Efficacy profile of the CYD-TDV dengue vaccine revealed by Bayesian survival analysis of individual-level phase III data.

Background: Sanofi-Pasteur's CYD-TDV is the only licensed dengue vaccine. Two phase three trials showed higher efficacy in seropositive than seronegative recipients. Hospital follow-up revealed increased hospitalisation in 2-5- year-old vaccinees, where serostatus and age effects were unresolved.
Methods: We fit a survival model to individual-level data from both trials, including year 1 of hospital follow-up. We determine efficacy by age, serostatus, serotype and severity, and examine efficacy duration and vaccine action mechanism.
Results: Our modelling indicates that vaccine-induced immunity is long-lived in seropositive recipients, and therefore that vaccinating seropositives gives higher protection than two natural infections. Long-term increased hospitalisation risk outweighs short-lived 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 'screen-then-vaccinate' programs. Since CYD-TDV acts as a silent infection, long-term 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 Sanofi-Pasteur’s CYD-TDV (marketed as Dengvaxia). CYD-TDV 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 post-first 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 long-term 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’ disease-free 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 low-risk natural infection, would after vaccination instead experience a ‘secondary-like’ 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 post-vaccination, normally associated with tertiary and quaternary infection [Figure 1].

Figure 1.

Model Schematic 1: vaccine as silent infection.

Top row: unvaccinated individuals are naive, or infected with either: their first dengue infection with moderate disease risk; their second higher risk infection; or their third or fourth lower risk infection. Middle row: vaccinating seropositive individuals with a single prior infection lowers the disease risk associated with secondary infection to that associated with tertiary and quaternary infection. Bottom row: vaccinating naive (seronegative) individuals increases disease risk upon their first natural infection. Figure adapted from Ferguson et al., 2016 with permission.

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 year-old 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 anti-dengue non-structural 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 follow-up 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 long-term follow-up (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 CYD-TDV’s safety and efficacy, and demonstrate the need for long-term follow up in the phase three trials of other dengue vaccine candidates currently in development.

Materials and methods

Data

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

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 (non-severe/non-hospitalised = 0, severe/hospitalised = 1)). We consider a country-specific baseline hazard of disease (or force of infection, i.e. the risk of disease among susceptibles) as a spline λ(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 is the relative risk of disease associated with natural infection. M is the multiplier of the baseline hazard associated with baseline serostatus b, equal to 1 for seronegatives and fitted for seropositives. This parameter reflects seropositive participants’ reduced infection risk due to their immunity to at least one serotype.

Figure 2.

Model schematic 2: vaccine-induced transient immunity model hierarchy.

In all model variants, we allow the initial magnitude and mean duration of transient immunity to vary by baseline serostatus (exponential waning is assumed). (A) Our main model allows transient immunity magnitude to vary by age and serotype, as well as baseline serostatus. For each serostatus, we model transient immunity with age, and serotype effects are incorporated additively (see Materials and methods for details). We further include an age-specific multiplier of the baseline hazard. (B) and (C) show reduced model variants that dispense with serotype and age effects, respectively. (D) Shows our simplest model variant without explicit age or serotype effects.

ρ ∈ [0,1] is the proportion of serotype d in country c (assumed to be constant, with , see below); Z(α) is the multiplier of the force of infection for age α; δ is the Kronecker delta defined by

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

That is, positive values of transient immunity wane exponentially (to reflect previously observed antibody dynamics Clapham et al., 2016). Additional details on age-specific transient immunity I(α) and duration τ, 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 = 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 = K. Our model considers serostatus to be binary (either seropositive or seronegative), and so we define the risk of disease among seropositive participants, which is an aggregate of the risks of disease given monotypic or multitypic infection history, shown below.

Our main model considers vaccination to alter the risk of disease associated with prior exposure, by acting as a silent, disease-free infection (Figure 1). Therefore, the relative risks are defined as follows:when considering the active phase of the trial (or symptomatic disease of any severity) andwhen 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

We 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 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 non-severe disease (or equivalently between hospitalised and non-hospitalised 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. In practice, these two interpretations of the relative risk parameters are largely equivalent as non-hospitalised 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 non-standardised 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 = K = 0.25 (Ferguson et al., 2016), while the proportion of symptomatic secondary infections that require hospitalisation (or that result in severe disease) K 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

We model the baseline hazard for each country as a quadratic spline. We divide the follow-up period of length T into n-1 intervals with , and define 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 4-month intervals. For polynomial , we solve the following equations for coefficients :

The knot locations are fixed and their values are fitted parameters.

