Efficacy profile of the CYDTDV dengue vaccine revealed by Bayesian survival analysis of individuallevel phase III data
Abstract
Background:
SanofiPasteur’s CYDTDV is the only licensed dengue vaccine. Two phase three trials showed higher efficacy in seropositive than seronegative recipients. Hospital followup revealed increased hospitalisation in 2–5 yearold vaccinees, where serostatus and age effects were unresolved.
Methods:
We fit a survival model to individuallevel data from both trials, including year 1 of hospital followup. We determine efficacy by age, serostatus, serotype and severity, and examine efficacy duration and vaccine action mechanism.
Results:
Our modelling indicates that vaccineinduced immunity is longlived in seropositive recipients, and therefore that vaccinating seropositives gives higher protection than two natural infections. Longterm increased hospitalisation risk outweighs shortlived immunity in seronegatives. Independently of serostatus, transient immunity increases with age, and is highest against serotype 4. Benefit is higher in seropositives, and risk enhancement is greater in seronegatives, against hospitalised disease than against febrile disease.
Conclusions:
Our results support vaccinating seropositives only. Rapid diagnostic tests would enable viable ‘screenthenvaccinate’ programs. Since CYDTDV acts as a silent infection, longterm safety of other vaccine candidates must be closely monitored.
Funding:
Bill & Melinda Gates Foundation, National Institute for Health Research, UK Medical Research Council, Wellcome Trust, Royal Society.
Clinical trial number:
NCT01373281 and NCT01374516.
Introduction
Over 40% of the world population is at risk of dengue infection. An estimated 105 million infections and approximately 50 million symptomatic cases occur each year (Stanaway et al., 2016; Cattarino et al., 2020). Dengue disease is caused by four distinct viruses, termed serotypes (DENV 1–4). Infection confers lifelong immunity to a homologous serotype, but against a heterologous serotype protective immunity is only temporary (St John and Rathore, 2019). Furthermore, secondary infection with a heterologous serotype drastically increases the likelihood of disease (St John and Rathore, 2019).
Traditional vector control interventions have had little impact on dengue disease burden (Guzman et al., 2010) and no antiviral treatments yet exist. Several vaccine candidates are in development, but the only licensed vaccine is SanofiPasteur’s CYDTDV (marketed as Dengvaxia). CYDTDV is a live attenuated tetravalent chimeric vaccine, where genes for the structural proteins (E and prM) are taken from the four DENV serotypes, while the other proteins are based on the yellow fever 17D vaccine strain. The vaccine has now been licensed in 21 countries and the EU. A phase two trial in 2012 (ClinicalTrials.gov number NCT00842530) (Sabchareon et al., 2012) reported moderate efficacy of 30.2% (−13.4% to 56.6%) and showed the vaccine to be well tolerated and largely safe. Two large scale phase three trials followed: the CYD14 trial (ClinicalTrials.gov number NCT01373281) in South East Asia of 10,275 children aged 2–14 (Capeding et al., 2014), and the CYD15 trial (ClinicalTrials.gov number NCT01374516) in Latin America of 20,869 children aged 9–16 (Villar et al., 2015). After stratifying by age, participants were randomly assigned to vaccine or control arms in a 2:1 ratio, and vaccine doses were given at baseline then 6 and 12 months later. For a subset of participants (approximately 20% for CYD14% and 10% for CYD15), immunogenicity and prior dengue exposure was determined using baseline sera. Participants were actively surveilled by weekly phone calls for 25 months postfirst dose (where any symptomatic disease was detected), after which surveillance was passive using routine hospital surveillance, (where only hospitalisations were detected). See (Capeding et al., 2014; Villar et al., 2015; Hadinegoro et al., 2015) for further details of the trial design.
The CYD14 and CYD15 trials showed overall vaccine efficacies of 56.5% (43.8%–66.4%) and 60.8% (52.0%–68.0%) respectively, with efficacy varying significantly by serotype and prior exposure. However, in 2015, results from the first year of longterm follow up (Hadinegoro et al., 2015) showed that while the vaccine remained beneficial overall, the number of hospitalisations among 2–5 year olds was significantly greater in vaccinees than in controls. A potential explanation for these results considered age as a proxy for serostatus (Aguiar and Stollenwerk, 2018), and that the vaccine may act as a ‘silent’ diseasefree infection that primes host immunity (Ferguson et al., 2016; Flasche et al., 2016). Therefore, a seronegative child, who would ordinarily experience their first and relatively lowrisk natural infection, would after vaccination instead experience a ‘secondarylike’ infection that is more predisposed to clinically apparent disease. Conversely, a child with a single prior natural infection would have a lower risk of disease when exposed to dengue postvaccination, normally associated with tertiary and quaternary infection [Figure 1].
The immunogenicity subset was only a small fraction of the entire trial, and the estimated efficacy in seronegatives had wide confidence intervals indicating neither benefit nor harm, and so it was not possible to determine conclusively whether age or lack of prior exposure was the dominant factor in the increased hospitalisation of 2–5 yearold vaccinees. Further, it was not possible to retroactively expand the immunogenicity subset to determine prior dengue exposure, as Dengvaxia can elicit antibody responses that would test positive under a plaque reduction neutralisation test (PRNT). Therefore, and because the vaccine showed the greatest benefit in children aged nine or older, the vaccine was licensed for use above this age, independent of baseline serostatus.
An ELISA assay detecting antidengue nonstructural protein 1 (NS1) IgG antibodies then provided a novel approach to retrospectively assess the serostatus of trial participants prior to vaccination (Nascimento et al., 2018). Dengvaxia expresses yellow fever NS1, not dengue NS1, and therefore this assay can distinguish between natural infection and exposure to the vaccine. Blood samples of trial participants who contracted virologically confirmed dengue during followup were analysed using the NS1 assay in the CYD14 and CYD15 trials. The results provided clear evidence of the enhanced risk of hospitalised or severe dengue disease in baseline seronegative vaccinees (Sridhar et al., 2018) and these were in line with refined estimates of vaccine efficacy obtained with machine learning (Dorigatti et al., 2018). Subsequently, in November 2017, Dengvaxia was recommended only in persons with a confirmed prior dengue infection (WHO, 2018).
Here we present a survival model with time and age varying hazards, which we fit to the individual level phase three CYD14 and CYD15 data, up to and including the first year of longterm followup (Hadinegoro et al., 2015). We characterize the efficacy profile and mode of action of the vaccine, which we find to be consistent with the ‘vaccine as silent infection’ hypothesis. We refine previous estimates, and examine the vaccine’s duration of protection and its efficacy against both febrile dengue disease and hospitalized disease. Our results provide a comprehensive characterization of CYDTDV’s safety and efficacy, and demonstrate the need for longterm follow up in the phase three trials of other dengue vaccine candidates currently in development.
Materials and methods
Data
We use the individuallevel 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 followup. 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 serotypespecific effects omit all cases of unknown serotype. We rightcensor after date of first case for each patient, and so do not consider multiple cases per patient.
Model
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 (nonsevere/nonhospitalised = 0, severe/hospitalised = 1)). We consider a countryspecific 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.
