Evidence synthesis and decision modelling to support complex decisions: stockpiling neuraminidase inhibitors for pandemic influenza usage

Introduction

Like many other potentially catastrophic events for which governments need to prepare, influenza pandemics are rare. Although the risk is considered to be 3–4% per annum¹, the public health consequences are widely recognised to be potentially severe². The epidemiology of only a small number of influenza pandemics has been well studied and evidence for the effectiveness of remedial influenza treatments in a pandemic scenario is scant. Yet, governments around the world still have to decide whether or not to stockpile anti-influenza medication like neuraminidase inhibitor (NAI) antivirals, such as oseltamivir (Tamiflu®) and zanamivir (Relenza®), as a defence against pandemic influenza.

The stockpiling of NAIs has been a controversial issue. Firstly, stockpiling may be seen to be a waste of large amounts of public money if the pandemic fails to materialise or if it is mild. In the United Kingdom, the previous Chief Medical Officer was criticised for spending £560 million on medicine that went largely unused in the 2009–10 pandemic³. However, taking a default position of not stockpiling, or making the decision on the basis of intuition alone, is not justifiable given the rare but potentially catastrophic losses associated with pandemic influenza and the large cost of stockpiling.

Secondly, there has been a lack of conclusive evidence on the effectiveness of NAIs. Recent meta-analyses of randomised controlled trials (RCT) of seasonal influenza cases demonstrated reductions in rates of hospitalization, lower respiratory complications, and a decreased time to symptom alleviation but were unable to confirm or refute an effect of NAIs on more important clinical end points such as mortality^4,5. A caveat of these studies, which were required for licensure of drug in healthy adults, is that they were not powered to determine low frequency but critical end points such as mortality in a largely healthy adult population. A further meta-analysis of observational data from pandemic influenza did find evidence of a reduction in the risk of mortality when NAIs were given to patients hospitalised with influenza⁶. Some authors have criticised it for being subject to a large degree of bias and rejected it as a suitable form of evidence with which to formulate policy decisions^7,8, though others argue that this evidence strongly supports the use of NAI treatment for influenza in hospitalised patients⁹.

Evidence that has a bearing on death rates is not confined to measurement of mortality alone – there are other sources of relevant evidence. Clinical trials show that NAIs have beneficial effects on a number of outcomes as described above^4–6. The treatment has a plausible rationale and it works in vitro and in animal models for this zoonosis¹⁰. An arguably extreme position is to assume that these observations contain no information regarding effectiveness in preventing the rarer, but more severe outcomes, such as death. People who take to heart Bradford Hill’s list of factors that should affect the interpretation of data (Box 1), would reject such a completely non-theoretical stance. But even within this framework conflicting conclusions may still be drawn, especially when inappropriately filtered through the lens of statistical significance. Estimation of potentially small effect sizes on rare endpoints is often characterised by uncertain and often conflicting evidence and many recent studies do conflict with those that support the effectiveness of NAIs^11–13. Both an observed reduction and an increase in the risk of mortality are therefore potentially consistent with the aforementioned evidence. There is thus a compelling case for the synthesis of and extrapolation from various forms of evidence in order to examine the investment decision facing decision makers.

Previous studies have estimated how cost-effective NAI stockpiling would be under a range of different pandemic influenza scenarios^14–19. Stockpiling is generally estimated to be cost-effective. However, these studies took observational evidence of effectiveness, often from seasonal influenza studies, at face value and did not model potential biases that may have led to overestimation of benefits. Moreover, they only examined a limited number of specific future scenarios. The results of such cost-effectiveness models hinge on the available evidence of effectiveness and it may not be immediately clear to decision makers the implications of new evidence. We have therefore taken a different approach.

The calculation of the number of deaths from an influenza pandemic is simply calculated from a number of relevant variables such as the size of the population, the clinical attack rate, and the case fatality ratio. The effectiveness of NAIs in terms of relative risks can then be used to estimate the potential number of deaths averted through their use. A simple model can provide a useful framework to synthesise the available evidence while also remaining clear and transparent to decision makers. There is a large degree of uncertainty regarding the variables in the model, due to factors such as random mutations in the influenza virus, individual behaviour, and distribution of NAIs, nevertheless appropriate distributions can be specified for each variable and the uncertainty propagated through the model to estimate the distribution of possible numbers of deaths and resulting QALYs under the stockpiling and no stockpiling options. The model presented here exemplifies an approach to decision making under the types of uncertainty described above using a simple, transparent model to assist decision makers and to help inform the stockpiling decision.

