Model overview
We used a previously published compartmental (Susceptible-Infected-Recovered-Vaccinated) dynamic transmission model capturing the pairwise interactions of two influenza A strains, A/H1N1 and A/H3N2, and two influenza B lineages, B/Yamagata and B/Victoria [26]. Interactions between the strains were assumed to occur via both natural and vaccine-conferred partial cross-reactive immunity. We assumed that influenza A to B cross-protection is negligible, and modeled only pairwise cross-protection between the two A strains, and between the two B lineages, respectively. The overall structure is thus of a pair of essentially independent two-strain models. Age-dependent contact patterns were specified using a contact matrix [27, 28] to calculate the force of infection. This model was run over a 10-year time horizon, following a 30-year burn-in period. A detailed description of model structure, assumptions and calibration methodology are given in [26]
The model’s structure makes it capable of reproducing the key transmission dynamics of seasonal influenza, specifically herd immunity, strain interaction, waning immunity and dependence on population contact patterns. A small background contribution to the force of infection (corresponding to case importation) varies randomly from season to season, (separately for influenza A and B), thus rendering individual simulations stochastic. Model parameters were fit using an approximately Bayesian computation (ABC) parameter fitting scheme [29], similar to those used previously for fitting human papillomavirus models [30, 31]. The model was calibrated using, as fitting targets, the United States of America (US) unvaccinated (natural) influenza attack rates and year-to-year relative amount of influenza A compared to influenza B [21, 32]. Calibrating on only the unvaccinated population removes direct dependence of the attack rate on the efficacy and uptake of influenza vaccine in the population, though it is still coupling through herd immunity; for this reason the season-by-season vaccine uptake in the US population was also included in the calibration. Further details of the calibration process are given in [26]. The resultant posterior distribution of sets of influenza natural history parameters was then applied to the populations of two countries considered in this analyses - Canada and the UK. The detailed methodology of the calibration of this model is described in Thommes et al. [26].
Model input data and assumptions
Baseline demographic, cost, utility and vaccine-related input parameters for the dynamic transmission model were obtained from locally available databases and published literature, details of which are described below (for details see Additional file 1).
Intervention strategy
In Canada, where TIV is predominantly used in provincial or territorial public programs, we evaluated a full switch from TIV to QIV in individuals of all age groups, at the current nationwide vaccine uptake level (2014). To capture current recommendations and practice in the UK [18, 19], we evaluated two strategies: Children aged 2–17 years who receive the live-attenuated influenza vaccine (LAIV), while individuals of ages 18 and above receive TIV. In this analysis, the latter age group undergoes a switch from TIV to QIV and children aged 2–17 years undergo an analogous switch from the trivalent formulation of LAIV to the quadrivalent formulation of LAIV (QLAIV). Given that the pediatric vaccination program in the UK is currently in its rollout phase, two different vaccination uptake scenarios in children (denoted UK1 and UK2) were evaluated.
Demographics
Demographic data, including birth and all-cause mortality rates for Canada were based on the year 2012 and were obtained from the Statistics Canada’s CANSIM online database [33]. For the UK, demographic data, birth and all-cause mortality rates were obtained from the Office of National Statistics (data based on mid-2010 population estimates) [34]. Age-dependent contact patterns specific to Canada are unavailable and hence data from the US were used [35]. For the UK, the relevant contact matrix from Mossong et al. (physical and non-physical contacts) was used [36]. The UK matrix is in terms of number of daily contacts, whereas the US matrix is in terms of daily minutes of contact; since the natural history parameter calibration was performed using the US matrix, the UK matrix had to be converted. We did this assuming a linear relationship between daily minutes and the number of contacts, with the scaling factor chosen to yield the same dominant eigenvalue for UK matrix as for the US.
