Estimating the per-exposure effect of infectious disease interventions

Analysing vaccine efficacy evaluated in phase 3 clinical trials carried out during outbreaks

In this paper we examine several definitions of vaccine efficacy (VE) that we found in the literature, for diseases that express themselves in outbreaks, that is, when the force of infection grows in time, reaches a maximum and then vanishes. The fact that the disease occurs in outbreaks results in several problems that we analyse. We propose a mathematical model that allows the calculation of VE for several scenarios. Vaccine trials usually needs a large number of volunteers that must be enrolled. Ideally, all volunteers should be enrolled in approximately the same time, but this is generally impossible for logistic reasons and they are enrolled in a fashion that can be replaced by a continuous density function (for example, a Gaussian function). The outbreak can also be replaced by a continuous density function, and the use of these density functions simplifies the calculations. Assuming, for example Gaussian functions, one of the problems one can immediately notice is that the peak of the two curves do not occur at the same time. The model allows us to conclude: First, the calculated vaccine efficacy decreases when the force of infection increases; Second, the calculated vaccine efficacy decreases when the gap between the peak in the force of infection and the peak in the enrollment rate increases; Third, different trial protocols can be simulated with this model; different vaccine efficacy definitions can be calculated and in our simulations, all result are approximately the same. The final, and perhaps most important conclusion of our model, is that vaccine efficacy calculated during outbreaks must be carefully examined and the best way we can suggest to overcome this problem is to stratify the enrolled volunteer's in a cohort-by-cohort basis and do the survival analysis for each cohort, or apply the Cox proportional hazards model for each cohort.

Identification of Vaccine Effects When Exposure Status Is Unknown

Results from randomized controlled trials (RCTs) help determine vaccination strategies and related public health policies. However, defining and identifying estimands that can guide policies in infectious disease settings is difficult, even in an RCT. The effects of vaccination critically depend on characteristics of the population of interest, such as the prevalence of infection, the number of vaccinated, and social behaviors. To mitigate the dependence on such characteristics, estimands, and study designs, that require conditioning or intervening on exposure to the infectious agent have been advocated. But a fundamental problem for both RCTs and observational studies is that exposure status is often unavailable or difficult to measure, which has made it impossible to apply existing methodology to study vaccine effects that account for exposure status. In this study, we present new results on this type of vaccine effects. Under plausible conditions, we show that point identification of certain relative effects is possible even when the exposure status is unknown. Furthermore, we derive sharp bounds on the corresponding absolute effects. We apply these results to estimate the effects of the ChAdOx1 nCoV-19 vaccine on SARS-CoV-2 disease (COVID-19) conditional on postvaccine exposure to the virus, using data from a large RCT.

Randomization for the susceptibility effect of an infectious disease intervention

Randomized trials of infectious disease interventions, such as vaccines, often focus on groups of connected or potentially interacting individuals. When the pathogen of interest is transmissible between study subjects, interference may occur: individual infection outcomes may depend on treatments received by others. Epidemiologists have defined the primary parameter of interest-called the "susceptibility effect"-as a contrast in infection risk under treatment versus no treatment, while holding exposure to infectiousness constant. A related quantity-the "direct effect"-is defined as an unconditional contrast between the infection risk under treatment versus no treatment. The purpose of this paper is to show that under a widely recommended randomization design, the direct effect may fail to recover the sign of the true susceptibility effect of the intervention in a randomized trial when outcomes are contagious. The analytical approach uses structural features of infectious disease transmission to define the susceptibility effect. A new probabilistic coupling argument reveals stochastic dominance relations between potential infection outcomes under different treatment allocations. The results suggest that estimating the direct effect under randomization may provide misleading conclusions about the effect of an intervention-such as a vaccine-when outcomes are contagious. Investigators who estimate the direct effect may wrongly conclude an intervention that protects treated individuals from infection is harmful, or that a harmful treatment is beneficial.

A compelling demonstration of why traditional statistical regression models cannot be used to identify risk factors from case data on infectious diseases: a simulation study

BACKGROUND

Regression models are often used to explain the relative risk of infectious diseases among groups. For example, overrepresentation of immigrants among COVID-19 cases has been found in multiple countries. Several studies apply regression models to investigate whether different risk factors can explain this overrepresentation among immigrants without considering dependence between the cases.

