Thirty-five years of leaky vaccines

Abstract

Editor’s note: The opinions expressed in this article are those of the authors and do not necessarily reflect the views of the American Journal of Epidemiology.

Introduction

Over the past 35 years, the term “leaky vaccine” has gained widespread use in both mathematical modeling and epidemiologic methods for evaluating vaccine efficacy and effectiveness. It generally means a multiplicative reduction in the probability of being infected if exposed. In discussion with a few colleagues recently, it turned out they did not know how the term leaky vaccine came to be. This motivated us to write this short history.

In the early and mid 1980s, there was terrific excitement and optimism that good, stage-specific malaria vaccines were just over the horizon. The malaria parasite has a complex life cycle in humans and female Anopheles mosquitoes.¹ Here, we are interested in Plasmodium falciparum, 1 of 5 species of human malaria that causes the most deaths. A person becomes infected when an infected female Anopheles mosquito bites the person and injects sporozoites from its salivary glands into the bloodstream. The sporozoites travel to the liver, where they multiply in the liver cells and develop into merozoites. After a week or so, the merozoites leave the liver and invade red blood cells. This is the asexual blood stage of the parasite. Merozoites multiply in the red blood cells, which burst, releasing the merozoites to invade more red blood cells—the basis of malaria symptoms. Some merozoites in the red blood cells transform into a sexual stage of the parasite called gametocytes. When a female Anopheles mosquito bites a human with gametocytes, the mosquito ingests the gametocytes into its gut. There, gametes are set free from the gametocytes and mate to produce the next form. This form multiplies and creates the sporozoites that migrate to the mosquito salivary gland, ready to infect another human when the female Anopheles mosquito bites again.¹

The 3 main stages of the malaria parasite—sporozoites, merozoites, and gametocytes—are antigenically distinct, meaning that a different vaccine needs to developed for each stage. Thus, they are called stage-specific vaccines. In the 1980s, considerable discussion centered around how a vaccine targeting sporozoites might work. It might completely prevent infection by inhibiting invasion of liver cells or by impairing effective reproduction once the parasite was in the liver. This would presumably also prevent formation of merozoites and gametocytes, and thus prevent formation of blood stages and also prevent transmission to mosquitos. Alternatively, inhibition by a sporozoite vaccine of invasion of the liver might not be complete. In this case, a sporozoite vaccine might reduce the probability of developing a brood of parasites from any given sporozoite-containing mosquito bite. It could also reduce the number of sporozoites breaking through the liver to produce parasitemia with asexual blood forms and gametocytes.

Beginning in the fall of 1984, while taking a course on malariology at the Harvard School of Public Health, we developed an interest in modeling stage-specific malaria vaccines. We developed a deterministic malaria model² that was a modification of the Garki model^3,4 to allow for loss of immunity and boosting of immunity by natural infection, among other things. Using that model, we explored population-level effects of stage-specific malaria vaccines that might depend on natural boosting under a number of different assumptions.⁵ In an 1989 article about that work, we used the word “leaky” to describe a sporozoite vaccine mechanism that reduced the probability of being infected by a sporozoite-containing mosquito bite. We also considered an infection-blocking sporozoite vaccine. We cite at least 12 articles from the 1980s on the development of the sporozoite vaccines when we discuss possible mechanisms for sporozoite vaccines. However, we do not find the word leaky in those articles. We actually are not certain if malaria vaccine researchers used that term at least informally, or whether we coined it during our stage-specific malaria vaccine modeling research. Certainly the concept of possible leakiness is in the literature, even if the term leaky was not used. In any event, the term comes from the graphic idea that the sporozoite vaccine immunity might not completely block infection (hence, it could be leaky), allowing malaria parasites into the liver, then into the bloodstream. For vaccines against viral infections, a leaky vaccine might correspond to one where the antibody titers do not stop all viruses from infecting human host cells. We also modeled different gametic vaccines, those that completely blocked transmission to mosquitoes and those that were leaky (ie, reduced the probability that an infectious human host transmitted to a mosquito when bitten).

