Serostatus testing and dengue vaccine cost–benefit thresholds

The World Health Organization (WHO) currently recommends pre-screening for past infection prior to administration of the only licensed dengue vaccine, CYD-TDV. Using a threshold modelling analysis, we identify settings where this guidance prohibits positive net-benefits, and are thus unfavourable. Generally, however, our model shows test-then-vaccinate strategies can improve CYD-TDV economic viability: effective testing reduces unnecessary vaccination costs while increasing health benefits. With sufficiently low testing cost, those trends outweigh additional screening costs, expanding the range of settings with positive net-benefits. This work highlights two aspects for further analysis of test-then-vaccinate strategies. We found that starting routine testing at younger ages could increase benefits; if real tests are shown to sufficiently address safety concerns, the manufacturer, regulators and WHO should revisit guidance restricting use to 9-years-and-older recipients. We also found that repeat testing could improve return-on-investment (ROI), despite increasing intervention costs. Thus, more detailed analyses should address questions on repeat testing and testing periodicity, in addition to real test sensitivity and specificity. Our results follow from a mathematical model relating ROI to epidemiology, intervention strategy, and costs for testing, vaccination and dengue infections. We applied this model to a range of strategies, costs and epidemiological settings pertinent to CYD-TDV. However, general trends may not apply locally, so we provide our model and analyses as an R package available via CRAN, denvax. To apply to their setting, decision-makers need only local estimates of age-specific seroprevalence and costs for secondary infections.


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S6 Maximum Vaccine Cost Fraction Allowing Net Benefit. The approximate maxima for ν based 55 on Eq. 8-9, including their convergence at younger ages. These curves represent the thresholds for 56 vaccine costs given real tests, i.e. non-free with less than perfect sensitivity and specificity. Note that 57 these curves only represent the restriction on ν for some benefit; the amount of benefit is generally 58 shrinking faster than the cap on vaccine cost, particularly for the ordinal test. We facet by epidemio-59 logical parameters here: seroprevalence in 9-year-olds (a surrogate for dengue transmission level) and that interventions have no effect beyond the individual, which effectively ignores any changes to transmission. 84 Similarly, all benefits and cost are on the margin, so for example expenditure on testing and vaccination is 85 independent of coverage level. However, economies of scale could be incorporated by, say, adjusting the vaccine or 86 test prices to account for lower unit costs.

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Our model is on a discrete, annual time scale. Practically, this means representing all dengue natural history 88 effects as discrete-year effects (e.g. transient cross-serotype immunity). Likewise, interventions only occur once a 89 year, and all data is interpreted at this yearly scale. 90 We assume dengue is an environmental risk, rather than a dynamically spread infection, For dengue disease natural history, we assume only the first and second infections have potentially associated 106 disease. 107 We assume that, aside from infection-history-derived disease outcomes, vaccination has no impact on infections 108 over life. That is, the transient immunity observed during CYD-TDV trials does not change the number of lifetime 109 infections any individual experiences. We justify this based on the relatively short duration of immunity compared 110 to life expectancy. By making this assumption, we can use pre-sampled life infection trajectories without having to 111 perturb them by vaccination. We also assume the vaccination perfectly replaces one natural infection; this is equivalent 112 to assuming it is perfectly efficacious against disease in seropositive recipients. Estimates indicate that seropositive 113 efficacy is more like 70-80% [1]. We used an optimistic assumption because we are computing a threshold. Additionally, 114 assuming a leaky vaccine would be incompatible with pre-computing life histories. However, the derivation that follows 115 could accommodate a non-leaky, imperfect vaccine efficacy. 116 Finally, we assume tests are perfectly sensitive and specific. This provides an upper bound on benefit, which can 117 be used to preclude combinations of strategy and price for vaccines and tests, irrespective of test performance. The 118 detailed cost performance of real tests will vary by setting, test properties, and intervention approach. We assume 119 any extant individual test history (e.g. previous lab confirmed dengue infection) is irrelevant to this strategy on a 120 longer term basis, and so we ignore that testing; going forward, any non-vaccine related testing could be reasonably 121 considered part of our cost estimate.