ρ_{cd} ∈ [0,1] is the proportion of serotype d in country c (assumed to be constant, with $\sum _{d=1}^{4}{\rho}_{cd}}=1$, 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 agespecific 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, diseasefree 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.
Severity analysis
Request a detailed protocolWe interpret relative risks in two different ways depending on our analysis. The probability of case detection depends on the degree of trial surveillance, and so by default we allow relative risks to differ between the active and passive trial phases. For example, K_{i = 2, D = 0} is the risk of clinically apparent disease (of any severity) in the active phase for those with two or more prior infection. Alternatively, when distinguishing between severe and nonsevere disease (or equivalently between hospitalised and nonhospitalised disease), risk of disease does not differ between trial phases but between disease severities, for example, the risk of severe disease in seronegatives would be K_{i = 0, D = 1}. In practice, these two interpretations of the relative risk parameters are largely equivalent as nonhospitalised disease is detected exclusively by active surveillance and passive surveillance only detects hospitalised or severe disease. It does however change the calculation of survival probabilities. We allow relative risks of hospitalised disease to differ between CYD14 and CYD15 trials to account for the nonstandardised hospitalisation criteria between Southeast Asia and Latin America. We do not do so when modelling severe disease since the trials used the WHO dengue severity criteria to ascribe disease severity in all trial sites. We fix the ratios K_{0,1} /K_{1,1} = K_{2,1}/K_{1,1} = 0.25 (Ferguson et al., 2016), while the proportion of symptomatic secondary infections that require hospitalisation (or that result in severe disease) K_{1,1} are fitted parameters.
It should be stressed that in our formulation overall vaccine benefit cannot be measured by transient immunity alone, but rather in combination with the change in relative risk induced by vaccination.
Baseline hazard splines
Request a detailed protocolWe model the baseline hazard for each country as a quadratic spline. We divide the followup period of length T into n1 intervals ${\left\{{t}_{k}\right\}}_{k=1}^{n}$ with ${t}_{k}=k\times \frac{T}{n}$, and define ${\lambda}_{c}\left({t}_{k}\right)={\kappa}_{ck}$ as the knots of the spline for country c.
The observation period is approximately T = 4 years, and we use n =10 knots, spaced at 4month intervals. For polynomial $\sum _{i=0}^{2}{\beta}_{ick}}{t}^{i$, we solve the following equations for coefficients $\{{\beta}_{0ck},{\beta}_{1ck},{\beta}_{2ck}\}$:
The knot locations ${\left\{{t}_{k}\right\}}_{k=1}^{n}$ are fixed and their values ${\left\{{\kappa}_{ck}\right\}}_{k=1}^{n}$ are fitted parameters.
Relative risk in seropositives
Request a detailed protocolIf h_{c} is the constant historical force of infection in country c, then the probability of remaining seronegative until age α is given by
${p}_{0c}\left(\alpha \right)={e}^{{h}_{c}\times \alpha}$.
Therefore, the probability of seropositivity (i.e. at least one infection) by age α is given by $1{e}^{{h}_{c}\times \alpha}$. Assuming that each serotype carries an equal force of infection, then the probability of exactly one infection with any serotype is given by
The relative risk of disease φ_{cD}(α) in seropositive participants is therefore a weighted average of the risk in participants with one or more than one prior exposure.
Note that the historical hazards h_{c} refer to infection, not disease, and that this approximation assumes that historical force of infection is equal across serotypes.
Serotype proportions
Request a detailed protocolThe proportions ρ_{cd} of serotype d in country c must satisfy $\sum _{d}^{4}{\rho}_{cd}}=1$ for all c. Therefore, given proportions for three serotypes, the fourth is explicitly determined. We fit three parameters q_{cy} (y = 1, 2, 3) for each country c and calculate
Each parameter q_{cy} is fitted with prior Unif(0,1).
Age effects
Request a detailed protocolWe use a step function to model agespecific transient immunity and force of infection multiplier. This function is constant within the age groups 2–5, 6–11 and 12–16 years. We also considered a quadratic spline formulation, similar to the baseline hazard, with four knots placed at ages 2, 6, 12 and 16 years, although this did not sufficiently improve model fit.
We model serotype and age effects additively (Figure 2A), that is, if A_{b}(α) gives the relationship between transient immunity and age for serostatus b, then the (initial) magnitude of transient immunity I_{bd}(α) for baseline serostatus b and serotype d for age α is given by
where s_{bd} is the intercept for baseline serostatus b and serotype d (fixed at 0 for serotype d = 1).
Likelihood
Request a detailed protocolIf 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 rightcensored 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
Data augmentation
Request a detailed protocolWe 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 $\mathbb{P}\left({S}_{+}\rightC;\theta )$ and $\mathbb{P}\left({S}_{}\rightC;\theta )=1\mathbb{P}({S}_{+}C;\theta )$ respectively denote the probabilities of seropositivity and seronegativity at baseline given clinical outcome C, by Bayes’ theorem we have
For example, a noncase 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
Hazard ratios
Request a detailed protocolIf $\mathcal{\mathcal{V}}$ and $\mathcal{\mathcal{C}}$ are the sets of vaccinees and controls, respectively, then within any given stratum of interest $\mathcal{\mathcal{S}}$ (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 postfirst dose t* are given by
where $\left\mathcal{\mathcal{S}}\right$ denotes the number of trial participants in stratum $\mathcal{\mathcal{S}}$.
For hazard ratios HR(t*,d) of a particular disease severity D and serotype d, we have
Survival curves
Request a detailed protocolFor stratum $\mathcal{\mathcal{S}}$ as at t* days postfirst dose, posterior survival probabilities ${\mathbb{P}}_{\mathcal{\mathcal{S}}}(t*)$ are calculated as
and if ${n}_{\mathcal{\mathcal{S}}}(t*)$ denotes the number of cases in stratum $\mathcal{\mathcal{S}}$ that occurred within t* days postfirst dose, then the observed survival probabilities are given by
Attack rates
Request a detailed protocolThe 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 followup 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 variants and fitting
Request a detailed protocolModel fitting was performed using the Metropolis–Hastings algorithm for parameter inference and Gibbs sampling for data augmentation. Parameters fitted include the relative risks, vaccineinduced transient immunities (by baseline serostatus, serotype and age) and their durations. For each countryspecific 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 burnin 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 vaccineinduced 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.
Results
Trial data
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 postfirst dose), where surveillance could detect both hospitalised and nonhospitalised 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 2–5yearold vaccinees show a greatly increased risk of hospitalisation than controls. In both trials, a mix of infecting serotypes among cases was observed.
Model outputs
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.
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 shortlived immunity, combined with an almost sixfold longterm 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 longterm followup 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 2–5yearold 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 longterm 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 longterm 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 longterm 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).
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 preexisting 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 longlived, 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 preexisting 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 longterm increase in disease risk is shortlived.
We find that the age groupspecific 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 2–5yearold age group in the mean posterior estimates. While both credible intervals encompass 1 (indicating no difference), model runs that omit this agespecific 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).
Model fits
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).
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 2–5yearold vaccinees observed in the CYD14 trial (Figure 7).
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).