Methods

Modelling approach

The methods used in this study are founded in normative decision theory^20,21, which considers what decisions we ought to take, and Bayesian statistics. We used a well-established technique based on expected utility theory^20,21 to model the binary decision to stockpile or not to stockpile NAIs. Within this framework, the decision simplifies to a question of whether the expected net benefits of the stockpiling decision are positive²².

The net benefit associated with stockpiling was set as the value of the deaths averted minus the costs of stockpiling. If the expected net benefit of stockpiling is positive then the decision would be to stockpile, and if it is negative, not to stockpile.

The value of the deaths averted was modelled as:

                     Pop × Prob × CAR × CFR × Hospital × Treated × (1 – θ) × QALY × λ

Firstly, the number of pandemic influenza deaths was calculated by multiplying the number of adults in the UK (Pop) by: the probability of there being a pandemic within the stockpile shelf-life (Prop), the clinical attack rate (CAR), and the case fatality ratio (CFR). We further multiply by the probability a pandemic influenza death occurred in hospital (Hospital), and the probability one of these patients receives NAIs (Treated). The number of deaths averted by NAI treatment in this population of NAI-treated adults was given by the relative risk reduction in mortality associated with NAI treatment (1 – θ). Finally, the value of these deaths averted was calculated by multiplying by the quality adjusted life years (QALY) associated with each pandemic influenza mortality (QALY), and the societal willingness to pay per QALY (λ). This model is further explicated in Figure 1.

Figure 1. Explanation of the model used to derive the value of the deaths averted due to neuraminidase inhibitor stockpiling.

We considered reductions in mortality among symptomatic adults resulting from stockpiling, but did not take into account possible additional effects on complications such as pneumonia or that community use might reduce complications, hospitalisation, or mortality. Only adults were considered on the grounds that NAI effectiveness^4,6 is less certain in children and to determine if the decision to stockpile could be justified on the basis of any benefit among adults alone.

Decision modelling is founded in the Bayesian paradigm, which was used to evaluate the stockpiling decision for a future pandemic with unknown epidemiological variables and unknown effectiveness of NAI. A sub-model was specified for each epidemiological variable in the decision model. Data from previous pandemics were assumed to be observations from an underlying common distribution, the parameters of which were estimated using these data as described in the following section. The decision was then evaluated over posterior predictive distributions for the epidemiological parameters. We used a bias corrected effectiveness estimate for the effectiveness of NAIs as described below. The model was estimated using Markov Chain Monte Carlo (MCMC) with 10,000 iterations using R 3.2.3 and Stan 2.11.0. This method obviates the need to conduct separate probabilistic sensitivity analyses since the posterior distribution of the net benefits represents the uncertainty about future influenza pandemics and NAI effectiveness. The expected net benefits represent the gains or losses from stockpiling, on average, given the different distributions for the different parameters. Convergence of the MCMC chains was assessed by visual inspection of autocorrelation, running mean, and trace plots in R.

Results

Main results

Table 2 shows the results from various scenarios considered. The expected net benefit of stockpiling in the baseline analysis was £444 million ($668 million). The decision would be therefore to stockpile NAIs. Figure 2 shows the posterior distribution of net benefits. The mean number of deaths averted was 3,218. There was a 77% probability that the benefits were negative implying that no pandemic occurred, an insufficiently large pandemic occurred, or NAIs were not effective enough to justify the stockpile. The median net benefit was £-560 million in each case as in the majority of scenarios no pandemic occurred and there was only the net cost of the stockpile. Nevertheless, the mean estimated net benefit was positive, which was caused by the very large number of deaths, many of which may be prevented by stockpiling, in the unlikely event of a severe pandemic. This can be seen in the long tail on the left of the distribution in Figure 2.

Table 2. Results from baseline analysis and secondary analysis varying the proportion of hospitalised cases receiving NAIs.