METHODS

We study the appropriateness of traditional statistical regression methods for identifying risk factors for infectious diseases, by a simulation study. We model infectious disease spread by a simple, population-structured version of an SIR (susceptible-infected-recovered)-model, which is one of the most famous and well-established models for infectious disease spread. The population is thus divided into different sub-groups. We vary the contact structure between the sub-groups of the population. We analyse the relation between individual-level risk of infection and group-level relative risk. We analyse whether Poisson regression estimators can capture the true, underlying parameters of transmission. We assess both the quantitative and qualitative accuracy of the estimated regression coefficients.

RESULTS

We illustrate that there is no clear relationship between differences in individual characteristics and group-level overrepresentation -small differences on the individual level can result in arbitrarily high overrepresentation. We demonstrate that individual risk of infection cannot be properly defined without simultaneous specification of the infection level of the population. We argue that the estimated regression coefficients are not interpretable and show that it is not possible to adjust for other variables by standard regression methods. Finally, we illustrate that regression models can result in the significance of variables unrelated to infection risk in the constructed simulation example (e.g. ethnicity), particularly when a large proportion of contacts is within the same group.

CONCLUSIONS

Traditional regression models which are valid for modelling risk between groups for non-communicable diseases are not valid for infectious diseases. By applying such methods to identify risk factors of infectious diseases, one risks ending up with wrong conclusions. Output from such analyses should therefore be treated with great caution.

SARS-CoV-2 breakthrough infections in vaccinated individuals: measurement, causes and impact

Breakthrough infections with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in fully vaccinated individuals are receiving intense scrutiny because of their importance in determining how long restrictions to control virus transmission will need to remain in place in highly vaccinated populations as well as in determining the need for additional vaccine doses or changes to the vaccine formulations and/or dosing intervals. Measurement of breakthrough infections is challenging outside of randomized, placebo-controlled, double-blind field trials. However, laboratory and observational studies are necessary to understand the impact of waning immunity, viral variants and other determinants of changing vaccine effectiveness against various levels of coronavirus disease 2019 (COVID-19) severity. Here, we describe the approaches being used to measure vaccine effectiveness and provide a synthesis of the burgeoning literature on the determinants of vaccine effectiveness and breakthrough rates. We argue that, rather than trying to tease apart the contributions of factors such as age, viral variants and time since vaccination, the rates of breakthrough infection are best seen as a consequence of the level of immunity at any moment in an individual, the variant to which that individual is exposed and the severity of disease being considered. We also address key open questions concerning the transition to endemicity, the potential need for altered vaccine formulations to track viral variants, the need to identify immune correlates of protection, and the public health challenges of using various tools to counter breakthrough infections, including boosters in an era of global vaccine shortages.

Force of infection: a determinant of vaccine efficacy?

Vaccine efficacy (VE) can vary in different settings. Of the many proposed setting-dependent determinants of VE, force of infection (FoI) stands out as one of the most direct, proximate, and actionable. As highlighted by the COVID-19 pandemic, modifying FoI through non-pharmaceutical interventions (NPIs) use can significantly contribute to controlling transmission and reducing disease incidence and severity absent highly effective pharmaceutical interventions, such as vaccines. Given that NPIs reduce the FoI, the question arises as to if and to what degree FoI, and by extension NPIs, can modify VE, and more practically, as vaccines become available for a pathogen, whether and which NPIs should continue to be used in conjunction with vaccines to optimize controlling transmission and reducing disease incidence and severity.

Identification of causal intervention effects under contagion

Defining and identifying causal intervention effects for transmissible infectious disease outcomes is challenging because a treatment - such as a vaccine - given to one individual may affect the infection outcomes of others. Epidemiologists have proposed causal estimands to quantify effects of interventions under contagion using a two-person partnership model. These simple conceptual models have helped researchers develop causal estimands relevant to clinical evaluation of vaccine effects. However, many of these partnership models are formulated under structural assumptions that preclude realistic infectious disease transmission dynamics, limiting their conceptual usefulness in defining and identifying causal treatment effects in empirical intervention trials. In this paper, we propose causal intervention effects in two-person partnerships under arbitrary infectious disease transmission dynamics, and give nonparametric identification results showing how effects can be estimated in empirical trials using time-to-infection or binary outcome data. The key insight is that contagion is a causal phenomenon that induces conditional independencies on infection outcomes that can be exploited for the identification of clinically meaningful causal estimands. These new estimands are compared to existing quantities, and results are illustrated using a realistic simulation of an HIV vaccine trial.