Severity analysis
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 nonhospitalised and hospitalised disease (or alternatively between nonsevere 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 longlasting protection against disease, and more so against hospitalised disease. In seronegatives, against nonhospitalised disease, hazard ratios again show only minor (and sometimes nonsignificant) 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 nonsevere disease.
Age, serotype and serostatusspecific 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 nonstandardised 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 nonsevere disease, we reproduce observed survival curves at trial level for nonsevere disease, but fits are less good for severe disease (Figure 6—figure supplement 1). This is due firstly to limited data (nonsevere 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 nonsevere 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 (nonhospitalised febrile disease is not detected by passive surveillance) (Figure 7—figure supplements 5 and 6).
Alternative model variants
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 shortlived in seronegatives and longlived in seropositives.
Discussion
Our results provide a comprehensive profile of SanofiPasteur’s CYDTDV vaccine (Dengvaxia). We investigated multiple mechanisms of vaccine action and analysed its dependence on serotype, baseline serostatus and age. We further examined efficacy by disease severity.
There was substantial heterogeneity in transient immunity by serotype and serostatus. Vaccineinduced protection against each serotype was higher in seropositive recipients than in seronegatives, and these findings were robust across model variants. The incorporation of serotypespecific transient immunity improved model fits to country breakdowns, but had little effect on fits to age breakdowns. Interestingly, transient immunity was found to increase with age in seropositives and to a lesser extent in seronegatives. While one mechanism of our model (change in relative risk through ‘silent infection’) separates seropositivity into monotypic and multitypic immunity, the other (conferral of transient immunity) does not, and so it is possible that the age trend in seropositives also reflects increasing transient immunity for multitypic immunes, although the slight age trend in seronegatives could not be explained this way. In general, heterogeneity between countries' Kaplan–Meier curves can be explained by serotype and seroprevalence, although these factors are insufficient to explain differences in vaccine efficacy by age, for which agespecific effects (independent of serostatus) are required.
In every model variant examined, vaccination substantially decreased disease risk in seropositives, but increased risk in seronegatives (particularly risk of hospitalised/severe disease). These findings are consistent with and largely predict the NS1 data and longterm followup data (Sridhar et al., 2018). We further found larger differences in efficacy between seropositives and seronegatives when considering hospitalised disease: benefit to seropositives and risk enhancement in seronegatives is greater than against febrile disease. Our findings here may be affected by the data used: the passive surveillance in the first year of hospital followup does not detect nonhospitalised disease.
While our analysis demonstrates that serostatus is the dominant factor in efficacy, the data do not allow us to consider the order of infecting serotype, which recent work suggests affects disease risk (Aguas et al., 2019) and therefore perhaps efficacy also. While we have analysed the vaccine’s effect against different serotypes and different severities of disease, we have not analysed efficacy against infection (OliveraBotello et al., 2016). It would be helpful to examine the degree to which efficacy is dependent upon antibody titres (Salje et al., 2018; Katzelnick et al., 2017) as opposed to a binary serostatus. The latter may determine whether vaccine immune priming is age dependent.
Our model does not disaggregate seropositives into monotypic or multitypic immunity, and we were unable to test models whereby transient immunity applies only to multitypic seropositives. The use of antibody titres could be informative, although we are ultimately limited by the small size of the immunogenicity subset. Additionally, we do not model either serotypespecific natural immunity or transient immunity that arises from natural infection.
Our model estimates an enhancement of risk for seronegative vaccinees for every serotype (although more so for serotypes 1 and 2 than for serotypes 3 and 4), whereas previous work indicated the vaccine’s better performance against serotype 4 (Sridhar et al., 2018). This is likely due to the fact that we do not consider serotypespecific relative risks (and therefore serotypespecific changes in relative risk induced by ‘silent infection’ vaccination). While we attempted previously to resolve this issue, there is insufficient power to resolve these parameters, particularly for the passive phase or hospitalised disease. Further, serotypespecific transient immunity durations would likely have diminished or altogether removed the predicted risk enhancement for serotype 4. Again though, there is insufficient power to resolve such serotype effects, particularly seeing as transient immunity durations by serostatus were not precisely inferred.
Current WHO guidance recommends serological testing of potential vaccine recipients before vaccination and only vaccinating seropositives (Dengue vaccine, 2019). Age targeting of vaccination is therefore important: too young an age, and most of those tested will be seronegative, too old and most will have already experienced secondary dengue infection.
Distinguishing between monotypic and multitypic infection is not usually possible in clinical practice. However, our results suggest that all seropositives are likely to benefit from vaccination, and further that vaccinating them will be more beneficial than merely boosting their immunity to that of someone with two previous natural infections. Importantly, this means it may be more beneficial to vaccinate multitypic seropositives than other models have predicted (Flasche et al., 2016), at least to the extent that seropositive transient immunity is longlived and acts in both monotypic and multitypic seropositive vaccine recipients.
Highresolution maps of dengue seropositivity are now available, and alongside improved rapid diagnostic tests and ‘screenthenvaccinate’ programmes (Flasche and Smith, 2019), optimal deployment of the vaccine could reduce the increasing worldwide burden of dengue disease by as much as 30% (Cattarino et al., 2020). Therefore, targeting only seropositive recipients with this vaccine is an increasingly viable public health strategy.
Appendix 1
Simplest model without age or serotype effects
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 CYD14 age groups (Figure 6—figure supplement 3). This is likely due to an uneven age distribution in CYD14: age groups 2–5 and 12–14 constitute 24.2% and 22.7% of CYD14 (or 7.9% and 7.5% of combined CYD14 and CYD15 data), whereas 6–11 years olds comprise 53.2% of the CYD14 data (17.5% of combined data). CYD15 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). Lowerquality 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 countryspecific 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 vaccineinduced 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 longlasting benefit to seropositives beyond the effect of immune priming (Table 1).
Model with age effects only
Adding agespecific 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 CYD14 2–5 and 12–14yearold 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).
Model with serotype effects only
Adding serotypespecific 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, agestratified 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. Vaccineinduced 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. Agespecific variation in transient immunity and the force of infection are required to fit the age distribution of cases well, and serotypespecific transient immunities are necessary to fit observed attack rates by country.
Model without agespecific force of infection
Because our estimates of the agespecific 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 CYD14 are adversely affected in 2–5 year olds and 6–11 year olds (Figure 6—figure supplement 6).
Model without immune priming
Our main model considers vaccination to prime host immunity akin to a natural diseasefree infection, and this must be considered alongside estimates of vaccineinduced 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 2–5year CYD14 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.
Model with agespecific durations of transient immunity
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 longerlived in older children (Figure 5—figure supplement 5). As posteriors for durations are already imprecisely inferred when not agespecific, and since fits are largely unchanged, we do not allow duration to vary in our main model.
