Introduction
Simulation models are widely used in pharmacology, epidemiology and health economics (HEs). These models can explicitly link concepts and ideas to data in order to produce outcomes that are useful to healthcare decision makers [Reference Weinstein1]. Importantly, there have been no attempts to incorporate the models from pharmacology, epidemiology and HEs into a single integrated model.
While still performed infrequently, the importance of epidemiological modelling to inform economic analyses of prevention and treatment strategies for infectious diseases is well accepted [Reference Jit and Brisson2]. Cost-effectiveness analyses (CEAs) are typically conducted using static models in which the probability of disease exposure is independent of interventions designed to treat or prevent it. While this is realistic for non-transmissible diseases, it is not suited for communicable diseases given interventions in such circumstance can have a significant impact on disease exposure. For example, vaccines can reduce the susceptible population and antiviral treatments can reduce viral shedding, thus reducing viral transmission. Accordingly, dynamic transmission models are needed when there is interdependence between intervention and disease exposure [Reference Lugner, Mylius and Wallinga3]. These models allow the indirect or herd immunity effect to be predicted. Indeed, static and dynamic models produced dramatically different results [Reference Brisson and Edmunds4, Reference Brisson and Edmunds5]. Importantly, a recent review on economic evaluations of interventions for pandemic influenza planning reported most of the studies have used static models [Reference Lugner and Postma6].
In pharmacology, population pharmacokinetic/pharmacodynamic (PK/PD) models are used to identify optimal dosing regimens [Reference Duffull, Wright and Winter7] and were used recently to demonstrate that elevated doses of oseltamivir may result in reduced viral shedding [Reference Rayner8]. This has important implications for the economic evaluation of influenza pandemic planning as influenza viral transmission is a function of viral shedding [Reference Bulik9]. These indirect effects, which can be larger than the direct effects [Reference Pradas-Velasco, Antonanzas-Villar and Martinez-Zarate10], are often neglected in cost-effectiveness analyses. Any economic analysis failing to consider these indirect effects will have inaccuracies [Reference Pitman11].
Globally, the emergence or re-emergence of influenza outbreaks has been challenging [Reference Girard12–14]. Several economic evaluation studies have been conducted to facilitate the management of influenza outbreaks [Reference Kelso15, Reference Milne, Halder and Kelso16]. A recent systematic review reported that most economic studies used models that were incapable of incorporating variability of all parameters and did not consider the viral transmission process [Reference Pradas-Velasco, Antonanzas-Villar and Martinez-Zarate10]. Most importantly, existing models did not consider the indirect effects which are crucial in a pandemic mitigation strategy.
The current study explored the feasibility of linking pharmacology, epidemiology and HE models within the realm of anti-influenza treatment for pandemic influenza. We previously published an overall framework for the linking without a full description of HE models [Reference Kamal17]. To our knowledge, this is the first CEA to directly integrate data from PK/PD and disease transmission models into the economic analysis.
Methods
Linking of pharmacology and epidemiology to HEs models
Previously, a single semi-mechanistic framework assessed quantitatively the impact of oseltamivir pharmacology and treatment approaches on the burden of influenza infection in a hypothetical population of 100 000 individuals across a 1-year flu season [Reference Kamal17]. This model connected three discrete quantitative modules viz. a population pharmacokinetic model for oseltamivir; a PK/PD evaluation of oseltamivir carboxylate (OC, active metabolite) on viral shedding; and a susceptible-exposed-infected-recovered (SEIR) epidemiologic model, adapted to incorporate the impact of antiviral therapy.