Modelling the Effectiveness of Epidemic Control Measures in Preventing the Transmission of COVID-19 in Malaysia

Malaysia is currently facing an outbreak of COVID-19. We aim to present the first study in Malaysia to report the reproduction numbers and develop a mathematical model forecasting COVID-19 transmission by including isolation, quarantine, and movement control measures. We utilized a susceptible, exposed, infectious, and recovered (SEIR) model by incorporating isolation, quarantine, and movement control order (MCO) taken in Malaysia. The simulations were fitted into the Malaysian COVID-19 active case numbers, allowing approximation of parameters consisting of probability of transmission per contact (β), average number of contacts per day per case (ζ), and proportion of close-contact traced per day (q). The effective reproduction number (Rt) was also determined through this model. Our model calibration estimated that (β), (ζ), and (q) were 0.052, 25 persons, and 0.23, respectively. The (Rt) was estimated to be 1.68. MCO measures reduce the peak number of active COVID-19 cases by 99.1% and reduce (ζ) from 25 (pre-MCO) to 7 (during MCO). The flattening of the epidemic curve was also observed with the implementation of these control measures. We conclude that isolation, quarantine, and MCO measures are essential to break the transmission of COVID-19 in Malaysia.

Heterogeneous susceptibility to rotavirus infection and gastroenteritis in two birth cohort studies: Parameter estimation and epidemiological implications

Cohort studies, randomized trials, and post-licensure studies have reported reduced natural and vaccine-derived protection against rotavirus gastroenteritis (RVGE) in low- and middle-income countries. While susceptibility of children to rotavirus is known to vary within and between settings, implications for estimation of immune protection are not well understood. We sought to re-estimate naturally-acquired protection against rotavirus infection and RVGE, and to understand how differences in susceptibility among children impacted estimates. We re-analyzed data from studies conducted in Mexico City, Mexico and Vellore, India. Cumulatively, 573 rotavirus-unvaccinated children experienced 1418 rotavirus infections and 371 episodes of RVGE over 17,636 child-months. We developed a model that characterized susceptibility to rotavirus infection and RVGE among children, accounting for aspects of the natural history of rotavirus and differences in transmission rates between settings. We tested whether model-generated susceptibility measurements were associated with demographic and anthropometric factors, and with the severity of RVGE symptoms. We identified greater variation in susceptibility to rotavirus infection and RVGE in Vellore than in Mexico City. In both cohorts, susceptibility to rotavirus infection and RVGE were associated with male sex, lower birth weight, lower maternal education, and having fewer siblings; within Vellore, susceptibility was also associated with lower socioeconomic status. Children who were more susceptible to rotavirus also experienced higher rates of rotavirus-negative diarrhea, and higher risk of moderate-to-severe symptoms when experiencing RVGE. Simulations suggested that discrepant estimates of naturally-acquired immunity against RVGE can be attributed, in part, to between-setting differences in susceptibility of children, but result primarily from the interaction of transmission rates with age-dependent risk for infections to cause RVGE. We found that more children in Vellore than in Mexico City belong to a high-risk group for rotavirus infection and RVGE, and demonstrate that unmeasured individual- and age-dependent susceptibility may influence estimates of naturally-acquired immune protection against RVGE.

Differences in susceptibility can help explain why some individuals, and not others, acquire infection and exhibit symptoms when exposed to infectious disease agents. However, it is difficult to distinguish between differences in susceptibility versus exposure in epidemiological studies. We developed a modeling approach to distinguish transmission intensity and susceptibility in data from cohort studies of rotavirus infection among children in Mexico City, Mexico, and Vellore, India, and evaluated how these factors may have contributed to differences in estimates of naturally-acquired immune protection between the studies. Given the same exposure, more children were at high risk of acquiring rotavirus infection, and of experiencing gastroenteritis when infected, in Vellore than in Mexico City. The probability of belonging to this high-risk stratum was associated with well-known individual factors such as lower socioeconomic status, lower birth weight, and incidence of diarrhea due to other causes. We also found the risk for rotavirus infections to cause symptoms declined with age, independent of acquired immunity. These findings can, in part, account for estimates of lower protective efficacy of acquired immunity against rotavirus gastroenteritis in high-incidence settings, mirroring estimates of reduced effectiveness of live oral rotavirus vaccines in low- and middle-income countries.