Data availability
Qualified researchers may request access to patient level data and related study documents including the clinical study report, study protocol with any amendments, blank case report form, statistical analysis plan, and dataset specifications. Patient level data will be anonymized and study documents will be redacted to protect the privacy of trial participants. Further details on Sanofi's data sharing criteria, eligible studies, and process for requesting access can be found at: https://www.clinicalstudydatarequest.com. Additional details of the trial designs and data can be found in Sridhar et al (NEJM 2018). All model code is available at https://github.com/dlaydon/DengVaxSurvival (copy archived at https://archive.softwareheritage.org/swh:1:rev:d4964b7240312a371b2767533099643c59025dbf), which is linked to in the manuscript. This repository also contains simulated data, generated to closely match the trial data, giving comparable case numbers across strata. When our model is fitted to the simulated data, the resulting parameter estimates closely approximate the results presented in this analysis.
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Decision letter

Ben S CooperReviewing Editor; Mahidol University, Thailand

Eduardo FrancoSenior Editor; McGill University, Canada

James A WatsonReviewer; Mahidol Oxford Tropical Medicine Research Unit, Thailand
In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.
Acceptance summary:
This paper presents a detailed, modelbased, characterisation of the efficacy of the only licensed dengue vaccine as a function of baseline serostatus and age. The results reinforce the hypothesis of "vaccination as a silent infection" and demonstrate the need for targeted vaccination using rapid diagnostic tests. Although this finding is not novel per se, having a precise characterisation of the timevarying risk is important for determining vaccine utility and optimal implementation strategies.
Decision letter after peer review:
Thank you for submitting your article "Efficacy profile of the CYDTDV dengue vaccine revealed by Bayesian survival analysis of individuallevel Phase III data" for consideration by eLife. Your article has been reviewed by 2 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and a Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: James A Watson (Reviewer #2).
The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.
Essential revisions:
These revisions either reflect a need to temper some of the claims made in the paper or to improve clarity of the work.
1) The authors assume in their models that immunity wanes in seronegatives (over 1 year) and is stable in seropositives (maintained over time). It is unclear why these assumptions were made and clarification is needed.
2) The authors should adjust the statement "vaccinating seropositives gives greater longlasting immunity than two natural infections" to reflect the fact that immunity in seropositives may also wane over time in a way that cannot be accurately measured with the current data.
3) On lines 329330 the authors state "Therefore it may be more beneficial to vaccinate multitypic seropositives than simpler models have predicted [11]." How do the authors know it is the multitypics that benefit as opposed to those with primary immunity before vaccination?
4) It would be helpful if the authors further discussed ageeffects and their relationship with being multitypic immune.
5) Please address reviewer 1's concern that the results of this manuscript do not support the claim on lines 311 – 315. Please also address concerns about lines 316320.
6) Could the authors comment on whether the fact that serotype effects are more similar than might be expected based on previous articles on these data might relate to the way serotype effects are modeled, or whether this constitutes a major difference from what has been shown previously?
7) Please consider reviewer 1's suggestions to improve readability by defining KiD in the main text and revising table 1.
8) Line 349 – Where does the value of 0.7 for seropositives come from?
9) Please explain the big K notation in the Results section.
10) Please add a parameter table to the methods section and add a section on the data.
11) Please justify choice of priors and/or consider sensitivity of results to choice of priors.
12) Please provide access to the model code. The statement "Model code is available from the authors" does not meet eLife requirements: "Regardless of whether authors use original data or are reusing data available from public repositories, they must provide program code, scripts for statistical packages, and other documentation sufficient to allow an informed researcher to precisely reproduce all published results."
Reviewer #1:
Laydon et al. have conducted an elegant analysis that provides a clear and comprehensive guide to the mechanism of difference of CYDTDV for dengue virus seropositive vs. seronegative vaccine recipients. The paper includes relevant hypothesis and model schemes as well as figures that show differences between seropositive and seronegative vaccine recipients across a range of covariates. The authors demonstrate, in a clearer way than has been shown before, that CYDTDV increases disease across all ages in both trials in seronegatives. The authors also show that the enhancing effect is stronger against hospitalized disease than febrile disease. Many of these results have already been presented previously in other papers analyzing the same data, but the modeling approach does provide a new perspective that adds to the story of the CYDTDV vaccine.
Overall, the paper is clearly written and easy to follow, especially given the complexity of the model and subject matter. However, numerous claims are made in the abstract and the discussion that inaccurately reflect the results presented in this paper. In particular, major conclusions of the paper relate to the benefit of the vaccine for seropositive individuals (lines 1819, 327328) and an increasing effect of vaccination for seropositive individuals with age (lines 286290, 329330). There are potential issues with the modeling approach and how it relates to these conclusions. Further, a discussion about the longterm effects of the vaccine for seronegatives is speculative and problematic (311320).
Comments for the authors:
1) Lines 1819. "Vaccinating seropositives gives greater longlasting immunity than two natural infections." The claim that fixedtime immunity induced by vaccination of seropositives is maintained at a high level over time is not well supported. The authors assume in their models that immunity wanes in seronegatives (over 1 year) and is stable in seropositives (maintained over time). First, it is unclear why these assumptions were made. The reference for these model choices does not seem to cover immune kinetics over this period of time (Clapham et al. 2016 PLOS Comp Bio). Second, the authors actually tested different assumptions about waning immunity in supplement (lines 667 – 694), which are not described in the main text. In the supplement, the authors demonstrate waning immunity out to 4.5 years (with wide confidence intervals) in both seronegative and seropositive vaccinated individuals. In both cases, the duration of waning is outside of the observational period of the study, and the authors write: "We conclude that three years of follow up data from each patient is insufficient to infer durations." Thus, the authors should adjust the statement "vaccinating seropositives gives greater longlasting immunity than two natural infections" to reflect the fact that immunity in seropositives may also wane over time in a way that cannot be accurately measured with the current data.
2) Lines 329330. "Therefore it may be more beneficial to vaccinate multitypic seropositives than simpler models have predicted [11]." How do the authors know it is the multitypics that benefit as opposed to those with primary immunity before vaccination? It would be helpful if the authors could further support this statement by discussing the results that relate to this point. This is especially important in relation to the discussion about dengue rapid diagnostic tests (e.g. lines 2324), which have very low sensitivity for detecting monotypic DENV immunes.
3) Lines 286 290. "Interestingly, fixedtime immunity was found to increase with age in seropositives. In general, heterogeneity between countries' KaplanMeier curves can be explained by serotype and seroprevalence, although these factors are insufficient to explain differences in vaccine efficacy by age, for which agespecific effects (independent of serostatus) are required." The conclusion about the benefit of the vaccine even to multitypic immunes seems to be derived from the observation that fixedeffect immunity induced by the vaccine in seropositive individuals increases with age. The authors observe large agespecific fixedtime immunity differences by serostatus (Figure 5), although it is not clear there is much difference across age groups in vaccine efficacy (Figure 4). While the authors state that age specific effects are independent of serostatus, the age effects only occur in seropositives and thus are most plausibly related to more prior infections in children of older ages. It would be helpful if the authors further discussed ageeffects and their relationship being multitypic immune.