Relative risk in seropositives

If h is the constant historical force of infection in country c, then the probability of remaining seronegative until age α is given by

.

Therefore, the probability of seropositivity (i.e. at least one infection) by age α is given by . 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(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 refer to infection, not disease, and that this approximation assumes that historical force of infection is equal across serotypes.

Serotype proportions

The proportions ρ of serotype d in country c must satisfy  for all c. Therefore, given proportions for three serotypes, the fourth is explicitly determined. We fit three parameters q (y = 1, 2, 3) for each country c and calculate

Each parameter q is fitted with prior Unif(0,1).

Age effects

We use a step function to model age-specific 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(α) gives the relationship between transient immunity and age for serostatus b, then the (initial) magnitude of transient immunity I(α) for baseline serostatus b and serotype d for age α is given bywhere s is the intercept for baseline serostatus b and serotype d (fixed at 0 for serotype d = 1).

Likelihood

If the hazard due to all serotypes combined is given bythen where relative risks distinguish between trial phases, we letwhere t is the date that active surveillance ends and passive surveillance begins, and define the integrated hazard between start and end times t and t as

Our model does not consider multiple disease episodes for the same patient over the observation period, and subjects are right-censored after they become a case for the first time. Therefore, when relative risks distinguish between the severity of disease, ‘survival’ between times t and t 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 of remaining disease free from between times t and t is given byand so the probability of disease from serotype d of type D at time t is given bywhere T is the time interval within which the hazard is assumed to be constant. We take T to be 1 day.

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

If h denotes the constant historical force of infection in country c, then the probabilities π(α) of having serostatus b in country c at age α are given bythen the likelihood of parameters θ is given by

Data augmentation

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

Abbreviating and letting and respectively denote the probabilities of seropositivity and seronegativity at baseline given clinical outcome C, by Bayes’ theorem we have

For example, a non-case of age α in country c has the following probability of seropositivity at baselinefor parameters θ. Similarly, for a case of severity D of age α in country c we have

Hazard ratios

If and are the sets of vaccinees and controls, respectively, then within any given stratum of interest (e.g. in a particular country, age or serostatus subset, or combination thereof), then posterior ratios of hazards of any disease severity and due to any serotype HR(t*) for all serotypes combined at time post-first dose t* are given bywhere denotes the number of trial participants in stratum .

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

Survival curves

For stratum  as at t* days post-first dose, posterior survival probabilities are calculated asand if denotes the number of cases in stratum that occurred within t* days post-first dose, then the observed survival probabilities are given by

Attack rates

The period for which participants were under active or passive surveillance varies by patient. Therefore, we calculate attack rates usingwhere and are the start and end times of the trial period for patient ( is the start of follow-up and is arbitrary here). To compute attack rates for observed data, we use the same formula, but takes value 0 if the patient is a case between and , 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

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

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

Table 1.

Parameter values by model variant.

A, B, C, D refer to panels A, B, C and D of Figure 2. WBIC: Widely-Applicable Bayesian Information Criterion.

