We use the individual-level trial data from the CYD14 and CYD15 trials, in both the active phase (25 months post first dose) and the 1^st year of passive phase hospital follow-up. In the active phase, all symptomatic dengue disease is detected, but in the passive phase only hospitalisations were detected. All cases refer to virologically confirmed dengue. Infecting serotype is known for almost all cases (97.6% for CYD14, 95.8% for CYD15, 96.7% overall). Baseline serostatus is known for only a minority of subjects (19.3% for CYD14, 9.6% for CYD15, 12.7% overall). Model variants (including our main model) that consider serotype-specific effects omit all cases of unknown serotype. We right-censor after date of first case for each patient, and so do not consider multiple cases per patient.

We divide trial participants by trial arm a and baseline serostatus b (0 = seronegative or 1 = seropositive at baseline), as described in Figures 1 and 2. Disease risk is allowed to vary by the number of prior dengue exposures and by disease type (where disease type refers either to trial phase (active = 0; passive = 1) or disease severity (non-severe/non-hospitalised = 0, severe/hospitalised = 1)). We consider a country-specific baseline hazard of disease (or force of infection, i.e. the risk of disease among susceptibles) as a spline λ_c(t), and we link baseline seropositivity to each participant’s age and the background transmission intensity in their country (see below). A trial participant of age α in trial arm a, with baseline serostatus b, in country c is subject to the following hazard from serotype d of disease type D at time t:

where $R_{abcD}^{}\left(\alpha \right)$ is the relative risk of disease associated with natural infection. M_b is the multiplier of the baseline hazard associated with baseline serostatus b, equal to 1 for seronegatives and fitted for seropositives. This parameter reflects seropositive participants’ reduced infection risk due to their immunity to at least one serotype.

Figure 2

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ρ_cd ∈ [0,1] is the proportion of serotype d in country c (assumed to be constant, with ${\displaystyle \sum _{d=1}^4{\rho }_{cd}}=1$, see below); Z(α) is the multiplier of the force of infection for age α; δ_αVac is the Kronecker delta defined by

We define the transient immunity I_bd*(α, t, t_F) against serotype d for vaccinees of age α and baseline serostatus b at time t, given time of most recent vaccine dose t_F by

That is, positive values of transient immunity wane exponentially (to reflect previously observed antibody dynamics Clapham et al., 2016). Additional details on age-specific transient immunity I_bd(α) and duration τ_b, and force of infection Z(α) are given below [Figure 2A].

The relative risk of disease of type D for a subject with i prior dengue exposures is given by K_iD. K_{1 0} = 1 (secondary febrile dengue illness) is taken to be the baseline, and we assume the relative risk is the same for tertiary and quaternary infection of either type, and so K_2D = K_3D. Our model considers serostatus to be binary (either seropositive or seronegative), and so we define the risk of disease ${\phi }_{cD}\left(\alpha \right)$ among seropositive participants, which is an aggregate of the risks of disease given monotypic or multitypic infection history, shown below.

Our main model considers vaccination to alter the risk of disease associated with prior exposure, by acting as a silent, disease-free infection (Figure 1). Therefore, the relative risks are defined as follows:

when considering the active phase of the trial (or symptomatic disease of any severity) and

when considering the passive phase of the trial or hospitalised/severe disease. A glossary of the above terms can be found in Supplementary file 1.

If the hazard due to all serotypes combined is given by

then where relative risks distinguish between trial phases, we let

where t_P is the date that active surveillance ends and passive surveillance begins, and define the integrated hazard between start and end times t_S and t_E as

Our model does not consider multiple disease episodes for the same patient over the observation period, and subjects are right-censored after they become a case for the first time. Therefore, when relative risks distinguish between the severity of disease, ‘survival’ between times t_S and t_E refers to surviving disease of both severities, and we therefore define the integrated hazard additively as

This interpretation assumes that hazards are proportional between disease severities (although not between trial arms, countries or between number of prior infections).

In both formulations, the probability ${\mathbb{P}}_{abc}(t_S,t_E,\alpha )$ of remaining disease free from between times t_S and t_E is given by

and so the probability ${\mathbb{Q}}_{abcdD}(t_S,t_E,\alpha )$ of disease from serotype d of type D at time t_E is given by

where T_I is the time interval within which the hazard is assumed to be constant. We take T_I to be 1 day.