Briefly, OC PK variability was incorporated using a published population PK model [Reference Kamal18] for OC incorporating 390 healthy and infected subjects ranging from 1–78 years across a dose range of 20–1000 mg. The final covariate model from this population PK analysis included allometric scaling and a relationship between weight on the OC central volume of distribution and between weight and creatinine clearance on OC clearance. From this final covariate model, OC PK parameter profiles in 5000 70-kg adult patients aged 18–65 with normal renal function receiving the standard 75 mg twice daily (BID) and 150 mg BID oseltamivir for 5 days was simulated. The area under the concentration-time curve (AUCs) for each patient were quantified and the fraction of patients with OC AUCs above a published PK/PD value associated with faster cessation of viral shedding (14 180 ng.h/ml) [Reference Rayner8] was calculated for each dosing regimen; and denoted as F AUChigh.
PD variability was integrated via incorporating viral shedding (T shed) distributions for placebo subjects, and those above and below the PK/PD target as obtained from literature [Reference Rayner8]. These PK/PD distributions and other SEIR input parameters (Table 1), allowed the average number of infected cases per 100 000 population to be determined for a range of scenarios relating to dose, viral transmissibility and treatment uptake (vide infra). The important innovation in the current work is the extension of the aforementioned quantitative framework to a decision analytic model to estimate the cost and outcomes of interventions of interest (Fig. 1). Both virus transmissibility and impact of anti-influenza agents alter the number of infected cases entering into the decision analytic model. As previously described, ß governs transmissibility, and is a composite of both frequencies of individual interactions, and the probability that an interaction will result in a successful influenza infection in a susceptible individual [Reference Kamal17]. The impact of antiviral treatment is via reducing the time an infected subject is infectious; governed by the duration of viral shedding. As an individual disease model is currently unavailable (Fig. 1), the severity of illness associated with influenza virulence is assumed to directly alter the probabilities of complications and associated costs in the decision analytic model.
Fig. 1. Overarching Pharmacology to payer system including ‘modules’. The solid lines indicate that adequate data exists to be able to create semi-mechanistic links to each of adjacent ‘modules’. The dotted lines and light grey describe where significant unknowns remain and are not mature enough to have been incorporated into the current framework. PopPK, population pharmacokinetic; SEIR, susceptible-exposed-infected-recovered; ß, the rate of infectivity; TShed, viral shedding; VK, viral kinetics.
Table 1. Parameters used in the SEIR model
κ, the delay rate between exposure to influenza and symptom development; F AUChigh, the mean (SD) fraction of the simulated population receiving oseltamivir with an AUC > 14 180 ng.h/ml, obtained from the pharmacology module; γ0, the duration of viral shedding under no treatment; γlow, the mean (SD) duration of viral shedding if OC AUC is <14 180 ng.h/ml; γhigh, the mean (SD) duration of viral shedding if OC AUC is >14 180 ng.h/ml, ß, the rate of infectivity; AUC, area under the concentration–time curve; BID, twice daily.
Health economics model structure and data inputs
The decision analytic model (Fig. 2) was developed to evaluate the cost and outcomes of oseltamivir standard (75 mg BID) or high (150 mg BID) dose or no treatment under pandemic influenza scenarios. The number of infected patients entering into the model was simulated from the SEIR model. A cost-utility analysis was undertaken based on the US population of healthy adults, aged 18–64 years old from the payer and societal perspective. Societal perspective included direct and indirect costs. Total costs, quality-adjusted life years (QALYs), and incremental cost-effectiveness ratios (ICERs) were determined over a 1-year time horizon.
Fig. 2. Decision analytic model. Influenza patients entered the decision analytic model from epidemiology model. They received treatment in outpatient or inpatient setting. OPD, outpatient; ED, emergency department; AVR, antiviral; GW, general ward; ICU, intensive care unit; ARDS, acute respiratory distress syndrome.
The infected individual entered the HE model either as an outpatient or inpatient (Fig. 2). Those admitted as inpatient would be admitted to a general ward or an intensive care unit, may experience either pneumonia, sepsis and acute respiratory distress syndrome (ARDS) [Reference Jain19–Reference Skarbinski21]. We assumed that patients could only experience one influenza-related complication. The infected patient either recovered from the infection or died. We assumed that oseltamivir was prescribed within 48 h of influenza symptoms and all patients were 100% adherent to treatment received.