Model variant			Main model A	Age effects onlyB	Serotype effects onlyC	Simplest modelD
WBIC			−28627.1	−29065.33	−28591.5	−29018.16
Relative risks	Trial phase	No. prior infections
	Active (K0,0)	0	0.7 (0.36, 0.98)	0.53 (0.26, 0.9)	0.52 (0.28, 0.83)	0.43 (0.24, 0.78)
	Active (K0,1)	1 (baseline)	1 (1, 1)	1 (1, 1)	1 (1, 1)	1 (1, 1)
	Active (K0,2)	two or 3	0.31 (0.14, 0.63)	0.32 (0.14, 0.65)	0.2 (0.1, 0.4)	0.21 (0.089, 0.45)
	Passive (K1,0)	0	0.053 (0.034, 0.078)	0.054 (0.035, 0.078)	0.051 (0.033, 0.073)	0.052 (0.034, 0.074)
	Passive (K1,1)	1	0.21 (0.14, 0.31)	0.22 (0.14, 0.31)	0.2 (0.13, 0.29)	0.21 (0.14, 0.3)
	Passive (K2,1)	2 or 3	0.053 (0.034, 0.078)	0.054 (0.035, 0.078)	0.051 (0.033, 0.073)	0.052 (0.034, 0.074)
Seronegative transient immunity	Any serotype	Any age	-	-	-	0.64 (0.34, 0.81)
		2–5 years	-	0.48 (0.085, 0.77)	-	-
		6–11 years	-	0.65 (0.36, 0.85)	-	-
		12–16 years	-	0.61 (0.25, 0.85)	-	-
	Serotype 1	Any age	-	-	0.47 (0.12, 0.74)	-
		2–5 years	0.16 (–0.34, 0.61)	-	-	-
		6–11 years	0.39 (–0.0023, 0.73)	-	-	-
		12–16 years	0.4 (0.022, 0.73)	-	-	-
	Serotype 2	Any age	-	-	0.29 (0.0095, 0.62)	-
		2–5 years	−0.11 (–0.72, 0.46)	-	-	-
		6–11 years	0.12 (–0.38, 0.57)	-	-	-
		12–16 years	0.14 (–0.39, 0.6)	-	-	-
	Serotype 3	Any age	-	-	0.69 (0.29, 0.96)	-
		2–5 years	0.43 (–0.17, 0.86)	-	-	-
		6–11 years	0.65 (0.15, 0.96)	-	-	-
		12–16 years	0.67 (0.17, 0.97)	-	-	-
	Serotype 4	Any age	-	-	0.78 (0.59, 0.92)	-
		2–5 years	0.54 (0.11, 0.85)	-	-	-
		6–11 years	0.76 (0.53, 0.93)	-	-	-
		12–16 years	0.78 (0.48, 0.98)	-	-	-
Seropositive transient immunity	Any serotype	Any age	-	-	-	0.43 (0.041, 0.73)
		2–5 years	-	0.23 (0.0089, 0.6)	-	-
		6–11 years	-	0.49 (0.11, 0.74)	-	-
		12–16 years	-	0.65 (0.37, 0.82)	-	-
	Serotype 1	Any age	-	-	0.29 (0.015, 0.64)	-
		2–5 years	0.21 (0.011, 0.55)	-	-	-
		6–11 years	0.42 (0.063, 0.7)	-	-	-
		12–16 years	0.54 (0.22, 0.78)	-	-	-
	Serotype 2	Any age	-	-	0.4 (0.041, 0.75)	-
		2–5 years	0.26 (0.015, 0.63)	-	-	-
		6–11 years	0.47 (0.1, 0.76)	-	-	-
		12–16 years	0.59 (0.28, 0.83)	-	-	-
	Serotype 3	Any age	-	-	0.54 (0.12, 0.84)	-
		2–5 years	0.36 (0.06, 0.72)	-	-	-
		6–11 years	0.57 (0.19, 0.83)	-	-	-
		12–16 years	0.69 (0.39, 0.9)	-	-	-
	Serotype 4	Any age	-	-	0.79 (0.44, 0.98)	-
		2–5 years	0.52 (0.2, 0.86)	-	-	-
		6–11 years	0.73 (0.37, 0.96)	-	-	-
		12–16 years	0.85 (0.56, 0.99)	-	-	-
Transient-immunity duration		Seronegative (τ0)	4.5 (1, 9.6)	5 (1.1, 9.7)	4.1 (0.97, 9.4)	4.9 (1.2, 9.6)
		Seropositive (τ1)	11 (2.3, 20)	12 (2.9, 20)	9.5 (1.2, 19)	10 (1.3, 20)
Age-specific hazard multiplier Z(α)		2–5 years (baseline)	1 (1,1)	1 (1, 1)	-	-
		6–11 years	1.2 (0.91, 1.5)	1.1 (0.88, 1.4)	-	-
		12–16 years	1.1 (0.79, 1.5)	1 (0.76, 1.4)	-	-
Infection risk multiplier		Seronegative (M0, baseline)	1 (1,1)	1 (1, 1)	1 (1,1)	1 (1, 1)
		Seropositive (M1)	0.77 (0.43, 0.99)	0.61 (0.31, 0.96)	0.69 (0.4, 0.97)	0.57 (0.33, 0.94)