For brevity, we combine the above to denote the probability of clinical outcome C given parameters θ by

If h_c denotes the constant historical force of infection in country c, then the probabilities π_bc(α) of having serostatus b in country c at age α are given by

then the likelihood of parameters θ is given by

We have baseline immunity data for only around 10% of subjects, and the above likelihood requires the baseline serostatus of each trial participant. We employ data augmentation, in which the baseline serostatus of each participant outside the immunogenicity subset is treated as a parameter, to infer the immunological status of each participant with missing baseline serostatus. This has the advantage that fitted parameters are less dependent on initial assignment of baseline serostatus and can be considered as marginal distributions over possible values of baseline immunity. We use Gibbs sampling to calculate the conditional probability of seropositivity, given the current state of the parameter chain θ and the patient’s age, trial arm, country and clinical outcome C.

Abbreviating and letting $\mathbb{P}\left(S_{+}\right|C;\theta )$ and $\mathbb{P}\left(S_{-}\right|C;\theta )=1-\mathbb{P}(S_{+}|C;\theta )$ respectively denote the probabilities of seropositivity and seronegativity at baseline given clinical outcome C, by Bayes’ theorem we have

For example, a non-case of age α in country c has the following probability of seropositivity at baseline

for parameters θ. Similarly, for a case of severity D of age α in country c we have

If $\mathcal{𝒱}$ and $\mathcal{𝒞}$ are the sets of vaccinees and controls, respectively, then within any given stratum of interest $\mathcal{𝒮}$ (e.g. in a particular country, age or serostatus subset, or combination thereof), then posterior ratios of hazards of any disease severity and due to any serotype HR(t*) for all serotypes combined at time post-first dose t* are given by

where $\left|\mathcal{𝒮}\right|$ denotes the number of trial participants in stratum $\mathcal{𝒮}$.

For hazard ratios HR(t*,d) of a particular disease severity D and serotype d, we have

For stratum $\mathcal{𝒮}$ as at t* days post-first dose, posterior survival probabilities ${\mathbb{P}}_{\mathcal{𝒮}}(t*)$ are calculated as

and if $n_{\mathcal{𝒮}}(t*)$ denotes the number of cases in stratum $\mathcal{𝒮}$ that occurred within t* days post-first dose, then the observed survival probabilities are given by

The period for which participants were under active or passive surveillance varies by patient. Therefore, we calculate attack rates using

where $t_{A_i}$ and $t_{B_i}$ are the start and end times of the trial period for patient $i$ ($t_{S_i}$ is the start of follow-up and is arbitrary here). To compute attack rates for observed data, we use the same formula, but ${\mathbb{P}}_{a_i{b}_i{c}_i}(t_{S_i},t,{\alpha }_i)$ takes value 0 if the patient $i$ is a case between $t_{S_i}$ and $t$, and 1 otherwise. We use exact binomial confidence intervals on aggregate observed survival probabilities. For predicted attack rates, we use 95% credible intervals of posterior samples.

Model fitting was performed using the Metropolis–Hastings algorithm for parameter inference and Gibbs sampling for data augmentation. Parameters fitted include the relative risks, vaccine-induced transient immunities (by baseline serostatus, serotype and age) and their durations. For each country-specific baseline hazard, the logged knots of the spline are the fitted parameters, which explicitly determine all values of the baseline hazard. Prior distributions for parameters and augmented data were uniform (Supplementary file 1), and proposal distributions were normal. Each model variant was run for 1,100,000 iterations with a burn-in period of 100,000, storing 1 in every 100 iterations as posterior samples. Convergence was assessed visually. The model was coded in C++ using OpenMP (Dagum and Menon, 1998), and results were analysed in R 3.6.1 (R Development Core Team, 2019). All model code is available at https://github.com/dlaydon/DengVaxSurvival (Laydon, 2021; copy archived at swh:1:rev:d4964b7240312a371b2767533099643c59025dbf).

