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RRR performed the analysis. RRR, IML, MBF, and SIS designed the study and wrote the paper.

The authors have declared that no competing interests exist.

Trials in macaque models play an essential role in the evaluation of biomedical interventions that aim to prevent HIV infection, such as vaccines, microbicides, and systemic chemoprophylaxis. These trials are usually conducted with very high virus challenge doses that result in infection with certainty. However, these high challenge doses do not realistically reflect the low probability of HIV transmission in humans, and thus may rule out preventive interventions that could protect against “real life” exposures. The belief that experiments involving realistically low challenge doses require large numbers of animals has so far prevented the development of alternatives to using high challenge doses.

Using statistical power analysis, we investigate how many animals would be needed to conduct preclinical trials using low virus challenge doses. We show that experimental designs in which animals are repeatedly challenged with low doses do not require unfeasibly large numbers of animals to assess vaccine or microbicide success.

Preclinical trials using repeated low-dose challenges represent a promising alternative approach to identify potential preventive interventions.

Trials of HIV vaccines in animals using repeated low- dose challenges of the virus are feasible and may be more true to life.

Before trials of medicines or vaccines are done in humans, most are tested in animals. There are many controversies about these animal trials, including whether they mimic the human disease accurately. In testing vaccines for HIV, animals are mostly given high doses of the virus, whereas in real life people are often repeatedly exposed to small amounts of the virus. No vaccine that has been tested against HIV prevents infection in animals. It is possible that some of this lack of success may be due to the design of the vaccine trials rather than the vaccine itself.

They wanted to look at experimental designs that allowed assessment of protection against infection with lower, and thus more realistic, doses of virus. Previously, researchers had suggested that many animals would be needed for this type of study. The authors wanted to see whether this was correct. They developed a model to test how well single and multiple low-dose experiments performed. They did this by simulating the experiments with doses of virus, assessing the results, and then repeating this procedure 100,000 times to estimate how valid a given experimental design was.

Their modeling showed that by repeatedly giving animals low doses of virus, it was possible to use a smaller number of animals than was needed for trials with a single low dose.

It may be possible to use these results to plan trials of vaccines in animals that mimic more closely the way that humans are exposed to HIV, and hence the results may be more reliable for human disease.

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Worldwide approximately 40 million people are infected with HIV, and more than 3 million people died of AIDS last year alone [

Research on HIV vaccines and prevention relies strongly on preclinical studies in macaque models for the identification and evaluation of potential vaccines or prophylactic treatment strategies [

The inability of most vaccine candidates to induce protection against infection in animal studies may be due, at least in part, to unintended consequences of the design of the animal trials, rather than to problems inherent in the vaccination approaches themselves. In most animal studies that seek to test the efficacy of a given preventive intervention, very high challenge doses are used, typically of approximately 10–100 times the infectious dose at which 50% of the animals become infected (_{50}). The motivation for using such high challenge doses is mostly practical: the experimenter wants to ascertain infection success in unvaccinated/untreated animals, which can then be compared to the hopefully lower infection success in vaccinated/treated animals. There are, however, concerns with using high challenge doses. Firstly, the extremely high probability of infection in high-dose challenge studies conflicts with the low transmission rate of HIV per sex act [

The problems of using high virus doses in animal studies can be illustrated by the discrepancy between the protection zidovudine (AZT) confers in animals and humans. Whereas macaques [

The belief that experiments involving realistically low challenge doses require unfeasibly large numbers of animals has prevented the development of low-dose challenge models. In this theoretical study, we show that, contrary to this widely held belief, low-dose challenge experiments can be designed such that they do not require large numbers of animals. Using statistical power analysis, we compare two experimental designs (see

Figure shows designs for single (A) and repeated (B) low-dose challenge designs. Small arrows denote challenges, and white and red symbols denote uninfected and infected animals, respectively.

In the following, we are going to discuss the case of assessing whether a vaccine candidate induces sterilizing immunity. All the considerations in this article, however, apply equally to other preventive interventions, such as microbicides.

To assess the quality of the single and the repeated low-dose challenge designs, we conducted a statistical power analysis. The statistical power of an experimental design is defined as the probability that an effective vaccine or treatment is correctly determined to be effective. This analysis consists of simulating the experiments, evaluating them, and then repeating this procedure thousands of times to estimate the statistical power of a given experimental design.