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 post-first dose), where surveillance could detect both hospitalised and non-hospitalised disease. In the passive phase (next 11 months following active phase), there are considerably fewer cases, owing to its shorter duration and detection of only hospitalised cases. Further, the benefits of vaccination in the passive phase are less than the active, and 2–5-year-old vaccinees show a greatly increased risk of hospitalisation than controls. In both trials, a mix of infecting serotypes among cases was observed.

Figure 3.

Summary of trial data.

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.

Figure 4.

Posterior hazard ratios by trial, age group and baseline serostatus over time (main model).

Each plot shows posterior hazard ratios (vaccine: control) for each age group at 0, 12, 25 and 36 months (0, 1, 2 or 3 years) of follow-up. Hazard ratios consider symptomatic disease regardless of serotype or hospitalisation status. Grey line indicates a ratio of 1, that is, no difference between the trial arms. Red line is the mean posterior estimate, and pink intervals represent 95% credible intervals of posterior samples. Rows show ratios when not broken down by serostatus (top row), for seronegatives (middle row) and seropositives (bottom row), for CYD14 (left column) and CYD15 (right column).

As per Figure 4. Hazard ratios consider symptomatic disease regardless of hospitalisation status.

As per Figure 4. Left and right columns show hazard ratios for non-hospitalised and hospitalised disease, respectively (regardless of serotype). Ratios are almost identical when considering severe and non-severe disease (not shown).

As per Figure 4. Ratios are almost identical when considering non-severe disease (not shown).

As per Figure 4. Ratios are almost identical when considering severe disease (not shown).

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

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

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

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

Figure 4—figure supplement 1.

Posterior hazard ratio estimates by trial, age group, baseline serostatus and serotype over time (main model).

As per Figure 4. Hazard ratios consider symptomatic disease regardless of hospitalisation status.

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 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).

We estimate the relative risk parameters K and K to be 0.7 (0.36–0.98) and 0.31 (0.14–0.63), respectively. That is, among unvaccinated individuals, primary infection is 70% as likely, and tertiary/quaternary infection is 31% as likely, to cause symptomatic disease as secondary infection. However, considering vaccination as a silent infection, seronegative vaccinees increase their long-term risk of symptomatic disease by a factor of K/K = 1.5 (1.0–2.7), whereas vaccinees with a single prior infection multiply their long-term disease risk by a factor of K/K = 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, K and K) to be 0.053 (0.034–0.078), 0.21 (0.14–0.31) and 0.053 (0.034–0.078), respectively. Therefore, in seronegatives, vaccination increases long-term risk of hospitalisation by a factor of K = 6.1 (4.1–11), whereas for those with a single prior infection hospitalisation risk is multiplied by a factor of K 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 and K), 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).

Figure 5.

Age-specific transient immunity estimates (main model).

Profiles of age-group-specific transient immunity by serostatus for serotypes 1–4. Mean posterior estimates are shown in red, with 95% credible intervals surrounding.

Durations τ (b = 0, 1) of transient immunity by serostatus. We allow seronegative duration (left) to vary between 0 and 10 years and seropositive duration (right) to vary between 0 and 20 years.

Serotypes 1–4 are shown in red, grey, blue and orange, respectively. There is wide variation between countries in their serotype prevalence.

As per Figure 5.

Age-specific durations of transient immunity by serostatus. modelled as a step function. Mean posterior estimates are shown in red, with 95% credible intervals surrounding. We allow seronegative durations to vary between 0 and 10 years and seropositive durations to vary between 0 and 20 years.

Age-specific transient immunity estimates (age effects model without serotype effects).

Age-specific transient immunity durations (model with fitted age-specific transient immunity durations).

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).

Figure 5—figure supplement 1.

Transient immunity duration posteriors.