We consider alternative model variants that do not incorporate explicit serotype or age effects (Figure 2B–D, Table 1), and also a variant without vaccine-induced immune priming. Model fit is assessed both visually and using the Bayesian Information Criterion (BIC) (Bhat and Kumar, 2010) and the Widely Applicable Bayesian Information Criterion (WBIC) (Watanabe, 2013). For the WBIC, model variants with the highest values are to be preferred, in contrast to the BIC where model variants with the lowest values are preferred.

Figure 3 shows the proportion of participants with virologically detected dengue by trial, age group, trial phase, serotype and disease severity. Both trials show a clear benefit of vaccine across each age group for the active phase (25 months post-first dose), where surveillance could detect both hospitalised and non-hospitalised disease. In the passive phase (next 11 months following active phase), there are considerably fewer cases, owing to its shorter duration and detection of only hospitalised cases. Further, the benefits of vaccination in the passive phase are less than the active, and 2–5-year-old vaccinees show a greatly increased risk of hospitalisation than controls. In both trials, a mix of infecting serotypes among cases was observed.

Figure 3

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Because we consider both transient immunity and the change in disease risk induced by vaccination, the vaccine’s overall effect can be difficult to interpret using only parameter estimates. We therefore summarise model output using hazard ratios (vaccine/control). Figure 4 shows estimated posterior hazard ratios for symptomatic disease (regardless of hospitalisation) by trial, serostatus and age group over time.

Figure 4 with 4 supplements see all

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The vaccine has the greatest benefit for seropositive recipients: hazard ratios remain low throughout the active phase and the first year of passive phase, and mean posterior and 95% credible intervals are below 1 for all ages, indicating consistent benefit. The decrease in hazard ratios over time in each age group reflects the greater benefit to seropositives against hospitalised/severe disease as only this disease outcome is measured in the passive phase.

For seronegative vaccinees, hazard ratios are neither significantly positive nor negative during the first year. Ratios rise dramatically afterwards, reflecting low and short-lived immunity, combined with an almost sixfold long-term increase in disease risk, in both trials and in all age groups. Because the passive phase trial surveillance detected only hospitalised disease, this increase in hazard ratios refers to an increase in risk of hospitalisation, consistent with the 2017 NS1 data (Sridhar et al., 2018), to which our model was not fitted.

When unstratified by baseline serostatus, the vaccine is broadly beneficial, although hazard ratios rise over time, and are above 1 for 2–5 year olds in the first year of passive follow up. Decreasing hazard ratios with age reflect increasing seropositivity with age, and to a lesser extent the increase with age in transient immunity that we infer for seropositives. Low seroprevalence in 2–5 year olds is the driving factor of their increased risk, and this is consistent with the risk enhancement observed in the first year of long-term follow-up data. Hazard ratios are similar between trials for comparable age groups.

The estimated trends with age, serostatus and time hold when broken down by serotype (Figure 4—figure supplement 1), although net vaccine efficacy varies by serotype. Vaccination respectively offers the least and greatest benefit to serotypes 2 and 4. Hazard ratios are higher for serotype 2, although the vaccine remains beneficial in seropositives. For serotypes 3 and 4, hazard ratios are lower, and vaccination provides some initial protection even in seronegatives, although again these ratios rise over time. Risk enhancement of 2–5-year-old vaccinees is much higher for serotypes 1 and 2 than for 3 and 4.

Table 1 shows parameter estimates for our main model. We infer relative risks by prior infection under both active and passive surveillance, and define K_i,D as the relative risk of disease of type D (in this instance referring to either the active or passive phase) given i previous infections. Disease risk in active phase secondary infections is our baseline (i.e. K_1,0: = 1).

We estimate the relative risk parameters K_0,0 and K_2,0 to be 0.7 (0.36–0.98) and 0.31 (0.14–0.63), respectively. That is, among unvaccinated individuals, primary infection is 70% as likely, and tertiary/quaternary infection is 31% as likely, to cause symptomatic disease as secondary infection. However, considering vaccination as a silent infection, seronegative vaccinees increase their long-term risk of symptomatic disease by a factor of K_1,0/K_0,0 = 1.5 (1.0–2.7), whereas vaccinees with a single prior infection multiply their long-term disease risk by a factor of K_2,0/K_1,0 = 0.31 (0.14–0.63), transient immunity notwithstanding.