Biased efficacy estimates in phase-III dengue vaccine trials due to heterogeneous exposure and differential detectability of primary infections across trial arms

Vaccine efficacy (VE) estimates are crucial for assessing the suitability of dengue vaccine candidates for public health implementation, but efficacy trials are subject to a known bias to estimate VE toward the null if heterogeneous exposure is not accounted for in the analysis of trial data. In light of many well-characterized sources of heterogeneity in dengue virus (DENV) transmission, our goal was to estimate the potential magnitude of this bias in VE estimates for a hypothetical dengue vaccine. To ensure that we realistically modeled heterogeneous exposure, we simulated city-wide DENV transmission and vaccine trial protocols using an agent-based model calibrated with entomological and epidemiological data from long-term field studies in Iquitos, Peru. By simulating a vaccine with a true VE of 0.8 in 1,000 replicate trials each designed to attain 90% power, we found that conventional methods underestimated VE by as much as 21% due to heterogeneous exposure. Accounting for the number of exposures in the vaccine and placebo arms eliminated this bias completely, and the more realistic option of including a frailty term to model exposure as a random effect reduced this bias partially. We also discovered a distinct bias in VE estimates away from the null due to lower detectability of primary DENV infections among seronegative individuals in the vaccinated group. This difference in detectability resulted from our assumption that primary infections in vaccinees who are seronegative at baseline resemble secondary infections, which experience a shorter window of detectable viremia due to a quicker immune response. This resulted in an artefactual finding that VE estimates for the seronegative group were approximately 1% greater than for the seropositive group. Simulation models of vaccine trials that account for these factors can be used to anticipate the extent of bias in field trials and to aid in their interpretation.

Impact of stochastically generated heterogeneity in hazard rates on individually randomized vaccine efficacy trials

Background/aims Network structure and individuals' level of exposure to a pathogen can impact results from efficacy evaluation studies of interventions against infectious diseases. Heterogeneity in infection risk can cause randomized groups to increasingly differ as a trial progresses and as more high-risk individuals become infected (described in prior work as the "frailty" phenomenon). Here, we show the impact this phenomenon can have on an individually randomized trial of a leaky vaccine in which all participants are exchangeable a priori. Methods We model a vaccine trial by generating a network of individuals grouped into communities, which are connected to a larger main population. We then simulate an epidemic, deterministically and with time-varying transmission rates in the main population and stochastically in the communities. The disease natural history follows a susceptible-exposed-infectious-recovered model. Simulation results are used to estimate vaccine efficacy [Formula: see text] with a Cox proportional hazards model. Results We find downward bias in [Formula: see text] associated with low connectivity between communities in the study population and high force of infection, even when all participants in the trial are exchangeable at the time of randomization. This phenomenon arises because the stochastic dynamics in such a setting randomly lead to community-level variation in the force of infection. Stratifying a Cox model by community alleviates this bias with no loss of power. Conclusion Understanding and accounting for the impact of heterogeneous hazard rates can allow for more accurate estimates of [Formula: see text] in epidemic settings.

Risk ratios for contagious outcomes

Epidemiologists commonly use the risk ratio to summarize the relationship between a binary covariate and outcome, even when outcomes may be dependent. Investigations of transmissible diseases in clusters-households, villages or small groups-often report risk ratios. Epidemiologists have warned that risk ratios may be misleading when outcomes are contagious, but the nature of this error is poorly understood. In this study, we assess the meaning of the risk ratio when outcomes are contagious. We provide a mathematical definition of infectious disease transmission within clusters, based on the canonical stochastic susceptible-infective model. From this characterization, we define the individual-level ratio of instantaneous infection risks as the inferential target, and evaluate the properties of the risk ratio as an approximation of this quantity. We exhibit analytically and by simulation the circumstances under which the risk ratio implies an effect whose direction is opposite that of the true effect of the covariate. In particular, the risk ratio can be greater than one even when the covariate reduces both individual-level susceptibility to infection, and transmissibility once infected. We explain these findings in the epidemiologic language of confounding and Simpson's paradox, underscoring the pitfalls of failing to account for transmission when outcomes are contagious.