	Hospitalised patients with influenza receiving NAIs (%)	Expected net benefit (£m), (95% credible interval)	Median net benefit	Decision
1	100	444 (-808, 8,383)	-560	Stockpile
2	70	143 (-734, 5,700)	-560	Stockpile
3	50	-58 (-684, 3,911)	-560	Not Stockpile
4	30	-259 (-634, 2,123)	-560	Not Stockpile

The decision is to stockpile if the expected net benefit is greater than zero and not to stockpile otherwise. The willingness to pay per QALY is £20,000/QALY in all scenarios.

Figure 2. Posterior distribution of the loss function for stockpiling NAIs showing the mean and median values of the distribution along with the decision threshold for stockpiling.

The x-axis has been truncated at £4·5b.

Figure 3 shows the decision under a range values for the effectiveness of NAIs, the percentage of hospitalised, symptomatic adults who would receive NAIs and willingness to pay per QALY threshold. If 100% of hospitalised, symptomatic adults with influenza received NAIs then the decision would be to stockpile as long as our threshold willingness to pay per QALY was greater than £11,116/QALY under our ‘bias corrected’ effectiveness estimate. When only 50% of hospitalised, symptomatic adults receive NAIs this threshold increases to £22,232/QALY, which would still be considered cost-effective in the range considered by NICE. The minimum percentage of hospitalised, symptomatic adults with influenza that would need to receive NAIs for the decision to be to stockpile at a threshold willingness to pay of £20,000/QALY is 56%. Conversely, when the proportions of hospitalised, symptomatic adults who receive NAIs is 50%, 75%, or 100%, the minimum value for the relative risk of mortality associated with NAIs required for the intervention to be considered cost-effective at a £20,000 per QALY threshold is 0.88, 0.92, and 0.94, respectively.

Figure 3. Stockpiling decisions that would be made under a range of different values for the effectiveness of NAIs, the percentage of hospitalised, symptomatic adults that would receive NAIs, and thresholds for willingness to pay per QALY.

The lines represent thresholds for decision makers. For any point inside the region bounded by a given line the decision maker should stockpile and conversely any point outside that region the decision maker should not stockpile.

Dataset 1.Raw data of ‘stockpiling neuraminidase inhibitors for pandemic influenza usage’.

Discussion

This study has found that the available evidence suggests that stockpiling NAIs for pandemic influenza is rational under a range of assumptions. Many of these assumptions are conservative, such as no reduction in adverse clinical outcomes other than mortality, no benefit in patients who would not have been hospitalised had there been no stockpile, and no effect in children. However, this decision required at least 56% of the influenza patients who would have died without a stockpile to receive NAIs if the threshold willingness to pay was £20,000/QALY. In the 2009 pandemic, 64% of hospitalised patients received NAIs⁶, and in the United Kingdom specifically this proportion was 75%³¹, suggesting that 56% is achievable, and that therefore, stockpiling is supported by the available evidence.

This paper is predicated on the purchase of a stockpile large enough to treat a large proportion of the population (80% in the UK) in the community and in hospital with NAIs. This may well be the correct strategy if new evidence emerges that community-based treatment reduces either complications, hospitalisations or mortality. Further research will be required; indeed, the Bayesian decision analysis used here can be extended to consider how much to stockpile rather than simply whether to stockpile. However, if the evidence base were to remain limited to mortality reductions in hospitalised patients, or if the societal willingness to pay per QALY was low, as it may be in many resource poor settings, a ‘hospital-treatment only’ policy might be considered. This would reduce the cost of the stockpile significantly. For example, in the 2009 pandemic only 0.5% of symptomatic cases were hospitalised³², these patients would require far fewer doses than the 1.16 million courses (at a minimum) of NAIs dispensed in the 2009 pandemic³³. For a population of 50.5 million adults with a CAR of 25%, a hospitalisation probability of 0.5% would lead to only approximately 60,000 admissions. The evidence also suggests that more timely treatment of NAIs (within two days of symptom onset) is more effective than treatment at any point⁶, which would suggest that the effectiveness of NAIs could be more favourable than modelled under the stockpiling policy. In all cases the decision would remain to stockpile NAIs.