We estimate the proportions of symptomatic primary, secondary and tertiary/quaternary infections that require hospitalisation (i.e. parameters K_0,1, K_1,1 and K_2,1) to be 0.053 (0.034–0.078), 0.21 (0.14–0.31) and 0.053 (0.034–0.078), respectively. Therefore, in seronegatives, vaccination increases long-term risk of hospitalisation by a factor of K_1,0 K_1,1/K_0,0 K_0,1 = 6.1 (4.1–11), whereas for those with a single prior infection hospitalisation risk is multiplied by a factor of K_2,0 K_2,1/K_1,0 K_1,1 = 0.078 (0.036–0.16), again without considering transient immunity. Because disease risk in tertiary and quaternary infection is assumed to be equal (i.e. K_2,1 = K_3,1 and K_2,2 = K_3,2), multitypic seropositives (those with more than one previous infection) are unaffected by this mechanism of vaccine action.

Estimates of transient immunity by age, serostatus and serotype are shown in Figure 5. For every serotype, seronegative transient immunity estimates do not vary for older age groups but are lower for 2–5 year olds. They are lowest for serotype 2 (with negative mean estimates of −11% (−72–46%) for 2–5 year olds) and relatively high for serotypes 3 and 4. For seropositives, while estimates are again higher for serotypes 3 and 4, they vary less by serotype but more by age, with immunity being lower for younger than older children. Our results imply that transient immunity varies by age, independently of serostatus, although more so in seropositives (Figure 5, Table 1).

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We could not precisely infer durations of transient immunity. Mean posterior estimates of seronegative and seropositive transient immunity duration are 4.5 (1–9.6) and 11 (2.3–20) years, respectively. However, a closer look at parameter posterior distributions (Figure 5—figure supplement 1, top row) is informative: in seropositives, approximately equal weight is given to longer durations of between 5 and 20 years (85% of posterior mass is above 5 years), whereas in seronegatives shorter durations are more likely (modal estimate is approximately 2 years and 62% of posterior mass is below 5 years).

If seropositive transient immunity were zero (or alternatively if the duration of transient immunity in seropositives was very short), then vaccination would only prime immunity and only individuals with pre-existing monotypic immunity would benefit from vaccination. Instead we estimate positive values for transient immunity for each age group and serotype. Further, model fits that fix seropositive transient immunity at zero do not reproduce the trial data. Therefore, for seropositives, to the extent that transient immunity is long-lived, vaccination confers benefit beyond that of priming immunity and consequent reduction of disease risk to that associated with natural tertiary and quaternary infection. Hence individuals with pre-existing multitypic immunity are also predicted to benefit from vaccination, with the caveat that we were not able to test a model in which transient immunity only applied to those with monotypic immunity. Conversely, in seronegatives, any positive benefit that mitigates long-term increase in disease risk is short-lived.

We find that the age group-specific multiplier of the baseline hazard increases with age for 6–11 year olds (1.2, 0.91–1.5), but then decreases for the 12–16 age group (1.1, 0.79–1.5) to be no different from the 2–5-year-old age group in the mean posterior estimates. While both credible intervals encompass 1 (indicating no difference), model runs that omit this age-specific hazard multiplier give a noticeably inferior visual fit (Appendix 1). Regardless of vaccination, we find that seropositives are 0.77 (0.43–0.99) times as likely to be infected as seronegatives due to their immunity to at least one serotype.

Estimates of the serotype proportions by country are shown in Figure 5—figure supplement 2, showing substantial heterogeneity between countries in their serotype distributions (e.g. Puerto Rico and Brazil’s cases are almost exclusively comprised of serotypes 1 and 4, respectively).

Observed Kaplan–Meier curves demonstrate a clear overall benefit of vaccination. Over the combined active and first year passive phase, controls acquire symptomatic disease more than vaccinees in every country and age group. In both trials, vaccine efficacy wanes over time, and the slopes in the Kaplan–Meier curves become more equal (Figure 6). The active phase lasted ~25 months (760 days), after which the slopes of the curves in each trial arm level off because only hospitalisations were detected. The model was fitted to the combined data from CYD14 and CYD15, and reproduces the observed Kaplan–Meier curves well across countries and age groups (Figure 6).