In our simulations of the single low-dose challenge experiments, we assume that we have

In the control group, we simulate single challenges of each animal with the _{50} by performing _{c}_{c}_{c},

By summing over the elements of _{c},_{c}

In the vaccinated group, we simulate single challenges with the _{50} similarly to the control group by performing Bernoulli trials. However, we assume that, because of vaccination, the probability of infection (or success) in the vaccinated group, _{v},_{c}_{v}_{S},

The results of these Bernoulli trials can again be written as a vector _{v},_{v}_{v}

The outcome of the simulated experiment can then be summarized in a contingency table as shown in

In our simulations of the repeated low-dose challenge experiments, we once more assume that we have

We again simulate challenges of each control animal with the _{50} by performing Bernoulli trials with a probability of success of _{c}_{max},_{c}_{c},

and _{c},

By summing over _{c},_{c}:

And, by summing over _{c},_{c}:

To simulate repeated low-dose challenges in the vaccinated group, we perform repeated Bernoulli trials with a probability of success _{v}_{S},_{v}_{v}_{v},_{v},_{v}

As in the case of the single low-dose challenge design, the outcome of the simulated experiment can be summarized in a contingency table (_{c}_{v},

In our mml:mathematical description of challenge experiments, we have assumed that animals within each group have equal infection probabilities—_{c}_{v},

The individual infection probabilities are drawn from a β-distribution, which is often used as a prior distribution for binomial proportions. The β-distribution has two shape parameters, α and β. Its probability density is given by

and its mean and variance are

We assume that μ = _{c}_{v} =_{S}_{c}

Hereby, _{c}_{v}_{S}_{c}

To incorporate potential heterogeneity in susceptibility into the virtual low-dose challenge experiments, we replaced the probability of success in the Bernoulli trials (see above) with the individual infection probabilities.

To calculate the statistical power of the single and the repeated low-dose challenge designs, we performed 100,000 such simulated experiments for a given number, _{S} =

For large numbers of animals per group,

Hereby, Φ denotes the cumulative normal distribution,

and _{α} is the standard normal deviate associated with the one-tailed probability α (the significance level). Furthermore, _{c}_{v}

For the repeated low-dose challenge design, the number of challenges is not the same as the number of animals, _{max}

and

Substituting the expected number of challenges for the actual number, we can approximate the statistical power of the repeated low-dose challenge design as

Hereby, γ = (1/〈η_{c}〉 + 1/〈η_{v}〉)/2 is the continuity correction. For _{max}

How would we measure protection against infection in a low-dose challenge model? The most straight-forward design would involve a large number of hosts, some vaccinated and some unvaccinated. After challenge with a low dose, one would determine the fraction of infected hosts in vaccinated and unvaccinated groups, and assess whether there is a statistically significant difference in the fractions (see

To assess how many animals would be required in a single low-dose challenge experiment, we performed a statistical power analysis (see

In virtual experiments, we then challenged each (virtual) animal once with a challenge dose of one _{50}, the dose at which on average 50% of the unvaccinated animals become infected after a single challenge. Using a one-sided Fisher's exact test, we tested whether the fraction of infected animals in the vaccinated group was significantly lower than in the control group. Performing 100,000 such virtual experiments for a given number

The result of this power analysis is shown by the green curves in

In our virtual experiments, we set the challenge dose equal to the _{50}, and assumed that the vaccine efficacy was 67% (dotted lines), 80% (dashed lines), or 90% (solid lines). The graph shows the statistical power of the repeated low-dose challenge design (black lines) and the single low-dose challenge design (green lines) for a given number of animals per group as determined from 100,000 virtual experiments. If the vaccine is 90% effective, the statistical power of the repeated low-dose challenge design is higher than 95% with only five animals per group, as compared to only 15% for the single low-dose challenge design.

We propose an alternative design involving repeated challenges of individual animals with low doses, which circumvents the disadvantage of the single low-dose challenge design that large numbers of host individuals are required. Repeated challenges effectively “recycle” host animals, thus increasing the statistical power of the experiment. In addition to increasing the statistical power of the experimental design, repeated challenges recapitulate much more realistically the circumstances of human exposure than single challenges. In this alternative design, the efficacy of a vaccine can be estimated by measuring the difference in the number of challenges needed to infect vaccinated versus unvaccinated hosts (see

To show that this alternative design does not require unfeasibly large numbers of animals, we performed a statistical power analysis (see

In virtual experiments, we then challenged the (virtual) animals repeatedly with a challenge dose of one _{50}. We allowed for a maximum number of 20 challenges of each individual animal.