4) Lines 311 – 315. "In high transmission settings where children would ordinarily receive at least two natural infections, we predict that even seronegatives would eventually benefit from vaccination, as they would experience one high risk infection, and all subsequent infections would have a much lower risk, in contrast to unvaccinated individuals who would ordinarily experience one moderate and one high risk infection [Figure 1]." The results of this manuscript do not support this claim. While the authors may expect this to be true based on the model scheme (referenced as Figure 1), the results, as currently described, do not prove this point. Further, the caveats provided afterward do not justify inclusion of this paragraph in the discussion (Lines 316320): "Important caveats include first that disease risk would increase in the short term. Second, and more seriously, a small subset of symptomatic infections are fatal, in which case vaccination could shorten life in seronegatives. Finally, while the eventual benefit to seronegatives is predicted by our model and the model fits well, this remains a prediction yet to be validated by empirical data."). This paragraph should be removed or significantly reworked because it is largely a question of medical ethics.
5) Figure 4. It is not clear why vaccine efficacy increases over time in the trial for vaccinated seropositives, even across all age groups. It does not seem to be explained by age effects, waning immunity, or serotype distributions. Is it related to differences in disease outcomes measured in the trial over time (e.g. Figure S8)?
6) It is surprising that the serotype effects are more similar than might be expected based on previous articles on these data, especially previous observations of greater efficacy against DENV4. Here the authors observe strong enhancement of DENV4 at later timepoints in the trial. Could the authors comment on whether this might relate to the way serotype effects are modeled, or whether this constitutes a major difference from what has been shown previously?
7) Table 1 and its explanation in the text are confusing. Instead of a traditional presentation of relative risk, which is described in the text, the table presents the probability of disease expected relative to secondary infections. One option would be to present relative risk estimates in table, and clearly indicate the reference groups in the table. Additionally, while KiD is clearly defined in the methods, it would be helpful to add one sentence to the main text to define KiD, given that the main text uses this notation in multiple paragraphs without explaining its interpretation.
Reviewer #2:
This paper uses individual trial participant data from two large phase 3 dengue vaccine randomised clinical trials to fit a Bayesian survival model of symptomatic dengue illness that is dependent on casecontrol status (vaccine vs placebo), baseline serostatus, age, and dengue serotype. The main finding is a detailed characterisation of how the relative risk of symptomatic illness changes as a function of time since vaccination and baseline serostatus. As previously reported, children who are seronegative at baseline have a drastically increased risk of symptomatic illness in years 2 and 3 of followup. Although this finding is not novel per se, having a precise characterisation of the timevarying risk is important for determining vaccine utility and optimal implementation strategies.
The survival model is fairly complex but this complexity reflects the complexity of the trial data and the inference problem at hand (multiple countries with different proportions of dengue serotypes, active and passive followup periods, agevarying effects). I particularly like the use of Gibbs sampling to treat the missing baseline serostatus as a latent variable in the model. This is an elegant method that allows for the analysis of the whole dataset and not restricted to just those with serostatus data (only 10% of participants).
My main comments are about clarity of the manuscript and reproducibility:
1. The Results section needs to explain the big K notation which is fairly complicated (but I can't see any easy way of simplifying it!)
2. The Methods section really needs a section on the data (this could be quite short). Otherwise it's hard to know exactly what sort of data are being used (eg right censoring after first illness is mentioned in the model bit)
3. The Methods section really needs a parameter table. Table 1 gives a summary of model outputs which is useful, but these are not parameters. What I would find useful is a table with all the main model parameters using the same notation as in the text (eg K_{0,0}) and the associated prior distributions. This would emphasize that the model has a lot of parameters. This would also be useful to emphasize which parameters were fixed in the model (eg M_{b}, sigma?).
4. It says all priors are uniform but this seems a bit odd. Maybe I am misunderstanding something, but the relative risk parameters can take values in (0, infinity) surely? A uniform prior is therefore improper. This is probably not the best choice (uniform priors are often not a good choice).
5. "Model code is available from the authors" and "The model was coded in C++" doesn't really meet eLife standards for reproducibility or inspire huge confidence. The paper is entirely based on the validity of the model fitting and this is a complex model that has been hand coded. I fully trust the competence of the authors, but I really think the code should be made available online (via a git repo for example) with a minimum working example for the fitting. If the authors can't make the full dataset openly accessible then a simulated dataset to test the model would be a good alternative.
6. Could you explain a bit more why the parameter M_{b} is fixed at 0.7? It says: "equal to 1 for seronegatives and 0.7 for seropositives, chosen to reflect seropositive participants' reduced disease risk due to their immunity to at least one serotype". I couldn't square this with fact that seropositives also can have increase risk as the secondary infection is more likely to be severe than the first? I get that you don't know how many infections a seropositive individual has had, but I can't really understand the justification for the 0.7.
https://doi.org/10.7554/eLife.65131.sa1Author response
Essential revisions:
These revisions either reflect a need to temper some of the claims made in the paper or to improve clarity of the work.
1) The authors assume in their models that immunity wanes in seronegatives (over 1 year) and is stable in seropositives (maintained over time). It is unclear why these assumptions were made and clarification is needed.
We have now amended our analysis to infer these durations, rather than assume them. The original rationale for fixing these values was that they were imprecisely inferred, although the overall picture was that of shortlived seronegative immunity and longlived seropositive immunity. Further, it is arguable that three years of followup data is insufficient to infer duration. On reflection, we agree with the reviewers that it is more transparent to fit these parameters rather than fix them, and explain where they are imprecisely inferred. We have amended the manuscript throughout to reflect these changes.
2) The authors should adjust the statement "vaccinating seropositives gives greater longlasting immunity than two natural infections" to reflect the fact that immunity in seropositives may also wane over time in a way that cannot be accurately measured with the current data.
This is a fair point and we have amended the text in the abstract to read, “Our modelling indicates that vaccineinduced immunity is longlived in seropositive recipients, and therefore that vaccinating seropositives gives higher protection than two natural infections.” to make it clearer. We have also included this point in the discussion text (e.g. lines 614621) where we are less constrained by word limits.
As our model fits the durations of what we now term “transient immunity”, this conclusion is less dependent on our model assumptions and more dependent on fitted parameter values. We think this conclusion is now sufficiently justified and caveated, and that vaccine benefit to multitypic immune subjects remains an important consideration for CYDTDV, but please let us know if further amendments are required.
3) On lines 329330 the authors state "Therefore it may be more beneficial to vaccinate multitypic seropositives than simpler models have predicted [11]." How do the authors know it is the multitypics that benefit as opposed to those with primary immunity before vaccination?
We had not phrased this clearly in the original draft. Under our model, vaccination has two mechanisms: (i) altering disease risk associated with natural infection (denoted by K_{i,D} values) and (ii) conferring transient immunity (denoted by the I_{bd} values). For multitypic seropositives, the first mechanism has no effect (as we consider the risk of disease from tertiary or quaternary infection to be equal, i.e. K_{2,D} = K_{3,D} for either disease type D). However, the second mechanism is still predicted to have an effect, and furthermore our results indicate that seropositive transient immunity is longlived (85% of posterior samples are above 5 years).
Additionally, the model could reject either of these mechanisms depending on the fitted parameter values. For example, seropositive transient immunity (I_{1d}) values of zero (or alternatively a very short duration) would indicate that only monotypic seropositive vaccinees would benefit, whereas we find positive values for every serotype. Further, we previously ran a sensitivity check where seropositive transient immunity was fixed at zero to see if the data could be explained more parsimoniously, but it could not. However, we were not able to test a model where transient immunity applied only to monotypically immune patients. We have now discussed these points in the results (lines 435447).