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Observed attack rates varied widely by country, trial arm, trial phase and age group (Figure 7, Figure 7—figure supplements 1 and 2). Attack rates were generally higher in CYD14 than CYD15, and they decrease with age in both arms. Our main model captures this variation well, and the mean predicted attack rates fall within the confidence intervals of the observed attack rates in every age group, country, trial arm and trial phase. Importantly, the mean estimates reproduce the increased hospitalisation among 2–5-year-old vaccinees observed in the CYD14 trial (Figure 7).

Figure 7 with 8 supplements see all

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Figure 7—figure supplements 3 and 4 show attack rates outputted from the immunogenicity subset only, where model predictions remain within the confidence intervals of observed attack rates. Attack rates again decrease with age in seropositives but not seronegatives, likely because of immunity to previously encountered serotypes (Figure 7—figure supplement 4). For seronegative vaccinees, increased disease risk in the passive phase is predicted for all age groups in both trials, and not only 2–5 year olds in CYD14. Conversely, predicted seropositive attack rates are lower for vaccinees than controls across both trials. Our estimates well reproduce the data that is not overly sparse and again largely predict the 2017 NS1 data (Sridhar et al., 2018). The observed distribution of seroprevalence by age in the immunogenicity subset is well mirrored in the augmented data (Figure 5—figure supplement 3).

Our default interpretation of relative risk parameters K_i,D distinguishes between differences in case detection under active and passive surveillance. However, we can also interpret these parameters to distinguish between non-hospitalised and hospitalised disease (or alternatively between non-severe and severe disease) (see Materials and methods).

We find that hazard ratios are consistent with our default interpretation which does not consider disease severity. However, here it is easier to distinguish between the vaccine’s temporal effects and its differing efficacy against hospitalised or severe disease. For seropositives, temporal effects are minimal, and vaccination confers high and long-lasting protection against disease, and more so against hospitalised disease. In seronegatives, against non-hospitalised disease, hazard ratios again show only minor (and sometimes non-significant) initial protection, but they do not rise to the same dramatic extent. However, against hospitalised disease there is immediate risk enhancement that substantially worsens over time (Figure 4—figure supplement 2). In summary, the differences between seronegative and seropositive efficacy are greater against hospitalised disease than against febrile disease.

These trends hold when broken down by serotype (Figure 4—figure supplements 3 and 4). Protection is greatest against serotype 4 and lowest against serotype 2. The rate at which vaccination enhances hospitalisation risk in seronegatives varies by serotype: against serotype 2, vaccination increases hospitalisation risk immediately after vaccination and only rises slowly during the following three years (to approximately sixfold); whereas for serotypes 3 and 4 the eventual risk enhancement is lower (approximately fourfold) but follows a delay (Figure 4—figure supplement 4). Hazard ratios are almost identical when considering severe and non-severe disease.

Age-, serotype- and serostatus-specific transient immunity estimates are similar to our default interpretation when considering hospitalised or severe disease (not shown). We allow the proportions of symptomatic disease requiring hospitalisation to differ between trials to reflect non-standardised criteria between countries. Among secondary infection, proportions differ slightly between the CYD14 and CYD15 trials at 0.30 (0.23–0.33) and 0.16 (0.12–0.21), respectively (values for primary and tertiary/quaternary infection are determined by fixed ratios). Relative risks of severe disease are considerably lower than hospitalised disease at 0.012 (0.0087–0.016), 0.047 (0.035–0.063) and 0.012 (0.0087–0.016) for primary, secondary and tertiary/quaternary infection.