Outcome probabilities
Four outcomes of symptomatic influenza were considered in this analysis – general practitioner (GP) visit, emergency room (ER) visit, hospitalization and death. In the absence of available Canada-specific outcomes probabilities, the US-derived values of Molinari et al. [37] for GP visits, hospitalization and death were used. Probability of an ER visit was derived from the probability of hospitalization using a fixed ratio between the two quantities [24]. For the UK, these outcome probabilities were obtained from Turner et al. [32] (GP visit), Tappenden et al. [38] (ER visit and hospitalization) and Meier et al. [39] (death) (Additional file 1, see Table 1.1, 1.2).
Utilities
Age-specific life-expectancy was obtained from the Life Tables and Interim Life Tables for Canada [40, 41] and the UK [42], respectively. Baseline utilities for Canada and the UK were obtained from Mittmann et al. [43] and Tappenden et al.[38], respectively (Additional file 1, see Table 1.3). For Canada, quality-adjusted life-year (QALY) loss per uncomplicated case and medically-attended influenza case were obtained from Tarride et al. [24] and Sander et al. [44], respectively. For the UK, these quantities were obtained from Tappenden et al. [38] (Additional file 1, see Table 1.4).
Vaccine uptake
Vaccine uptake rates for Canada in children aged 6–23 months and 2–11 years were obtained from Moran et al. [45] and for individuals aged ≥12 years from Statistics Canada’s CANSIM online database [33] (Additional file 1, see Table 1.5). For the UK, individuals, clinically at-risk (ages 18–64 years and 65+ years) are vaccinated and a universal childhood vaccination program for children of ages 2–17 years is being phased in as of 2013. Given the ongoing changes in child vaccine uptake, we thus considered two scenarios (UK1 and UK2) which differ only in the vaccine uptake in children 2–17 years of age (Additional file 1, see Table 1.6).
Vaccine efficacy and adverse events
Vaccine efficacy against influenza A was assumed to be identical for both TIV and QIV. The average efficacy of TIV against influenza A was estimated from three Cochrane reviews in healthy children [46] adults [47] and elderly individuals [48]. This is also supported on the basis of non-inferiority data of QIV and TIV from a vaccine effectiveness study comparing both vaccines [49]. TIV efficacy against influenza B for both a lineage match and mismatch was obtained from a meta-analysis of clinical trials [8]. QIV efficacy against both lineages of influenza B was assumed to always be that of TIV against the matched B lineage. Due to limitations in LAIV influenza B match-mismatch efficacy data in children of ages 3 and above [8], identical efficacies were used for matched LAIV, mismatched LAIV and QLAIV for ages 3–17 years (Additional file 1, see Table 1.7, 1.8). Vaccine-conferred protection against both influenza A and B was assumed to last only one year on average [50].
Data from clinical trials show that QIV and TIV have similar safety profiles [13, 15, 49]. Moreover, with both vaccines the occurrence of adverse events was low, and when present transient in nature [38]. Thus we excluded this parameter in the model.
Costs associated with resource use
All costs are reported in the national currencies of the two countries, i.e. the Canadian dollar ($) and Great British Pound (£). The reference year for costs was 2013. For Canada, when costs were unavailable for 2013, they were inflation-adjusted to 2013 using the Canadian Consumer Price Index [33]. In this analysis we considered the payer perspective and therefore only direct medical costs were included. Costs per GP and ER visit for Canada were obtained from Tarride et al. [24] For cost per hospitalization, data from the Canadian Institute for Health Information (CIHI) Patient Cost Estimator tool was used [51]. UK cost data was obtained using multiple sources, analogous to Van Bellinghen et al. [22] (Additional file 1, see Table 1.9).