Nevertheless, our results indicate that monotypics will benefit more than multitypics, and benefit to multitypics is dependent on seropositive immunity being longlived, and we have now included this caveat throughout the text in the abstract (lines 1819), results (lines 414417 and 427447) and discussion (lines 614621).
4) It would be helpful if the authors further discussed ageeffects and their relationship with being multitypic immune.
Please see our response to Reviewer 1’s point (3) below.
5) Please address reviewer 1's concern that the results of this manuscript do not support the claim on lines 311 – 315. Please also address concerns about lines 316320.
We agree with reviewer 1 and have removed the paragraph from the manuscript.
6) Could the authors comment on whether the fact that serotype effects are more similar than might be expected based on previous articles on these data might relate to the way serotype effects are modeled, or whether this constitutes a major difference from what has been shown previously?
Please see our response to Reviewer 1’s sixth comment below.
7) Please consider reviewer 1's suggestions to improve readability by defining KiD in the main text and revising table 1.
We have revised the notation and text accordingly. We have also adopted the reviewer’s suggestion of a parameter table/model glossary to aid readability. Please let us know if further revisions are required.
8) Line 349 – Where does the value of 0.7 for seropositives come from?
We have now fitted this parameter, and while comparable to what we assumed, it does differ slightly at 0.77 (0.43 – 0.99), and so we are pleased that this issue was raised. Other parameters and conclusions are largely unaffected.
9) Please explain the big K notation in the Results section.
Done.
10) Please add a parameter table to the methods section and add a section on the data.
We have added a parameter table/Model glossary which is now Table S1/Supplementary File 1. We have added a short statement on the data at the start of the Methods. Please let us know if anything further is required.
11) Please justify choice of priors and/or consider sensitivity of results to choice of priors.
Reviewer 2 has commented on our use of uniform priors, specifically regarding relative risks. While in theory these could be unbounded (and therefore improper), in practice this is not a concern (for instance they could be reasonably limited to be less than 100). Further, because we choose as our baseline symptomatic disease among subjects with a single previous infection, all other relative risks (e.g. hospitalized disease among seronegatives) can safely be assumed to be less than 1. We previously used wider relative risk ranges (Unif(0,100)), and while resulting parameter estimates were unaffected, it did lead to slower convergence.
We have amended our analysis to allow seronegative transient immunity to be negative, which it now is against serotypes 1 and 2 for 25yearolds, improving the fits to KaplanMeier curves this age group and also better demonstrating the risk to seronegatives.
12) Please provide access to the model code. The statement "Model code is available from the authors" does not meet eLife requirements: "Regardless of whether authors use original data or are reusing data available from public repositories, they must provide program code, scripts for statistical packages, and other documentation sufficient to allow an informed researcher to precisely reproduce all published results."
All model code is now available at https://github.com/dlaydon/DengVaxSurvival, together with simulated data that the model can be fitted to. Simulated data was sampled using the parameter posteriors, and preserves comparable case numbers across trial arms, trial phases, age groups, countries, serotypes, disease severities and serostatus. We have also provided example parameter files and precompiled binary executables to make running and fitting the model easier.
Reviewer #1:
Laydon et al. have conducted an elegant analysis that provides a clear and comprehensive guide to the mechanism of difference of CYDTDV for dengue virus seropositive vs. seronegative vaccine recipients. The paper includes relevant hypothesis and model schemes as well as figures that show differences between seropositive and seronegative vaccine recipients across a range of covariates. The authors demonstrate, in a clearer way than has been shown before, that CYDTDV increases disease across all ages in both trials in seronegatives. The authors also show that the enhancing effect is stronger against hospitalized disease than febrile disease. Many of these results have already been presented previously in other papers analyzing the same data, but the modeling approach does provide a new perspective that adds to the story of the CYDTDV vaccine.
Overall, the paper is clearly written and easy to follow, especially given the complexity of the model and subject matter. However, numerous claims are made in the abstract and the discussion that inaccurately reflect the results presented in this paper. In particular, major conclusions of the paper relate to the benefit of the vaccine for seropositive individuals (lines 1819, 327328) and an increasing effect of vaccination for seropositive individuals with age (lines 286290, 329330). There are potential issues with the modeling approach and how it relates to these conclusions. Further, a discussion about the longterm effects of the vaccine for seronegatives is speculative and problematic (311320).
Comments for the authors:
1) Lines 1819. "Vaccinating seropositives gives greater longlasting immunity than two natural infections." The claim that fixedtime immunity induced by vaccination of seropositives is maintained at a high level over time is not well supported. The authors assume in their models that immunity wanes in seronegatives (over 1 year) and is stable in seropositives (maintained over time). First, it is unclear why these assumptions were made. The reference for these model choices does not seem to cover immune kinetics over this period of time (Clapham et al. 2016 PLOS Comp Bio). Second, the authors actually tested different assumptions about waning immunity in supplement (lines 667 – 694), which are not described in the main text. In the supplement, the authors demonstrate waning immunity out to 4.5 years (with wide confidence intervals) in both seronegative and seropositive vaccinated individuals. In both cases, the duration of waning is outside of the observational period of the study, and the authors write: "We conclude that three years of follow up data from each patient is insufficient to infer durations." Thus, the authors should adjust the statement "vaccinating seropositives gives greater longlasting immunity than two natural infections" to reflect the fact that immunity in seropositives may also wane over time in a way that cannot be accurately measured with the current data.
We agree with the reviewer, and so have amended our analysis to fit these durations as opposed to fixing them. While we cannot precisely infer durations, this uncertainty is stated clearly in the results, and the overall picture is that of shortlived seronegative transient immunity and longlived seropositive transient immunity (lines 427434).
We also agree with the reviewer’s point that benefit to seropositives beyond two previous natural infections is valid to the extent that seropositive transient immunity is longlived, and there is some evidence that it is. We have amended the text accordingly in several places to make this caveat explicit (lines 1819, 414417, 427434, and 614621).
2) Lines 329330. "Therefore it may be more beneficial to vaccinate multitypic seropositives than simpler models have predicted [11]." How do the authors know it is the multitypics that benefit as opposed to those with primary immunity before vaccination? It would be helpful if the authors could further support this statement by discussing the results that relate to this point. This is especially important in relation to the discussion about dengue rapid diagnostic tests (e.g. lines 2324), which have very low sensitivity for detecting monotypic DENV immunes.
While one mechanism of vaccine action (change in relative risk) would not affect multitypics, the other mechanism (conferral of transient immunity) would benefit multitypics, for as long as this immunity was present.
We have now made this point more prominent in the results (lines 414417 and 427447) and elsewhere. Benefit to multitypics is now supported by fitted parameter values, and not merely values that we had previously assumed.
