect.

Declaration of interest

The appointment of P de Boer at the University of Groningen is partly supported by grants of Sanofi Pasteur, AstraZeneca, GlaxoSmithKline. The appointment of F Dolk at the University of Groningen is partly supported by grants of AstraZeneca, GlaxoSmithKline, Abbvie and ASC Academics. JC Wilschut has received advisory fees from Sanofi Pasteur, GlaxoSmithKline and Mymetics Corporation. R Pitman has received grants and honoraria from Sanofi Pasteur, AstraZeneca, GlaxoSmithKline, Novartis, Sanofi MSD and Pfizer. MJ Postma has received grants and honoraria from GlaxoSmithKline, Pfizer, Astellas, Astra Zeneca, Sanofi Pasteur, Sanofi Pasteur MSD, Vertex, SHIRE, Amgen, Novartis, Novavax, Intercept. MJ Postma owns 3% of shares of Ingress Health and is advisor to Mihajlovic Health Economics and ASC Academics. The authors have no other relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript apart from those disclosed.

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Funding

This paper was not funded.