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On balance, these assumptions tend to overvalue the intervention. We judge that the net effect is likely small 123 relative to estimating limiting space of a test-then-vaccinate regimen for the yes or no decision many settings now in these terms allows general results

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• C X , the total individual cost for scenario X (no intervention, vaccination without testing, etc.)

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• ∆ X , the difference between status quo (C 0 ; no vaccination) and intervention X: intervention to have net benefit, ∆ X ≥ 0 must be true 139 Note, that these costs may represent any perspective (individual, societal, etc.), but should be from a consistent 140 perspective.

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The population is stratified by total lifetime infections, as well as number of infections at the routine testing age • N and X can include modifiers, like X + to mean X or more, or have ∀ to mean any number of total infections 149 (by definition, X ≥ N ).

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• C{A}, the conditional probability of seroconverting between age A and A + 1, given seronegativity at age A.

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In general, we drop A, as it is the same for all terms in most equations. We only use it explicitly for multiple testing In a later section, we will define an exposure model to estimate these probabilities, but we may take the specifics 161 of that for granted while we layout the cost relationships. Because the cost model is defined only in terms of the 162 probabilities, we could replace the exposure model with another approach that provides the same probabilities, as Without vaccination, an individual's expected lifetime dengue burden would be: Note that the proportions are all independent of age, and only concern lifetime outcomes. When considering 167 interventions, age becomes a factor (implicit with the X P N terms, which are a function of A). With universal 168 vaccination (i.e., irrespective of serostatus), the cost would be: To begin understanding the cost model with testing, we imagine combining the vaccine with a free test (denoted 171 V ′ ); this assumption is obviously ludicrous-the test will cost resources to produce and use-but provides insight 172 about the limits of vaccine value for an epidemiological setting. 173 We assume this imaginary test identifies the number of past dengue infections, so we refer to it as the ordinal 174 test. This test enables us to only vaccinate seropositives that could have another disease-bearing infection, and avoid 175 vaccinating seronegatives until they seroconvert. We use the test every year from the routine testing age, until the 176 individual receives the vaccine. The cost for this hypothetical regimen is: Note that V ′ vaccination only occurs for seropositives that have only had one infection and individuals that se-178 roconvert after the routine testing age; because we assume no benefit against third and later infections, we do not 179 administer vaccine to those with multiple past infections. If we have a test that only detects seropositivity but not 180 detailed infection history, which we refer to as a binary test, then costs would be: which we distinguish by the V † term. The only change is on the coefficient for the V term (and the ν = V S terms, 182 when we switch to non-dimensional form); this result will be consistent as we consider more complicated models.

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D. Cost-Benefit Constraint Equations for Vaccination-Only and Free Testing Models Recall that by definition, vaccination without testing is only net beneficial if ∆ V ≥ 0. Testing can expand the region 186 of vaccine benefit, but only if ∆ V ′ ≥ 0 or ∆ V † ≥ 0, depending on the test mechanism. For routine vaccination at a 187 certain age to be net beneficial after the introduction of any real testing cost, the vaccine regimen cost must obey: Note that combined with either of the free tests, the constraint on vaccine cost depends only on three generic 189 parameters of the context (the average cost of second-like infections (S, implicit within ν), and the lifetime probabilities 190 of 0 or 2 + infections) and one parameter of the intervention (i.e., age A of consideration for vaccination, which 191 determines the fraction of the population that has had two or more infections, 2 + P ∀ , at that point). As the routine 192 age is shifted earlier, the probability of two infections prior to consideration for vaccination becomes vanishingly small, 193 i.e. 2 + P ∀ → 0. Therefore, at a young enough vaccine age the constraint equations converge to the ratio The approximate maxima for ν based on Eq. 8-9, including their convergence at younger ages. These curves represent the thresholds for vaccine costs given real tests, i.e. nonfree with less than perfect sensitivity and specificity. Note that these curves only represent the restriction on ν for some benefit; the amount of benefit is generally shrinking faster than the cap on vaccine cost, particularly for the ordinal test. We facet by epidemiological parameters here: seroprevalence in 9-year-olds (a surrogate for dengue transmission level) and disparity (a measure of risk heterogeneity).
(1 − P 0 ), and only individuals that experience multiple infections benefit (by avoiding S). Therefore, the maximum 197 value of V is the conditional probability of experiencing S given any infections.