A conservative approach involving oseltamivir acting only by reducing the duration of viral shedding and not directly on transmission rate was adopted. As such, only drug treatment effects and not prophylaxis effects were captured in the model. We assumed that oseltamivir reduces the time of symptom alleviation by 21 h and conservatively has no effects on complication, hospitalisation and mortality rate [Reference Burch22–Reference Michiels25]. Data about influenza disease progression, medical resource utilisation, cost of treatment and health state utilities were obtained from the literature (Medline searches) and Healthcare Cost and Utilization Project Nationwide Inpatient Sample database [26]. Where possible, data related to the 2009 pandemic H1N1 influenza was used. Meta-analyses were performed when applicable. All costs were converted to 2013 US dollars using the Consumer Price Index [27]. Base-case estimates and ranges for probabilities, costs, utilities and length of stay for hospitalisation are shown in Table 2; detailed descriptions available in Appendix 1.
Table 2. Input parameters, values and data sources used in the health economics model
CI, confidence interval; SE, standard error; ED, emergency department; GP, general practitioner; GW, general ward; ICU, intensive care unit; ARDS, acute respiratory distress syndrome; USD, United States Dollar; AWP, average wholesale price.
a Oseltamivir is available as 75 mg/capsule and in a pack of 10 capsules in the USA. The AWP for one pack of oseltamivir is USD 132.77.
b Weighted probability or cost estimate was calculated using probability or cost reported for two age groups, i.e. 18–49 and 50–64 years, assuming the age-distribution of the influenza adults is similar to that of the U.S. population in 2012 [50].
c Weighted cost or length of stay estimate was calculated using cost or length of stay reported for two age groups, i.e. 18–44 and 45–64 years.
d Reported as standard deviation.
e Calculated by multiplying 5 miles round trip and the standard business mileage rate 2013 for the use of a car.
f Calculated using the age- and sex-stratified median weekly earnings in the U.S. Bureau of Labor Statistics for the age group 18–64 years, taking account of the unemployment rate of 7.3%.
g Calculated using the length of stay reported and adding one additional day for convalescence [Reference Meltzer, Cox and Fukuda40].
h Khazeni et al. [Reference Khazeni41] adjusted for possible on-going disability following recovery from severe (all patients who received inpatient ICU care) influenza, which assumed an estimated quality of life of 0.9 for the remainder of those patients’ lifetimes. In our HE model, we assumed the value of 0.90 for the rest of the year for those patients.
Simulation scenarios and treatment comparison
We investigated the HE impact of two extreme hypothetical pandemic scenarios, namely, influenza virus with low virulence and low transmissibility and virus with high virulence and high transmissibility [Reference Russell51, Reference Kawaoka52]. The ß values for transmissibility were from Kamal et al. [Reference Kamal17], (see Table 1) whereas virulence was based on health care utilisation; low virulence was based on pH1N1 experience [Reference Girard12]; and the high virulence scenario involved doubling the probability of hospitalisation [Reference Lee53] for the low virulence scenario within the decision analytic model.
We evaluated three different management strategies: (1) no treatment, (2) the standard approved oseltamivir dose (75 mg BID) and (3) high dose (150 mg BID). We also evaluated the treatment strategies according to varying treatment uptake rates (25, 50 and 80%), defined as the percentage of infected subjects treated, across an infected population. Detailed descriptions of all values are available in Appendix 1. Analyses were performed using Berkeley Madonna™ version 8.3.18, R version 2.15.3 and Microsoft Excel 2010 (Redmond, Washington).