While our fitted parameters do predict greater immunity to seropositive vaccinees than two previous natural infections, and also that multitypics would benefit, it is true that we were not able to test a model where transient immunity applied only to monotypics (now mentioned in lines 443447 and 585587). That said, we believe that potential benefit to multitypics, even though they would benefit less than monotypics, is an important consideration for this vaccine, and we would very much like to leave this consideration in our paper if possible. This is particularly true seeing as we agree with the reviewer that it is difficult to identify monotypic immunes – benefit to multitypics would render this less of an issue, as all seropositives would benefit (we mention this in the discussion in lines 614627).
3) Lines 286 290. "Interestingly, fixedtime immunity was found to increase with age in seropositives. In general, heterogeneity between countries' KaplanMeier curves can be explained by serotype and seroprevalence, although these factors are insufficient to explain differences in vaccine efficacy by age, for which agespecific effects (independent of serostatus) are required." The conclusion about the benefit of the vaccine even to multitypic immunes seems to be derived from the observation that fixedeffect immunity induced by the vaccine in seropositive individuals increases with age. The authors observe large agespecific fixedtime immunity differences by serostatus (Figure 5), although it is not clear there is much difference across age groups in vaccine efficacy (Figure 4). While the authors state that age specific effects are independent of serostatus, the age effects only occur in seropositives and thus are most plausibly related to more prior infections in children of older ages. It would be helpful if the authors further discussed ageeffects and their relationship being multitypic immune.
The predicted benefit to multitypics does not arise from the agedependence in transient immunity (previously termed “fixedtime immunity”). Instead, it comes from the positive values and long durations of seropositive transient immunity – albeit with the significant caveat that we assumed transient immunity would affect monotypic and multitypic seropositives equally (now mentioned in lines 443447 and 585587). The “silentinfection” mechanism does not affect multitypics in our model, because we assume that disease risk from tertiary and quaternary infection is equal (i.e. K_{2,D} = K_{3,D}).
We have amended our analysis to allow seronegative transient immunity to be negative (which it is for seronegative 25yearolds against serotype 2), which allows for better fitting of the 25yearold KaplanMeier curves. There is now a slight age trend in seronegatives, in that values for 25yearolds differ from older age groups.
Nevertheless, the reviewer’s comment is interesting, and we had not thought of this before. It is possible that the increased transient immunity we estimate for older ages for all seropositives also reflects greater transient immunity in multitypics, although the similar age trend in seronegatives would perhaps argue against this explanation.
Please let us know if we have misunderstood the reviewer’s point. In any case, we have included these points in the discussion (lines 555561).
4) Lines 311 – 315. "In high transmission settings where children would ordinarily receive at least two natural infections, we predict that even seronegatives would eventually benefit from vaccination, as they would experience one high risk infection, and all subsequent infections would have a much lower risk, in contrast to unvaccinated individuals who would ordinarily experience one moderate and one high risk infection [Figure 1]." The results of this manuscript do not support this claim. While the authors may expect this to be true based on the model scheme (referenced as Figure 1), the results, as currently described, do not prove this point. Further, the caveats provided afterward do not justify inclusion of this paragraph in the discussion (Lines 316320): "Important caveats include first that disease risk would increase in the short term. Second, and more seriously, a small subset of symptomatic infections are fatal, in which case vaccination could shorten life in seronegatives. Finally, while the eventual benefit to seronegatives is predicted by our model and the model fits well, this remains a prediction yet to be validated by empirical data."). This paragraph should be removed or significantly reworked because it is largely a question of medical ethics.
This is a fair point. We agree have removed the paragraph from the manuscript.
5) Figure 4. It is not clear why vaccine efficacy increases over time in the trial for vaccinated seropositives, even across all age groups. It does not seem to be explained by age effects, waning immunity, or serotype distributions. Is it related to differences in disease outcomes measured in the trial over time (e.g. Figure S8)?
The reviewer is correct: the improvement in efficacy (the decline in hazard ratios) over time for seropositives reflect the better performance of the vaccine against hospitalised or severe disease (at least in as far as this can be inferred given relatively few passive phase case counts), as per what was Figure S8 (now Figure 4—figure supplement 2). We have updated the text accordingly to make this explicit (lines 369371), and we thank the reviewer for drawing this to our attention.
6) It is surprising that the serotype effects are more similar than might be expected based on previous articles on these data, especially previous observations of greater efficacy against DENV4. Here the authors observe strong enhancement of DENV4 at later timepoints in the trial. Could the authors comment on whether this might relate to the way serotype effects are modeled, or whether this constitutes a major difference from what has been shown previously?
There are some quite large differences in the transient immunity estimates by serotype for each serostatus. For example, in 25yearold seronegatives, transient immunity is 11% (72% – 46%) for serotype 2, but this rises to 54% (11%85%) for serotype 4. In 1216yearold seropositives, transient immunity is 54% (22%78%) for serotype 1 and 85% (56%99%) for serotype 4.
Hazard ratios, particular at later times post first dose, are more similar between serotypes, and this may be due to the fact that we do not model serotypespecific relative risks (and therefore serotypespecific change in relative risk induced by “silentinfection” vaccination). We did attempt to resolve this previously, but the trial data was less well fitted, and there is insufficient power to resolve the parameters, particularly for the passive phase/hospitalised disease. Even here though, the risk enhancement in 25yearold vaccinees is much larger for serotypes 1 and 2 than for serotypes 3 and 4 (either when considering seronegatives only or when considering both seronegatives and seropositives combined).
However, we agree with the reviewer that the greater efficacy previously observed for DENV4 are not as well captured by our analysis. If we had been able to model serotype specific durations of transient immunity, we think that this would have resulted in longer durations for seronegative transient immunity for DENV4, which would likely diminish the DENV4 risk enhancement our main model predicts. Unfortunately however, transient immunity durations that are not serotypespecific are already imprecisely inferred. We have added these limitations to the discussion of the main text in lines 582598.
7) Table 1 and its explanation in the text are confusing. Instead of a traditional presentation of relative risk, which is described in the text, the table presents the probability of disease expected relative to secondary infections. One option would be to present relative risk estimates in table, and clearly indicate the reference groups in the table. Additionally, while KiD is clearly defined in the methods, it would be helpful to add one sentence to the main text to define KiD, given that the main text uses this notation in multiple paragraphs without explaining its interpretation.
We have made the definition of K,_{iD} clear in the main text now, and have added in the baseline/reference groups to Table 1 for relative risks and agespecific multiplier of the hazard. That said, we are not sure we understand the reviewer as the relative risks presented in Table 1 are those given in the text. Please let us know if we have misunderstood or if further changes are required.
Reviewer #2:
This paper uses individual trial participant data from two large phase 3 dengue vaccine randomised clinical trials to fit a Bayesian survival model of symptomatic dengue illness that is dependent on casecontrol status (vaccine vs placebo), baseline serostatus, age, and dengue serotype. The main finding is a detailed characterisation of how the relative risk of symptomatic illness changes as a function of time since vaccination and baseline serostatus. As previously reported, children who are seronegative at baseline have a drastically increased risk of symptomatic illness in years 2 and 3 of followup. Although this finding is not novel per se, having a precise characterisation of the timevarying risk is important for determining vaccine utility and optimal implementation strategies.