When distinguishing between severe and non-severe disease, we reproduce observed survival curves at trial level for non-severe disease, but fits are less good for severe disease (Figure 6—figure supplement 1). This is due firstly to limited data (non-severe cases outnumber severe cases by 1223 to 58), and secondly because we do not allow transient immunity to vary by disease severity. When we instead consider hospitalisation (Figure 6—figure supplement 2), fits to survival curves are good regardless of hospitalisation status. In both scenarios, model fits to ‘either’ disease severity (e.g. surviving both severe and non-severe disease) closely resemble those of our default interpretation, where disease severity is not considered. Attack rates in each disease category are relatively well fitted, although passive phase attack rates are less well fitted for severe or hospitalised disease (non-hospitalised febrile disease is not detected by passive surveillance) (Figure 7—figure supplements 5 and 6).

We conducted a sensitivity analysis to examine whether more parsimonious models are sufficient to explain the complex trial data (Appendix 1). Broadly, it is necessary to include explicit age effects to reproduce the age distribution of cases and to include serotype effects to reproduce variation by country. While we could not precisely infer the duration of transient immunity, our analysis indicated that it is short-lived in seronegatives and long-lived in seropositives.

When we omit serotype and age effects (infection history notwithstanding) (Figure 2D), the hazard is given by

${\lambda }_{abcD}(t,\alpha )={\lambda }_c\left(t\right)M_b{R}_{abcD}^{}\left(\alpha \right)(1-{\delta }_{a,Vac}{I}_b^{*}(t,t_F\left)\right)$.

Here age is only considered alongside historical transmission intensity to determine the contributions of monotypic and multitypic infection to seropositive relative risks.

This reduced model fits observed Kaplan–Meier curves well at trial level, although age group breakdowns are more variable: vaccine efficacy is respectively overestimated and underestimated the 2–5 and 12–14 CYD-14 age groups (Figure 6—figure supplement 3). This is likely due to an uneven age distribution in CYD-14: age groups 2–5 and 12–14 constitute 24.2% and 22.7% of CYD-14 (or 7.9% and 7.5% of combined CYD-14 and CYD-15 data), whereas 6–11 years olds comprise 53.2% of the CYD14 data (17.5% of combined data). CYD-15 age breakdowns are better (Figure 6—figure supplement 3), attributable to its larger size and narrower age range, although efficacy is still slightly underestimated in the highest age group.

Fits to individual countries are more variable (Figure 6—figure supplement 3). Lower-quality fits in country and age group subsets are usually attributable to thinner data and specifically lower case numbers; however, this explanation is insufficient for Brazil, which has high case numbers, indicating country-specific effects that are not captured by reduced model. The estimates of serotype proportions (Figure 5—figure supplement 2) are instructive: Brazil and Mexico have vastly different serotype proportions (specifically serotypes with the highest and lowest vaccine-induced immunities, respectively), and therefore fits to these countries improve with the inclusion of serotype effects. In contrast, Indonesia, Thailand and Colombia have more equal serotype proportions, and thus their fits are not greatly improved. These results indicate that the effects of vaccination vary by age, independently of serostatus, and therefore that a more complex model is necessary to explain the trial data.

Relative risk parameters are lower but consistent with our main model, and initial seronegative transient immunity is 0.64 (0.34–0.74), whereas seropositive transient immunity is estimated to be 0.43 (0.041–0.73). Seronegative and seropositive durations are estimated at 4.9 (1.2–9.6) and 10 (1.4–20) years, respectively (and have similar posteriors to our main model), again indicating long-lasting benefit to seropositives beyond the effect of immune priming (Table 1).

Adding age-specific transient immunity and force of infection (Figure 2B) to the simplest model, we have the hazard

${\lambda }_{abcD}(t,\alpha )={\lambda }_c\left(t\right)M_{b}Z\left(\alpha \right)R_{abcD}^{}\left(\alpha \right)(1-{\delta }_{a,Vac}{I}_b^{*}(\alpha ,t,t_F\left)\right)$.

Fits in the CYD-14 2–5 and 12–14-year-old age groups are improved; however, fits to individual countries are largely the same as the simplest model (Figure 6—figure supplement 4). Further, each measurement of model fit is inferior to our main model (Table 1). We conclude that inclusion of age effects alone is insufficient to explain the trial data.

This model variant again shows an increasing trend with age in transient immunity for seropositives, but less so for seronegatives (Figure 5—figure supplement 4, Table 1). Mean transient immunity estimates are consistent with those from our main model when averaged over serotypes (Table 1).