Developing at that same time was increased interest in novel epidemiologic methods for evaluating vaccines using case-control studies. In 1984, Smith et al.⁶ published a thought-provoking article on different study designs for vaccines that had 2 different mechanisms of vaccine protection. Model 1 assumed vaccine protection was multiplicative on the hazard rate. Model 2 assumed that a fraction of people were completely protected and the others not at all. We were also interested in study design methodology for evaluating vaccines in populations^7,8 and knew this article quite well. However, whereas Smith et al. used the term Model 1, we chose the term leaky because of our background in malaria: the term relates to the underlying biology, and it is more descriptive. The 2 terms can be linked. Assuming random mixing, the hazard rate can be expressed as a product of the contact rate, the transmission probability, and the prevalence of infectives. A mechanism 1 vaccine would be multiplicative on the hazard rate if it reduced the probability of infection upon exposure to an infective.

We also chose the term “all-or-none” vaccine as more descriptive than “model 2.” One might consider that vaccinated people consist of responders, who possibly produce an immune response above a threshold that protects completely against infection, and nonresponders, who produce no immune response to the vaccine and, thus, are completely unprotected. The terms leaky and all-or-none are in common usage now, but this is not meant to detract from the original ideas in the 1984 article of Smith et al.⁶

A major difference in the 2 modes of vaccine action is that the simplest leaky model assumes the protection in the vaccinated population is homogeneous and the all-or-none model assumes that protection in the vaccinated population is heterogeneous. With a leaky model, with enough exposure, eventually all vaccinated individuals could get infected. In the all-or-none model, the fraction of the people who are protected by the vaccine will never get infected. Here, we do not consider waning or boosting, both of which complicate the picture. In the following, we assume here is no other difference between the responders and nonresponders aside from the immune response.

The 2 mechanisms, or distributions of protection, have implications for study design and analysis of vaccine efficacy. Assume we have a cohort of individuals randomized to be vaccinated or to receive a control. Smith et al.⁶ pointed out that in a study of vaccine against a control, if a vaccine were all-or-none (model 2), then the cumulative incidence would yield a time-invariant measure of vaccine efficacy. If a vaccine were multiplicative on the hazard (model 1; ie, leaky), then the hazard ratio would be time invariant and a Cox proportional hazards model would yield a time-invariant measure of vaccine efficacy. The time-invariant vaccine efficacy estimator under an all-or-none model estimates the proportion of individuals completely protected at the beginning of the study. The time-invariant vaccine efficacy estimator under a leaky model estimates the proportionate reduction in the hazard rate or transmission probability. Smith et al.⁶ pointed out some consequences of the 2 mechanisms and the estimand of interest for how to sample controls in a case-control study. The estimate of vaccine efficacy may appear to change over time, either waning or even increasing, even when it is not, if the estimator does not take properly into account the distribution of vaccine protection. More on modes of vaccine action and time-varying vaccine efficacy is discussed in Chapter 7 of Design and Analysis of Vaccine Studies by Halloran et al.⁹

The 2 different models of mechanisms by which vaccines induce protection or reduce risk produce a difference at the population level over time. Assume that in a cohort of young children, children are randomly vaccinated or left unvaccinated. In an age-structured dynamic transmission model, with a leaky vaccine, it will take more exposures for vaccinated people to get infected than unvaccinated people. Assuming equal exposure in the vaccinated and unvaccinated people, the age distribution of the vaccinated cases will be older than the age distribution of the unvaccinated cases. With an all-or-none vaccine, assuming there is no other difference between the responders and nonresponders, the age distribution of cases in the vaccinated children will be the same as the age distribution in the unvaccinated children. Our malaria models were some of the first that used a leaky vaccine mechanism. Previous to that, most dynamics models assumed efficacy was all-or-none, with vaccine efficacy being the proportion completely protected.

The leaky and all-or-none distributions are 2 extremes. One can consider models where some individuals are completely protected, whereas others are partially protected, possibly with a continuous distribution. Frailty mixture models can be used to estimate vaccine efficacy in such a case.^10,11 The general idea of a distribution of protection conferred by immunization in a population goes back over 100 years. In 1915, Greenwood and Yule published a seminal article in which they speculated at length on a continuous distribution of protection from immunization.¹² In the current context, one might think that the continuous protection is a type of leaky protection.

Despite the optimism of the 1980s, more than 35 years passed before 2 malaria vaccines were recommended by the World Health Organization.¹³ As of October 2, 2023, the RTS,S/AS01¹⁴ and R21/Matrix-M¹⁵ vaccines, both aimed against the sporozoite of P falciparum, were recommended by the World Health Organization to prevent malaria in children. We leave it to further research to determine whether those 2 malaria vaccines are leaky.

Funding

None declared.

Conflict of interest

The authors declare no conflict of interest.

References