Durations τ (b = 0, 1) of transient immunity by serostatus. We allow seronegative duration (left) to vary between 0 and 10 years and seropositive duration (right) to vary between 0 and 20 years.

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

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

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

Figure 5—figure supplement 2.

Posterior chains of serotype proportions by country.

Serotypes 1–4 are shown in red, grey, blue and orange, respectively. There is wide variation between countries in their serotype prevalence.

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).

Figure 6.

Fits to observed Kaplan–Meier curves by trial, age group and country (main model).

In each plot, vaccine and control survival probabilities are plotted against days post-first dose (vaccine or placebo). Dark lines denote observed curves, dashed lines are the mean posterior estimates, with 95% credible intervals around.

As per Figure 6, showing fits of model considering any disease severity (left column), non-severe disease (middle column) and severe disease (right column).

As per Figure 6, showing fits of model considering any disease severity (left column), non-hospitalised disease (middle column) and hospitalised disease (right column).

As per Figure 6.

As per Figure 6.

As per Figure 6.

As per Figure 6.

As per Figure 6.

As per Figure 6.

Fits to observed Kaplan–Meier curves by trial, age group and country (simplest model without age or serotype effects).

Fits to observed Kaplan–Meier curves by trial, age group and country (age effects model without serotype effects).

Fits to observed Kaplan–Meier curves by trial, age group and country (serotype effects model without age effects).

Fits to observed Kaplan–Meier curves by trial, age group and country (model without age-specific force of infection).

Fits to observed Kaplan–Meier curves by trial, age group and country (model without immune priming).

Fits to observed Kaplan–Meier curves by trial, age group and country (model with fitted age-specific transient immunity durations).

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

Figure 7.

Model fits to observed attack rates at trial level for active and first year passive phase.

Observed and predicted age group-specific attack rates are shown for CYD14 (left column) and CYD15 (right column), for first three years follow-up (active phase and first year hospital phase combined), and for the first year of follow-up only. Blue and red denote observed attack rates for control and vaccine groups, while light blue and pink denote model predictions for control and vaccine groups. Confidence intervals for observed attack rates are calculated using exact binomial confidence intervals, whereas the uncertainty around predicted rates are 95% posterior sample credible intervals.

As per Figure 7.

As per Figure 7.

As per Figure 7. Seronegative (top row) and seropositive (bottom row) observed and predicted attack rates for CYD14 (left column) and CYD15 (right column) for combined active and first year passive follow-up.

As per Figure 7. Seronegative (top row) and seropositive (bottom row) observed and predicted attack rates for CYD14 (left column) and CYD15 (right column) for first year passive follow-up only.

As per Figure 7, showing attack rates by age group for CYD14 (left column) and CYD15 (right column). The top row shows attack rates for non-hospitalised disease in the active phase (the majority of case data). Second and third rows show attack rates for hospitalised disease during the active phase (middle row) and first year passive phase (bottom row).

As per Figure 7, showing attack rates by age group for CYD14 (left column) and CYD15 (right column). The top row shows attack rates for non-severe disease in the active phase (the majority of case data). Second and third rows show attack rates for severe disease during the active phase (middle row) and first year passive phase (bottom row).

As per Figure 7.

As per Figure 7.

Figure 7—figure supplement 1.

Model fits to observed attack rates by country.

As per Figure 7.

Figure 7—figure supplement 2.

Model fits to observed first year passive phase attack rates by country.

As per Figure 7.

Model fits to observed attack rates at trial level for active and first year passive phase (model without immune priming).

Model fits to observed attack rates at trial level for active and first year passive phase (model with fitted age-specific transient immunity durations).

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).

Figure 7—figure supplement 3.

Model fits to observed immunogenicity subset attack rates.

As per Figure 7. Seronegative (top row) and seropositive (bottom row) observed and predicted attack rates for CYD14 (left column) and CYD15 (right column) for combined active and first year passive follow-up.

Figure 7—figure supplement 4.

Model fits to observed immunogenicity subset attack rates from first year passive phase.

As per Figure 7. Seronegative (top row) and seropositive (bottom row) observed and predicted attack rates for CYD14 (left column) and CYD15 (right column) for first year passive follow-up only.

Figure 5—figure supplement 3.