Simulations for designing and interpreting intervention trials in infectious diseases

BACKGROUND

Interventions in infectious diseases can have both direct effects on individuals who receive the intervention as well as indirect effects in the population. In addition, intervention combinations can have complex interactions at the population level, which are often difficult to adequately assess with standard study designs and analytical methods.

DISCUSSION

Herein, we urge the adoption of a new paradigm for the design and interpretation of intervention trials in infectious diseases, particularly with regard to emerging infectious diseases, one that more accurately reflects the dynamics of the transmission process. In an increasingly complex world, simulations can explicitly represent transmission dynamics, which are critical for proper trial design and interpretation. Certain ethical aspects of a trial can also be quantified using simulations. Further, after a trial has been conducted, simulations can be used to explore the possible explanations for the observed effects.

CONCLUSION

Much is to be gained through a multidisciplinary approach that builds collaborations among experts in infectious disease dynamics, epidemiology, statistical science, economics, simulation methods, and the conduct of clinical trials.

Vaccine Effects on Heterogeneity in Susceptibility and Implications for Population Health Management

Heterogeneity in host susceptibility is a key determinant of infectious disease dynamics but is rarely accounted for in assessment of disease control measures. Understanding how susceptibility is distributed in populations, and how control measures change this distribution, is integral to predicting the course of epidemics with and without interventions. Using multiple experimental and modeling approaches, we show that rainbow trout have relatively homogeneous susceptibility to infection with infectious hematopoietic necrosis virus and that vaccination increases heterogeneity in susceptibility in a nearly all-or-nothing fashion. In a simple transmission model with an R₀ of 2, the highly heterogeneous vaccine protection would cause a 35 percentage-point reduction in outbreak size over an intervention inducing homogenous protection at the same mean level. More broadly, these findings provide validation of methodology that can help to reduce biases in predictions of vaccine impact in natural settings and provide insight into how vaccination shapes population susceptibility.

Differences among individuals influence transmission and spread of infectious diseases as well as the effectiveness of control measures. Control measures, such as vaccines, may provide leaky protection, protecting all hosts to an identical degree, or all-or-nothing protection, protecting some hosts completely while leaving others completely unprotected. This distinction can have a dramatic influence on disease dynamics, yet this distribution of protection is frequently unaccounted for in epidemiological models and estimates of vaccine efficacy. Here, we apply new methodology to experimentally examine host heterogeneity in susceptibility and mode of vaccine action as distinct components influencing disease outcome. Through multiple experiments and new modeling approaches, we show that the distribution of vaccine effects can be robustly estimated. These results offer new experimental and inferential methodology that can improve predictions of vaccine effectiveness and have broad applicability to human, wildlife, and ecosystem health.

A Dynamic Transmission Model to Evaluate the Effectiveness of Infection Control Strategies

BACKGROUND

The advancement of knowledge about control of antibiotic resistance depends on the rigorous evaluation of alternative intervention strategies. The STAR*ICU trial examined the effects of active surveillance and expanded barrier precautions on acquisition of methicillin-resistant Staphylococcus aureus (MRSA) and vancomycin-resistant Enterococcus (VRE) in intensive care units. We report a reanalyses of the STAR*ICU trial using a Bayesian transmission modeling framework.

METHODS

The data included admission and discharge times and surveillance test times and results. Markov chain Monte Carlo stochastic integration was used to estimate the transmission rate, importation, false negativity, and clearance separately for MRSA and VRE. The primary outcome was the intervention effect, which when less than (or greater than) zero, indicated a decreased (or increased) transmission rate attributable to the intervention.

RESULTS

The transmission rate increased in both arms from pre- to postintervention (by 20% and 26% for MRSA and VRE). The estimated intervention effect was 0.00 (95% confidence interval [CI], -0.57 to 0.56) for MRSA and 0.05 (95% CI, -0.39 to 0.48) for VRE. Compared with MRSA, VRE had a higher transmission rate (preintervention, 0.0069 vs 0.0039; postintervention, 0.0087 vs 0.0046), higher importation probability (0.22 vs 0.17), and a lower clearance rate per colonized patient-day (0.016 vs 0.035).

CONCLUSIONS

Transmission rates in the 2 treatment arms were statistically indistinguishable from the pre- to postintervention phase, consistent with the original analysis of the STAR*ICU trial. Our statistical framework was able to disentangle transmission from importation and account for imperfect testing. Epidemiological differences between VRE and MRSA were revealed.