Our conclusions are in line with the decision that would be made on the basis of cost-effectiveness evidence from previous studies^14–19. However, our study does not take observational evidence at face value, but ‘downgrades’ it, thereby yielding a reduced estimate of effectiveness and wider credible limits. We have calculated the distribution of possible deaths from pandemic influenza using a relatively simple mathematical model and then ‘averaged’ over the distributions of the variables rather than examining cost-effectiveness on a scenario-by-scenario basis. This approach is intuitively simple and is aimed to provide correct inferences using a simple logical framework for the synthesis of the commonly available evidence in order to assist decision makers with a complex decision. The model allows the logical basis of the decision to be ‘reverse engineered’, allowing the decision to be critiqued within the framework established by the model. We note though that many people are highly sceptical about the benefits of NAIs. This study is not intended to be proscriptive. As Figure 3 illustrates, a decision maker with a highly sceptical belief about NAI effectiveness should not stockpile.

Obtaining an estimate for the bias in any particular study, or consolidated group of studies, is clearly an uncertain undertaking. There is an evidence base on bias arising from meta-regressions or other analyses comparing the results of imperfect studies to those of a ‘gold standard’. A recent Cochrane review comparing treatment effects reported in observational studies as compared to RCTs found that, “on average, there is little evidence for significant effect estimate differences between observational studies and RCTs...”³⁴ It is not surprising, given the considerable uncertainties surrounding the meta-analysis cited here, that the differences between the reported effects and our bias corrected effect resembles the differences in empirical studies comparing observational studies and RCTs^34–36.

We acknowledge weaknesses in our study. The only outcome considered in the analyses was mortality. Adverse events caused by NAIs may also generate increased costs and hence reduced benefit. For example, a review of clinical trial evidence of NAIs found an increased risk of nausea and vomiting associated with treatment⁴. The authors also reported a possible increase in the risk of psychiatric adverse events. However, this only reached statistical significance in exploratory analyses including a supra-licence dose and off-treatment periods. A more recent meta-analysis based on individual-level patient data of clinical trials focusing on licensed dose only found no such effects, but the number of events was small⁵. Neuraminidase inhibitors may also have protective effects against some adverse events such as cardiac events, and may reduce the risk of influenza-associated pneumonia and hospitalisation^4,5. The benefit of treatment is unlikely to be grossly over-estimated and is likely to be under-estimated given our conservative assumptions. We have also not considered potential effects on children or from reductions in complications, hospitalisations or mortality that might be associated with community-based treatment, or any benefit arising from changing disease dynamics and reduced transmission; nor have we considered wider societal effects, such as productivity gains, reduced community transmission, and the value placed on a stockpile for a potentially risk averse population, all of which may increase the benefits of stockpiling.

We note that our analysis is focussed on the United Kingdom but that it may be of use to other countries. The model for the benefits of NAIs can be simply applied to new contexts. However, the determination of the costs of the stockpile remains difficult. The costs depend on the treatment strategy planned for a given country and any price negotiations between the manufacturer and the government. A useful tool in this context is the ‘headroom’ method that asks instead what the maximum amount a decision maker should be willing to pay for an intervention, given a willingness to pay per unit benefit. This is a useful direction for future research.

We have assumed independence between the clinical attack rate and case fatality ratio, as well as other variables, however there is some evidence to suggest that they could be correlated³⁷. Nevertheless, the data are admittedly scant, and it is expected that this is a neutral assumption. Of course, if they are positively correlated then our conclusions become more conservative.

Our model examines the decision in the abstract and does not concern itself with externalities such as the possibility that availability of the drug will affect attitudes and hinder the effort to contain the spread of the disease, or that resistance to antivirals may develop. Nor have we considered the sensitivity of clinical diagnosis of influenza in identifying true positives or the costs and logistics of establishing a distribution process for the NAIs. The propensity to consult is also an important factor that may have affect the proportion of true positives, which in turn may have a bearing on the use of a stockpile if used on a “first come, first served” basis. Further research is required to optimize distribution and behaviour during a pandemic to ensure the cost-effectiveness of the stockpiling.

Conclusions

Taking into account the existing evidence on pandemic influenza and the effectiveness of NAIs the decision should be to stockpile, provided a utilitarian decision-making framework is used of minimising expected losses and hence maximising expected benefits.

Data availability

The data used to estimate the parameters in the model were obtained from documents compiled to assess pandemic influenza and thus represent the decision maker’s prior knowledge¹.

F1000Research: Dataset 1. Raw data of ‘stockpiling neuraminidase inhibitors for pandemic influenza usage’, 10.5256/f1000research.9414.d132653⁴⁴.