Observed and predicted age-specific seroprevalence by country and trial.

Severity analysis

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

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

Figure 4—figure supplement 2.

Posterior hazard ratios by hospitalisation status.

As per Figure 4. Left and right columns show hazard ratios for non-hospitalised and hospitalised disease, respectively (regardless of serotype). Ratios are almost identical when considering severe and non-severe disease (not shown).

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

Figure 4—figure supplement 3.

Posterior hazard ratios by serotype against non-hospitalised disease status.

As per Figure 4. Ratios are almost identical when considering non-severe disease (not shown).

Figure 4—figure supplement 4.

Posterior hazard ratios by serotype and hospitalised disease status.

As per Figure 4. Ratios are almost identical when considering severe disease (not shown).

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

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

Figure 6—figure supplement 1.

Fits to observed Kaplan–Meier curves by trial and disease severity.

As per Figure 6, showing fits of model considering any disease severity (left column), non-severe disease (middle column) and severe disease (right column).

Figure 6—figure supplement 2.

Fits to observed Kaplan–Meier curves by trial and hospitalisation status.

As per Figure 6, showing fits of model considering any disease severity (left column), non-hospitalised disease (middle column) and hospitalised disease (right column).

Figure 7—figure supplement 5.

Model fits to observed attack rates by trial, hospitalisation status and trial phase.

As per Figure 7, showing attack rates by age group for CYD14 (left column) and CYD15 (right column). The top row shows attack rates for non-hospitalised disease in the active phase (the majority of case data). Second and third rows show attack rates for hospitalised disease during the active phase (middle row) and first year passive phase (bottom row).

Figure 7—figure supplement 6.

Model fits to observed attack rates by trial, disease severity and trial phase.

As per Figure 7, showing attack rates by age group for CYD14 (left column) and CYD15 (right column). The top row shows attack rates for non-severe disease in the active phase (the majority of case data). Second and third rows show attack rates for severe disease during the active phase (middle row) and first year passive phase (bottom row).

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 short-lived in seronegatives and long-lived in seropositives.

Discussion

Our results provide a comprehensive profile of Sanofi-Pasteur’s CYD-TDV 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. Vaccine-induced protection against each serotype was higher in seropositive recipients than in seronegatives, and these findings were robust across model variants. The incorporation of serotype-specific 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 age-specific 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 long-term follow-up 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 follow-up does not detect non-hospitalised 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 (Olivera-Botello 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 serotype-specific 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 serotype-specific relative risks (and therefore serotype-specific 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, serotype-specific 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 long-lived and acts in both monotypic and multitypic seropositive vaccine recipients.

High-resolution maps of dengue seropositivity are now available, and alongside improved rapid diagnostic tests and ‘screen-then-vaccinate’ 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.

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Acceptance summary:

This paper presents a detailed, model-based, 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 time-varying 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 CYD-TDV dengue vaccine revealed by Bayesian survival analysis of individual-level 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 long-lasting 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 329-330 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 age-effects 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 316-320.

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 CYD-TDV 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 CYD-TDV 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 CYD-TDV 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 18-19, 327-328) and an increasing effect of vaccination for seropositive individuals with age (lines 286-290, 329-330). There are potential issues with the modeling approach and how it relates to these conclusions. Further, a discussion about the long-term effects of the vaccine for seronegatives is speculative and problematic (311-320).

Comments for the authors:

1) Lines 18-19. "Vaccinating seropositives gives greater long-lasting immunity than two natural infections." The claim that fixed-time 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 long-lasting 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 329-330. "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 23-24), which have very low sensitivity for detecting monotypic DENV immunes.

3) Lines 286 -290. "Interestingly, fixed-time immunity was found to increase with age in seropositives. 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 age-specific 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 fixed-effect immunity induced by the vaccine in seropositive individuals increases with age. The authors observe large age-specific fixed-time 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 age-effects 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 316-320): "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 case-control 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 follow-up. Although this finding is not novel per se, having a precise characterisation of the time-varying 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 follow-up periods, age-varying 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 K0,0) 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 Mb, 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 Mb 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.