Sensitivity analyses
One-way sensitivity analyses were performed to investigate the effects of altering parameters within the plausible ranges (Table 2). Additional sensitivity analysis was undertaken to determine the robustness of estimates when a different approach for productivity loss estimation was adopted. In the base-case analyses, we adopted the approach in Meltzer et al. [Reference Meltzer, Cox and Fukuda40] Alternatively, we calculated productivity loss using the relationship between ‘time to return to normal activity’ and ‘illness duration’ (Appendix 1). We also varied the probability of developing ARDS in highly virulent and highly transmissible pandemic influenza case. Probabilistic sensitivity analysis (PSA) was undertaken to address uncertainty in the assumptions underlying the model by allowing each input parameter values to vary simultaneously over their respective feasible ranges within the model; 5000 second-order Monte Carlo simulations were performed in which the parameter values were drawn from pre-defined distributions. Results from the PSA are presented as scatterplots in cost-effectiveness plane.
Results
Low virulence and low transmissibility
Based on a hypothetical cohort of 100 000 individuals, under low virulence and low transmissibility, standard-dose oseltamivir (75 mg BID) was cost-saving from both perspectives compared to no treatment (Table 3). It could save USD30,246,490 (USD81,272,885), USD33,352,767 (USD93,993,932) and USD30,406,894 (USD92,614,326) for oseltamivir uptakes of 25%, 50% and 80% by averting 706, 412 and 783 deaths, respectively, from payer (societal) perspective. This translates to 361, 430 and 441 QALYs gained for uptakes of 25%, 50% and 80%, respectively.
Table 3. Base-case analyses: high-dose vs. no treatment, and standard dose vs. no treatment
a All costs are expressed in 2013 USD.
High-dose oseltamivir (150 mg BID) when compared to no treatment was also cost-saving from payer (societal) perspective (Table 3), leading to cost-saving of USD29,839,058 (USD85,192,106), USD27,742,305 (USD89,785,170) and USD20,483,671 (USD83,687,273) for uptakes of 25%, 50% and 80% by preventing 376, 423 and 430 deaths, respectively, leading to the associated QALY gains of 392, 441 and 449, respectively.
Compared to low-dose, high-dose oseltamivir would avert −30, −11, −7 deaths at 25%, 50% and 80% uptakes, respectively, leading to the associated QALY gains of 31, 11, 7, respectively. It led to overall increased cost of USD407,432, USD5,610,462, USD9,923,223 from payer perspective for uptakes of 25%, 50%, 80% uptakes, respectively, resulting in USD13,117, USD546,753, USD1,353,188 per QALY gained. From societal perspective, using high-dose oseltamivir could save USD3,919,221 at 25% uptake (cost-saving) but incurred extra cost of USD4,110,702 and USD8,927,052 at 50% and 80% uptakes, leading to USD377,524 and USD1,217,344 QALY gained, respectively.
High virulence and high transmissibility
Under the scenario of high virulence and high transmissibility, compared with no treatment, oseltamivir 75 mg BID was dominant (Table 3). It could avert 168, 617 and 1098 deaths, translating to 174, 598 and 1063 QALYs gained for the uptakes of 25%, 50% and 80%, respectively (Table 3). The standard-dose could save USD11,885,337 (USD27,413,072), USD49,309,677 (USD101,904,191) and USD88,899,525 (USD179,850,525) for 25%, 50% and 80% uptakes from payer (societal) perspective.
When high-dose oseltamivir was compared to no treatment (Table 3), it was shown to save USD24,304,917 (USD53,631,551), USD63,252,396 (USD133,577,886) and USD95,501,955 (USD200,976,888) for uptakes of 25%, 50% and 80%, by preventing 341, 844 and 1288 deaths, respectively, leading to the associated QALY gains of 330, 818 and 1247, respectively.
Compared to low-dose, our model indicated that high-dose oseltamivir would save USD12,419,581 (USD26,218,479), USD13,942,719 (USD31,673,695) and USD6,602,430 (USD21,126,363) from the payer (societal) perspective for uptakes of 25%, 50% and 80% (Table 3). In addition, 174, 227 and 190 deaths could be prevented, leading to QALY gains of 174, 227 and 189, respectively.