Vaccination costs
For Canada, the blended price of TIV was estimated as an average from published sources at $6.18 per dose [24, 44, 52]. For the UK, the price of TIV was calculated as a weighted average of all TIV available on the UK market and estimated at £6.39 per dose [53]. For QIV in the UK, the list price of £9.94 per dose was used [54]. This constitutes a TIV-QIV price difference of a factor of ~1.56; a hypothetical QIV price for Canada of $9.61 per dose was derived assuming the same relative price difference. Finally, for LAIV and QLAIV, modeled only in the UK scenarios, the list price of £14.00 per dose was used [54]. For Canada, cost of vaccine administration is taken to be at $3.78 [44]. In the UK, vaccination was assumed to take place as part of a regular GP visit, and thus to incur no additional vaccine administration cost (Additional file 1, see Table 1.9).
Analyses
Base case analyses
Health and cost outcome measures resulting from the two vaccination strategies (QIV and TIV) and the difference between QIV and TIV are estimated. For Canada, calculations were performed using a discount rate of 5 % per year for monetary and utility costs as well as outcomes [55]. In the case of the UK, a discount rate of 3.5 % per year was applied to costs and outcomes [56] (see Additional file 1, Table 1.10). To determine the cost-effectiveness of implementing a switch from TIV to QIV, the incremental cost-utility ratio (ICUR) was calculated from the third party payer perspective. Cost-effectiveness thresholds of $40,000–50,000 per QALY gained [44] and £20,000 per QALY gained [57] were assumed for Canada and the UK, respectively.
To simulate the impact of a switch from TIV to QIV in Canada and the UK, we performed for each country a set of 1,000 pairs of simulations with the influenza natural history input parameters for each pair drawn from the aforementioned posterior parameter sets. Each pair consists of one simulation in which a switch from TIV to QIV occurs in the 2014–2015 season (the intervention), and another in which the use of TIV is continued (the comparator). For each simulation, results were recorded from the beginning of the 2014–2015 season to the end of the 2023–2024 season, i.e. over ten seasons. Seasonal averages of influenza infections were estimated for this time period.
Deterministic sensitivity analyses
In each scenario evaluated, the distributions of outcomes produced by our ensemble of 1,000 simulation pairs reflects both our uncertainty about the true natural history parameters of influenza, and the stochastic nature of the individual simulations. In other words, our ensemble of simulations constitutes a probabilistic sensitivity analysis (PSA) on natural history parameters of influenza as well as on the variability of influenza seasons.
We also performed a combination of univariate and multivariate sensitivity analyses to investigate the sensitivity of the model outcome, specifically, of the point estimate of cost per QALY gained (i.e. the ICUR) estimated by the model. Different parameters were varied:
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▪QIV price per dose (Canada and UK) to the upper and lower limits of their respective range values, see Additional file 1, Table 1.9.
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▪QALY loss (one-sided analysis; for the lower bound, we neglected all non-death QALY loss),
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▪All breakthrough infection outcomes: If vaccination reduces the severity of influenza in breakthrough infections (i.e. infections of people who are vaccinated within the current season), this has the potential to reduce the benefit of QIV relative to TIV. In this sensitivity analysis (multivariate and one-sided), the most extreme possible scenario was considered, wherein TIV and QIV both have 100 % efficacy against all influenza-associated outcomes (GP visit, ER visit, hospitalization and death). This was done by simultaneously setting all the corresponding outcomes probabilities to zero for breakthrough infections.
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▪Probability of hospitalization (P_hosp), breakthrough infection: Like all breakthrough infection outcomes above, but with 100 % vaccine efficacy only against hospitalization. Vaccine efficacy against all other outcomes is as in the base case, equal to the vaccine efficacy against infection.
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▪Outcomes probabilities: Multivariate analysis with all outcome probabilities varied simultaneously at their 95 % confidence interval (CI) lower and upper limits (see Additional file 1, Table 1.1, Table 1.2).
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▪Discount rate: For Canada (base case = 5.0 %) and the UK (base case = 3.5 %) one-sided sensitivity analysis using 3.5 % and 5.0 % discount rates, respectively, and,
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▪GP cost, ER cost, and hospitalization cost: For Canada and the UK to the upper and lower limits of their respective range values (see Additional file 1, Table 1.9).