The survival model is fairly complex but this complexity reflects the complexity of the trial data and the inference problem at hand (multiple countries with different proportions of dengue serotypes, active and passive followup periods, agevarying effects). I particularly like the use of Gibbs sampling to treat the missing baseline serostatus as a latent variable in the model. This is an elegant method that allows for the analysis of the whole dataset and not restricted to just those with serostatus data (only 10% of participants).
My main comments are about clarity of the manuscript and reproducibility:
1. The Results section needs to explain the big K notation which is fairly complicated (but I can't see any easy way of simplifying it!)
We agree. We have now split up the K parameters, which previously denoted too many related but distinct quantities and concepts. As before, K_{i,D} refers to the relative risk of disease given i prior infections of case type D (by default active phase/passive phase, or alternatively hospitalised/nonhospitalised or severe/nonsevere if considering disease severity). φ_{cD}(α) refers to the seropositive disease risk where number of previous infections is unknown, and so is a weighted average of K_{1,D} and K_{2,D}, for subjects of age α in country c. Finally, R_{abcD}(α) is the relative risk of disease of type D in stratum abc, which encompasses baseline serostatus, aggregate seropositive risk by age φ_{cD}(α), and the change in relative risk induced by vaccination (i.e. the vaccineassilentinfection model).
These definitions are given in the text and in the model glossary / parameter table. We think the manuscript is clearer as a result, but please let us know if additional changes are required.
2. The Methods section really needs a section on the data (this could be quite short). Otherwise it's hard to know exactly what sort of data are being used (eg right censoring after first illness is mentioned in the model bit)
We have added a short data section at the start of the Methods.
3. The Methods section really needs a parameter table. Table 1 gives a summary of model outputs which is useful, but these are not parameters. What I would find useful is a table with all the main model parameters using the same notation as in the text (eg K_{0,0}) and the associated prior distributions. This would emphasize that the model has a lot of parameters. This would also be useful to emphasize which parameters were fixed in the model (eg M_{b}, sigma?).
This is an excellent suggestion and we have now added a model glossary (Table S1/Supplementary File 1). This contains fitted and fixed parameters, their prior distributions, as well as various quantities derived from the parameters that should make the methods more readable.
4. It says all priors are uniform but this seems a bit odd. Maybe I am misunderstanding something, but the relative risk parameters can take values in (0, infinity) surely? A uniform prior is therefore improper. This is probably not the best choice (uniform priors are often not a good choice).
While we agree that in theory relative risks could be very large (though not unbounded), in practice this does not align with dengue epidemiology. Since we choose risk of disease among subjects with a single prior infection as our baseline (i.e. K_{1,1}:=1), relative risks can be expected to be lower than 1. We previously we did run fits where relative risks could vary between 0 and 100. This did not change results but did lead to considerably slower convergence. Further a prior of Unif(0,100) would mean that our prior belief considered disease risk in primary or tertiary/quaternary infection to be 99 times more likely to be greater than secondary infection, and this is obviously not the case.
In any case, the priors are not unbounded and are therefore integrable, and so they are not improper. Further, while the hard boundaries of uniform priors can lead to nonsymmetrical proposals, we are careful in preserving proposal symmetry. Proposed parameter values that lie outside parameter ranges are “reflected” in the opposite boundary (unfortunately the only analogy I can think of is PacMan!).
Please let us know if we have misunderstood your point or if any changes are still required.
5. "Model code is available from the authors" and "The model was coded in C++" doesn't really meet eLife standards for reproducibility or inspire huge confidence. The paper is entirely based on the validity of the model fitting and this is a complex model that has been hand coded. I fully trust the competence of the authors, but I really think the code should be made available online (via a git repo for example) with a minimum working example for the fitting. If the authors can't make the full dataset openly accessible then a simulated dataset to test the model would be a good alternative.
We agree. All model code, together with precompiled binaries and example parameter/batch files, is available at https://github.com/dlaydon/DengVaxSurvival. Unfortunately, the underlying trial data is at an individual level and owned by Sanofi Pasteur, and so we are not free to share it. However, as suggested we have provided simulated data, sampled from our parameter posteriors, that has comparable case numbers across serotypes, disease severities and various strata. When the model is fitted on run on this simulated data, it reproduces our results well, albeit with a little noise. We hope that this will be acceptable.
6. Could you explain a bit more why the parameter M_{b} is fixed at 0.7? It says: "equal to 1 for seronegatives and 0.7 for seropositives, chosen to reflect seropositive participants' reduced disease risk due to their immunity to at least one serotype". I couldn't square this with fact that seropositives also can have increase risk as the secondary infection is more likely to be severe than the first? I get that you don't know how many infections a seropositive individual has had, but I can't really understand the justification for the 0.7.
This language was careless on our part, and we thank the reviewer for drawing it to our attention. A seronegative individual, while less likely to become symptomatic upon infection, is susceptible to more serotypes than a seropositive individual, because seropositives have acquired natural immunity to at least one serotype. This susceptibility to fewer serotypes is what the M_{b} parameter refers to, and we have therefore amended the description of this parameter on lines 130132.
Nevertheless, we agree with the reviewer, and so we have updated all model runs so that the M_{b} parameter is fitted rather than fixed. Results are similar (exact values have been updated throughout the text), and the M_{b} parameter has a mean of 0.77 (0.430.99), slightly higher than we had previously assumed. We are grateful to the reviewer for raising this point and we think our manuscript is more robust as a result.
https://doi.org/10.7554/eLife.65131.sa2Article and author information
Author details
Funding
Bill & Melinda Gates Foundation (OPP1092240)
 Daniel J Laydon
 Gemma NedjatiGilani
 Neil M Ferguson
National Institute for Health Research (NIHR: PROD101720002)
 Daniel J Laydon
 Gemma NedjatiGilani
 Neil M Ferguson
Medical Research Council (MR/R015600/1)
 Daniel J Laydon
 Ilaria Dorigatti
 Wes R Hinsley
 Gemma NedjatiGilani
 Neil M Ferguson
Royal Society (Sir Henry Dale Fellowship grant 213494/Z/18/Z)
 Ilaria Dorigatti
Wellcome Trust (Sir Henry Dale Fellowship grant 213494/Z/18/Z)
 Ilaria Dorigatti
The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.
Acknowledgements
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: PROD1017–20002) 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 SanofiPasteur Ltd., without payment on the implications that this work has on the use of their vaccine. We thank Nick Jackson and JeanSebastien Persico at SanofiPasteur, 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.
Senior Editor
 Eduardo Franco, McGill University, Canada
Reviewing Editor
 Ben S Cooper, Mahidol University, Thailand
Reviewer
 James A Watson, Mahidol Oxford Tropical Medicine Research Unit, Thailand
Publication history
 Received: November 24, 2020
 Accepted: June 29, 2021
 Accepted Manuscript published: July 2, 2021 (version 1)
 Version of Record published: July 29, 2021 (version 2)
 Version of Record updated: August 4, 2021 (version 3)
Copyright
© 2021, Laydon et al.
This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.
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Funding: The Natural Science Fund for Distinguished Young Scholars of Zhejiang Province; National Natural Science Foundation of China; Key Project of Research and Development Plan of Hunan Province; the Swedish Heart Lung Foundation; the Swedish Research Council; the Swedish Cancer Society.