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Note that ν ′ ≥ ν † for any routine testing age, but the value of ν † grows faster with decreasing age (as it must for 199 them to converge).

E. Models with Non-Free Testing
If we now acknowledge the cost of testing, T , and consider only a single test (instead of potentially testing several 202 times), the individual costs are: and the intervention benefits are: Which makes our non-free, single testing constraints for cost effectiveness: Notably, there is still no dependence on the cost of first infections (F ). To be net beneficial, the costs of testing and vaccine (under a single test strategy) must result in a point below the relevant line (based on routine vaccination age and context). We show how the threshold line shifts with age. We facet by environmental sensitivity parameters here: seroprevalence in 9-year-olds (a surrogate for dengue transmission level) and disparity (a measure of risk heterogeneity).
Relative to C V T ′ or C V T † , lifetime seronegatives (P 0 ) will pay for L − 1 additional tests. The fraction of the 211 population in 0 P 1 + will pay for some number of additional tests, and possibly vaccination (i.e., for the proportion of 212 individuals seroconverting during the testing window). This means costs for this strategy will change some 0 P 1 + {A} 213 (i.e., seronegative at A, the routine initial testing age) to 1 P 1 + {A + n} at some later age prior to A + L − 1 (i.e., 214 seroconverting during the testing window, and therefore vaccinated).

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Relative to single testing, there will instead be some average number of tests, ⟨n(A, L)⟩, and additional vaccination 216 based on the amount of seroconversion during the testing period, thus increasing the cost of the intervention. In 217 return, there will be a reduction in the proportion incurring S. Relative to indefinite free testing, this reduction will 218 be incomplete, as some proportion will pass the entire L years of the testing period without seroconversion, but still 219 suffer multiple future infections.

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The average number of tests is related to the proportion of people already seropositive at the start of the testing which can be conveniently expressed as a summation of terms  note that for the case L = 1, the summation term is empty, and therefore ⟨n(A, 1)⟩ = 1, recovering the single test 227 case.

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Vaccination can also be considered in terms of this series, but since we are unconcerned about whether they the start of routine testing will also not be vaccinated; n.b., these categories are mutually exclusive. Therefore, the 233 proportion of the population vaccinated, P V is: Revisiting our net cost equations, using T * to mean either test scenario: Meaning the benefit constraint equations are: Again, the cost of first-like infections, F , does not appear anywhere in the constraints. We can also divide by S 237 and again work in the non-dimensional terms to find the net benefit constraint relationship:  Fig. S8 is the additional vaccination along the uppermost path, the trajectory corresponding to two or more infections prior to the routine vaccination age.

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As a final step, we compare the benefits of vaccination with and without testing. This allows us to determine 240 where adding testing of makes vaccination a more cost-effective intervention. Recalling C V and C V LT * from Eq. 2 241 and Eq. 21, respectively, we can write: For testing to improve the intervention cost-benefit, C V − C V LT * ≥ 0. Imposing that constraint, and re-arranging 243 to match the form of Eq. 23: Some notable results are derivable directly from this relationship. Increasing vaccine cost increases the advantage of 245 the testing intervention, which is intuitive: testing decreases vaccination rates, so the more expensive the vaccine, the to preventing S instead of F decreases, and thus so does value to testing. As explained in the Context Economics 250 section, we consider a pessimistic F S = 0.5.

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In general, we see that including testing makes the intervention more beneficial in lower transmission settings, while 252 it is wasted in high transmission settings. In high transmission settings, we already have a lot of information about 253 serostatus, so testing provides little benefit.

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As stated earlier, we assume there is a constant force-of-exposure. However, we also divide individuals into low or 256 high risk sub-populations, so there are three fundamental parameters in the model: the two exposure risks and the 257 proportion in high versus low risk.