_{S} =

To investigate how the maximum number of challenges affected the statistical power, we plotted the power against _{max}_{max},_{max}_{max},_{max},

For this plot we assumed trials with vaccine efficacies of _{S} =_{S} =_{S} =

To study how potential heterogeneity in susceptibility affected the power of low-dose challenge trials, we simulated experiments in which each animal was assigned an individual infection probability (see

(A) Susceptibility distributions for different levels of heterogeneity, measured by the coefficient of variation, _{S} =

(B) The statistical power depends on the coefficient of variation, _{S} =_{S} =_{S} =

We extended our power analysis by considering the impact of the heterogeneity parameter

Preclinical studies assessing the efficacy of potential vaccines, microbicides, or systemic chemoprophylaxis are usually conducted with very high virus challenge doses, which result in infection with certainty. Since these high challenge doses do not reflect the low probability of HIV transmission in humans, vaccines or prophylactic treatment strategies that are effective against “real life” exposures may go undetected in high-dose challenge experiments. For example, zidovudine was found to prevent a large fraction of perinatal HIV infections [

In this paper, we investigated how efficacy trials of vaccines and preventive treatment could be conducted with low challenge doses in animal models. We showed that the repeated low-dose challenge design is expected to require far fewer experimental animals than commonly believed. It may therefore be feasible to conduct trials with low challenge doses, which more realistically simulate exposures of humans to HIV, allowing us to more directly and sensitively assess vaccine or treatment efficacy than with high-dose challenge experiments.

Owing to the concerns with high challenge doses, several research groups, including our own, have started to develop low-dose challenge models [

Since adopting low-dose challenge approaches has far-reaching consequences for the design of efficacy trials of vaccines or preventive treatment in animal models, we would like to discuss how some important aspects of trial design, such as transient infections, the challenge schedule, the route of infection, and the phenotype and dose of the challenge strain, should be dealt with and could be optimized.

Using virus challenge doses that do not give rise to infection with certainty, one has to carefully define what one means by successful infection. This question is of particular importance in the repeated low-dose challenge design, because the efficacy of a preventive intervention is estimated on the basis of the number of challenges needed to infect an individual animal. Low-dose challenges have been observed to give rise to transiently detectable viremia [

The time interval between challenges is also an essential parameter in the design of repeated low-dose challenge experiments. In the four ongoing repeated low-dose challenge studies [

In parallel to using more realistic, lower challenge doses, other crucial parameters of the experimental infection process, such as the route of transmission and the coreceptor usage of the challenge virus, should also be chosen to be as realistic as possible. Thus, we propose infecting intra-vaginally or intra-rectally in experiments that aim to assess a vaccine or prophylactic treatment against sexual transmission of HIV. Further, we suggest using challenge viruses that utilize CCR5 as coreceptor, such as for example SHIV-SF162P [

The challenge dose in a low-dose challenge study is another parameter of crucial importance. Although the most realistic choice would be a challenge dose that gives rise to infection with a probability of approximately 0.0005–0.10 [_{50}. The _{50} can be estimated using well-established nonparametric methods like Spearman-Kärber [_{50} from data generated in titration experiments.

The inability to detect sterilizing immunity in high-dose challenge experiments led to a shift of focus towards indirect effects of vaccine candidates on the pathogenicity of the infection and the infectiousness of the vaccinee. This shift of focus required the development of novel statistical models that allowed the estimation of these indirect effects [

In addition to the potential to assess the vaccine or microbicide efficacy more sensitively and in a more realistic setting, a low-dose challenge approach may enable us to answer questions that cannot even be asked in high-dose challenge models. Some of the most relevant of these questions relate to the effect of challenges that do not lead to infection. If a low-dose challenge does not give rise to infection, where was the virus blocked? Did the virus fail to establish an infection at all? Or did it replicate transiently, but was cleared by the host's immunity? And, very importantly, is an unsuccessfully challenged animal partially immunized against further challenges, or, alternatively, do unsuccessful challenges facilitate future infection by “seeding” animals with defective proviruses that may recombine with complementing viruses upon subsequent exposures [

The answers to these questions would greatly enhance our understanding of HIV transmission and pathogenesis, and thus would provide further guidance toward an effective vaccine or microbicide. Furthermore, by assessing the protection against infection directly, we may be able to discern the specific types and levels of vaccine-induced cellular and humoral immune responses associated with sterilizing immunity [

In conclusion, the repeated low-dose challenge approach may enable us to assess the potential efficacy of vaccines and prophylactic treatment strategies more realistically, and more sensitively than the standard high-dose challenge approach. The increased sensitivity may allow us to more rapidly identify interventions that significantly reduce the transmission of low-dose infections that characterize the natural spread of HIV.

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We thank Rustom Antia, Steven Self, Mark Tanaka, and Andrew Yates for discussion. RRR was supported by the Deutsche Forschungsgemeinschaft grant number Re 1618/1–2 and the National Institutes of Health (NIH) grant AI-49334. The support of the NIH National Institute of Allergy and Infectious Disease grant 1 R21 AI54260 is gratefully acknowledged. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

infectious dose at which 50% of the animals become infected