Sensitivity analyses
The tornado diagrams (Fig. 3) summarise the results of 1-way sensitivity analyses. Under low virulence and low transmissibility, at 80% oseltamivir uptake, the ICER was most sensitive to the probability of hospitalisation for ED cases and baseline average quality of life. Under the high virulence and high transmissibility scenario, the baseline average quality of life and median weekly earnings in the USA were the two most influential factors. The results were also very similar to the other uptakes and thus not shown.
Fig. 3. Tornado diagram (150 mg vs. no treatment with 80% uptake of oseltamivir): One-way sensitivity analysis under (1a) low virulence and low transmissibility and (1b) high virulence and high transmissibility. (a) Low virulence and low transmissibility. #+/−: The higher value of the parameter leads to lower ICER. $−/+: The higher value of the parameter leads to higher ICER. (b) High virulence and high transmissibility. #+/−: The higher value of the parameter leads to lower ICER.
Monte Carlo simulations (5000) for different levels of viral virulence, transmissibility and oseltamivir uptake from the societal perspective are presented in Fig. 4. In both scenarios, a very large proportion of the simulated results fell in the south-east quadrant, suggesting that 75 mg BID vs. no treatment at 25%, 50% and 80% uptakes were highly likely to be cost-saving. The results of 150 mg BID from a societal perspective were also very similar (data not provided).
Fig. 4. Scatter plots (incremental cost vs. incremental QALY) of 75 mg vs. no treatment under societal perspective. (a) Low virulence and low transmissibility. (b) High virulence and high transmissibility.
Discussion
This is the first study to link pharmacology, epidemiology and HE models into a single integrated model. We examined the costs and outcomes of different levels of oseltamivir dosing for pandemic influenza planning using the information from the PK/PD model to ultimately inform an HE model by way of an SEIR model. While we applied this novel linked model within the context of pandemic influenza, its usefulness is not limited to this arena. Our approach can also be useful for policy-oriented decision making surrounding the use of other antimicrobials agents.
Indeed, our results show that using standard- or high-dose oseltamivir will afford a significant reduction in deaths due to three major influenza-related complications over a 1-year time horizon, thus leading to substantial savings in both life years and QALYs under various degrees of virus virulence and transmissibility. The extra cost for oseltamivir was offset by reductions in the number of disease episodes and influenza-related deaths, resulting in substantial savings.
Several economic evaluations on influenza pandemic preparedness strategies have been published, including studies evaluating vaccine, pharmaceutical and non-pharmaceutical (e.g. social distancing) interventions with the majority focusing on anti-influenza drugs [Reference Pradas-Velasco, Antonanzas-Villar and Martinez-Zarate10]. Pharmaceutical interventions combined with non-pharmaceutical interventions have been found to be relatively cost-effective in comparison to vaccines and/or antivirals alone. However, pharmaceutical interventions vary from cost-saving to being not cost-effective [Reference Pradas-Velasco, Antonanzas-Villar and Martinez-Zarate10]. The wide range of cost-effectiveness results is due to several factors such as different dosages and durations for prophylaxis as well as the comparator. Our results showing cost-savings of oseltamivir under all scenarios and dosages were possibly due to the absence of consideration of concomitant treatments and the social contact structure among various subpopulations.