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For natural history of the infection, we assume that exposure to a serotype leads to infection if the individual 259 has not been exposed to that serotype previously. We also assume that infection in one year precludes infection in 260 the following year, consistent with empirical observations of temporary cross immunity. Finally, we assume only one 261 dengue serotype is circulating in any given year. In the next section we consider relaxing these assumptions, and 262 justify our decision to use these simpler assumptions. 263 We can use age-seroprevalence data to fit this force-of-exposure model. These data allow us to estimate the 264 probability that individuals have experienced at least one infection by a given age. If we define the constant exposure 265 forces (and complementary avoidance probabilities) f X = 1 − s X and probability of being in the high risk group as ρ H , 266 the probability of being seropositive at age A is: Once we fit that model to specific age-seroprevalence data, we can then use simulation to estimate the relevant N P X 268 terms for that context, and thus the τ -ν constraints for that setting. While analytical derivation of these is probably 269 feasible for this set of assumptions, simulation affords us the ability to consider a broader range of assumptions in the 270 future without having to re-derive outcomes.

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Recall that for the particulars of our cost model, we need the following probabilities:

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The proportion of individuals that • C{A}, the conditional probability of seroconverting between age A and A + 1, given seronegativity at age A.

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A. Alternative Exposure Models

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If there were more readily available data, it might be worth considering models incorporating (1) maternally-derived 282 temporary immunity and (2) multiple serotype circulation.

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To include maternal immunity, we would need to consider the probability of having a previously infected mother as 284 part of the first exposure year. If an individual had an exposed mother, we would simply assume one the individuals 285 was immune in that year, meaning one fewer exposure year in their life history. We could derive the probability of 286 maternal exposure with maternal-age distribution and the age-seroprevalence from the fit, meaning we do not actually 287 need an additional parameter, just more data.

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For multiple simultaneously circulating serotypes, we considered allowing up-to four exposures per year, probabilis-289 tically ordered by relative weights. Since all the fitting is by first exposure, we could fit any one parameter model of 290 exposure (e.g. a four-trial binomial draw). This would tend to drive up second infection rates, perhaps more accu-291 rately representing high risk populations in hyper-endemic locales where all four dengue serotypes routinely circulate.

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This would in turn tend to drive the benefit curve towards earlier consideration for routine vaccination. However, the 293 data to correctly parametrise and constrain such a model (for example, age sero-ordinality surveys) is more detailed 294 and does not appear to be commonly available.
FIG. S12. Trends by Age of Relevant Population States. Assorted N P X trend lines, faceted by seroprevalence in 9-yearolds (a surrogate for overall force of exposure) and disparity level (a representation of population heterogeneity in exposure risk).

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To fit the force of exposure model, we change parameters to break the parameter symmetry (i.e., that either 297 risk category could be higher or lower) and express them parameters so that they have infinite domain, which is 298 preferable for most numerical solvers. The detailed code can be found in the denvax package source repository, 299 https://gitlab.com/cabp_LSHTM/denvax, particularly the serofit function and utility functions earlier in the Using this model, we fit to two data sets, Table S1 from the CYD14 trial [2] (reference Table 4; there is a discrepancy  Peru   5  261  146  6  307  209  7  340  244  8  368  269  9  353  273  10  340  273  11  327  272  12  320  257  13  267  222  14  238  209  15  205  187  16  147  135  17 98 93 Peru data is ideal for the maximum-likelihood style approach we used. The aggregated CYD-14 data, on the other 308 hand, throws away information and complicates model fitting, whether using maximum likelihood or other approaches.

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While the data may "look better" after aggregation, this mode of reporting in fact impedes further study. and β = s L A : where Eq. 30 can be solved with the quadratic equation, subject to β ∈ (0, 1), and substituted into Eq. 29. 318 We are being somewhat circular with the concept of disparity, in that we fit the serosurvey data assuming a two-319 group risk model, and then calculated the OR, rather than identifying mechanistically a useful distinguishing variable 320 (e.g. living with air conditioning versus not) and measuring OR. More targeted deployments may require finding such 321 a factor that predicts similar disparity as the serosurvey approach. For Malaysia, if we assume the public payer perspective, the benefit of preventing a second-like infection is roughly 331 S = 86 USD, therefore ν ≈ .9 and τ ≈ .2. For Peru, if we assume the public payer perspective, S = 223, ν ≈ .3 and 332 τ ≈ .1.

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In these two settings, we also estimated F S ; in Malaysia, it is F S ≈ 0.2 while in Peru F S ≈ 0.4. For our comparison to 334 vaccination without testing, we assumed F S = 0.5 as an upper limit.