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 short-lived seronegative immunity and long-lived seropositive immunity. Further, it is arguable that three years of follow-up 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 long-lasting 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 vaccine-induced immunity is long-lived 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 614-621) 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 CYD-TDV, but please let us know if further amendments are required.

3) On lines 329-330 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 values) and (ii) conferring transient immunity (denoted by the I 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 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 long-lived (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 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 435-447).

Nevertheless, our results indicate that monotypics will benefit more than multitypics, and benefit to multitypics is dependent on seropositive immunity being long-lived, and we have now included this caveat throughout the text in the abstract (lines 18-19), results (lines 414-417 and 427-447) and discussion (lines 614-621).

4) It would be helpful if the authors further discussed age-effects 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 316-320.

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 2-5-year-olds, improving the fits to Kaplan-Meier 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 pre-compiled 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 CYD-TDV 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 CYD-TDV 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 CYD-TDV 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 18-19, 327-328) and an increasing effect of vaccination for seropositive individuals with age (lines 286-290, 329-330). There are potential issues with the modeling approach and how it relates to these conclusions. Further, a discussion about the long-term effects of the vaccine for seronegatives is speculative and problematic (311-320).

Comments for the authors:

1) Lines 18-19. "Vaccinating seropositives gives greater long-lasting immunity than two natural infections." The claim that fixed-time 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 long-lasting 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 short-lived seronegative transient immunity and long-lived seropositive transient immunity (lines 427-434).

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 long-lived, and there is some evidence that it is. We have amended the text accordingly in several places to make this caveat explicit (lines 18-19, 414-417, 427-434, and 614-621).

2) Lines 329-330. "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 23-24), 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 414-417 and 427-447) 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 443-447 and 585-587). 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 614-627).

3) Lines 286 -290. "Interestingly, fixed-time immunity was found to increase with age in seropositives. 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 age-specific 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 fixed-effect immunity induced by the vaccine in seropositive individuals increases with age. The authors observe large age-specific fixed-time 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 age-effects and their relationship being multitypic immune.

The predicted benefit to multitypics does not arise from the age-dependence in transient immunity (previously termed “fixed-time 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 443-447 and 585-587). The “silent-infection” mechanism does not affect multitypics in our model, because we assume that disease risk from tertiary and quaternary infection is equal (i.e. K = K).

We have amended our analysis to allow seronegative transient immunity to be negative (which it is for seronegative 2-5-year-olds against serotype 2), which allows for better fitting of the 2-5-year-old Kaplan-Meier curves. There is now a slight age trend in seronegatives, in that values for 2-5-year-olds 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 555-561).

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 316-320): "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 369-371), 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 2-5-year-old seronegatives, transient immunity is -11% (-72% – 46%) for serotype 2, but this rises to 54% (11%-85%) for serotype 4. In 12-16-year-old 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 serotype-specific relative risks (and therefore serotype-specific change in relative risk induced by “silent-infection” 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 2-5-year-old 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 serotype-specific are already imprecisely inferred. We have added these limitations to the discussion of the main text in lines 582-598.

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, clear in the main text now, and have added in the baseline/reference groups to Table 1 for relative risks and age-specific 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 case-control 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 follow-up. Although this finding is not novel per se, having a precise characterisation of the time-varying 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 follow-up periods, age-varying 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 refers to the relative risk of disease given i prior infections of case type D (by default active phase/passive phase, or alternatively hospitalised/non-hospitalised or severe/non-severe if considering disease severity). φ refers to the seropositive disease risk where number of previous infections is unknown, and so is a weighted average of K and K, for subjects of age α in country c. Finally, R is the relative risk of disease of type D in stratum abc, which encompasses baseline serostatus, aggregate seropositive risk by age φ, and the change in relative risk induced by vaccination (i.e. the vaccine-as-silent-infection 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 K0,0) 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 Mb, 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), 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 non-symmetrical 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 Pac-Man!).

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 pre-compiled 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 Mb 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 parameter refers to, and we have therefore amended the description of this parameter on lines 130-132.

Nevertheless, we agree with the reviewer, and so we have updated all model runs so that the M parameter is fitted rather than fixed. Results are similar (exact values have been updated throughout the text), and the M parameter has a mean of 0.77 (0.43-0.99), 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.