Despite the implementation of the World Health Organization's (WHO's) pandemic preparedness plan and response guide during the 2009 pandemic H1N1, experience and evidence suggest that the global community is ill-prepared to respond to a severe influenza pandemic or to any similarly global, life-threatening public-health emergency [54]. The possibility of the avian H5N1 becoming pandemic has raised concern and has been anticipated by the public health authorities [Reference Fineberg55]. This strain is a significant threat given its high fatality rate in humans, the large reservoir of poultry in South-East Asia and that H5N1 influenza may be genetically modified to become more transmissible [Reference Russell51, Reference Herfst56, Reference Imai57]. Importantly, the global community should be prepared for the next pandemic by having a full understanding of the consequences of influenza pandemics and their related interventions. In the current study, by using the 2009 pandemic data in the linked models, we explored the cost-effectiveness of oseltamivir as a pandemic mitigation strategy in two hypothetical pandemic scenarios with different severity, inspired by the 2009 pandemic H1N1 and H5N1. Our study did not consider the reported case fatality ratio (CFR) of H5N1 by the WHO due to inconclusive findings on the real CFR estimate by different sources [Reference Li58, Reference Cowling59]. Furthermore, the CFR may decrease as more information becomes available or as the epidemic progresses. Several recent studies from the Cochrane collaboration [Reference Jefferson60] and Muthuri et al. [Reference Muthuri61] have called into question the efficacy of oseltamivir. Therefore, we conservatively estimated the drug effect of oseltamivir based solely on viral shedding in our pharmacology component of the integrated model. Subsequently, in the HEs model, assumptions were made that oseltamivir shortened the duration of influenza symptoms by 21–22 h, but had no effect on the progression to secondary complications, hospitalisation or mortality [Reference Burch22–Reference Hsu24]. These assumptions may underestimate the true effects of oseltamivir during an influenza pandemic.
Our work has several limitations. First, we did not take into consideration other interventions such as the use of masks, school closure and influenza vaccine. The concurrent use of other interventions may reduce the impact of oseltamivir. Second, we assumed that all infected cases seek medical care, which might not be true in reality. Third, our model was confined to only a healthy population between 18 and 65 years of age. However, the model could easily be extended to include other patient populations. Finally, it is noteworthy that patients’ viral shedding duration for 75 or 150 mg BID was based upon detailed shedding data from a human inoculation study, where adults receive oseltamivir at 28-h post-inoculation. In reality, the impact on viral shedding will decrease, as patients initiate treatment later in their disease course. Therefore, even though many assumptions above may underestimate the true effects of oseltamivir during an influenza pandemic, delayed initiation of treatment would result in smaller clinical and HE benefits.
Despite these limitations, our study has many, important strengths. First, because we used a dynamic transmission model, we were able to incorporate important indirect effects of oseltamivir treatment. Second, we undertook substantial effort through comprehensive literature review and meta-analysis to synthesise the best available evidence in generating input parameters. We, therefore, feel that our model inputs are of highest quality. Third, not only is our integration of pharmacology into an epidemiological model of influenza transmission novel, it also allows for a more realistic drug effect variability than previous efforts which have relied simply on blunt assumptions as to the efficacy of antivirals in reducing the infectiveness of the virus [Reference Ferguson62]. Because of the increased realism of the drug effect, the transmission dynamics in our model more closely mirror those that would occur in the real-world. Therefore, the results from our economic analysis will be more reflective of real-life, thus, improving the usability of this economic model for decision makers. Finally, including pharmacology, epidemiology and HEs into one integrated model may facilitate earlier meaningful dialogue between the key stakeholders, such as sponsors, regulators and payers. This concept provides a crucial element for so-called adaptive licensing approaches of drug development such as staggered approval, managed entry and progressive authorisation [Reference Eichler63].
Conclusions
This is the first study demonstrating the feasibility of linking of PK/PD–EPI/HE models. Our linked model, which explored the use of oseltamivir in pandemic influenza as an example, allows for direct integration of antiviral effectiveness on viral shedding to the disease transmission model. This, in turn, leads to better understanding of the effects of the different doses of oseltamivir on mortality, morbidity and economic outcomes that make up the outputs of our economic model. Simulations that better reflect reality lead to more informed policy making, which, in turn, can save healthcare costs as well as patient lives. However, efforts are needed to further refine the model to better represent the reality. It enables us to better inform multiple stakeholders even at the early phase of drug development.
Supplementary material
The supplementary material for this article can be found at https://doi.org/10.1017/S0950268818000158.
Acknowledgement
This work was supported by the funding from F. Hoffmann-La Roche Ltd.