Adding serotype-specific transient immunity to the simplest model (Figure 2C) gives the following hazard:

where again age is only present in seropositive relative risk. While survival curves of individual countries are well fitted, age-stratified survival curves are fitted no better than the simplest model and qualitatively worse than the model with age and serotype effects (Figure 6—figure supplement 5), and so we choose the latter model as our default. Vaccine-induced estimates from the model with only serotype effects are consistent with those from our main model when averaged over age groups (Table 1).

While these simpler model variants are more parsimonious, they do not explain the trial data as well as our main model. Age-specific variation in transient immunity and the force of infection are required to fit the age distribution of cases well, and serotype-specific transient immunities are necessary to fit observed attack rates by country.

Because our estimates of the age-specific force of infection multiplier were relatively imprecise and had credible intervals that spanned 1 (indicating no difference between age groups), we investigated a model that removed these effects, with the following hazard

Transient immunity and relative risk parameters are essentially unaffected by this omission; however, the age breakdowns in CYD-14 are adversely affected in 2–5 year olds and 6–11 year olds (Figure 6—figure supplement 6).

Our main model considers vaccination to prime host immunity akin to a natural disease-free infection, and this must be considered alongside estimates of vaccine-induced transient immunity. Here we consider a model without immune priming, and so relative risk parameters do not vary by trial arm, giving

and

In this model variant the benefit of the vaccine is purely a function of transient immunity and its duration.

Fits to the Kaplan–Meier curves (Figure 6—figure supplement 7) and attack rates (Figure 7—figure supplement 7) over the entire trial duration appear similar to our main model. However, passive phase attack rates in the 2–5-year CYD-14 age group are not reproduced at all, and indeed here the vaccine is erroneously predicted to be beneficial. Further, each measure of model fit is poorer for this variant. We conclude that immune priming is required to properly account for the trial data, explain the vaccine’s action mechanism and evaluate vaccine benefit and risk.

We investigated another model variant where we allowed the duration of protection τ_b(α) to vary with age, and so here

where τ_b(α) is a step function.

Fits to Kaplan–Meier curves and attack rates are almost indistinguishable from our main model (Figure 6—figure supplement 8 and Figure 7—figure supplement 8). We find no age dependence in seropositive durations, but there is some indication that seronegative transient immunity may be longer-lived in older children (Figure 5—figure supplement 5). As posteriors for durations are already imprecisely inferred when not age-specific, and since fits are largely unchanged, we do not allow duration to vary in our main model.

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

DJL, GNG, and NMF acknowledge grant funding from the Bill & Melinda Gates Foundation (grant OPP1092240). DJL, ID, WRH, GNG and NMF acknowledge joint centre funding from the UK Medical Research Council and Department for International Development (grant MR/R015600/1). DJL, GNG and NMF acknowledge funding from Vaccine Efficacy Evaluation for Priority Emerging Diseases (VEEPED) grant (ref. NIHR: PR-OD-1017–20002) from the National Institute for Health Research. ID acknowledges research funidng from a Sir Hentry Dale Fellowship funded by the Royal Society and Wellcome Trust (grant 21349/Z/18/Z). Views expressed do not necessarily represent those of the funders. DJL, ID and NMF have advised Sanofi-Pasteur Ltd., without payment on the implications that this work has on the use of their vaccine. We thank Nick Jackson and Jean-Sebastien Persico at Sanofi-Pasteur, and Ben Lambert, Anne Cori and Natsuko Imai at Imperial College London for useful discussions. We further thank our reviewers and editors for useful comments. All clinical trial data used for these models are publicly available in the original publications (cited), and model code is available at https://github.com/dlaydon/DengVaxSurvival. Role of the funding source: The funder of the study had no role in study design, data collection, data analysis, data interpretation or writing of the report. The corresponding author had full access to all the data in the study and had final responsibility for the decision to submit for publication.

1. Received: November 24, 2020
2. Accepted: June 29, 2021
3. Accepted Manuscript published: July 2, 2021 (version 1)
4. Version of Record published: July 29, 2021 (version 2)
5. Version of Record updated: August 4, 2021 (version 3)

© 2021, Laydon et al.

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