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.


Introduction
Lower apparent vaccine efficacy (VE) in low resource settings, when compared to VE observed in high resource settings, has been reported for several pathogens, most notably poliovirus, typhoid, and rotavirus. [1][2][3][4][5] Observed VE also varied when evaluating a malaria vaccine candidate in different parasite transmission settings. [6][7][8] Numerous economic, social, and biological factors A two-step approach was taken to interrogate the potential relationship between FoI and VE. The first explored three mathematical scenarios of VE as a function of various FoI settings. The second followed up on the decades old observations of lower apparent oral poliovirus vaccine (OPV) 1 and typhoid vaccine 5 VE in low resource settings when compared to high resource settings by assessing the correlation between the incidence of disease in the placebo population (as a surrogate of FoI in the study population) and the observed VE in different geographical settings. Recent Phase 3 studies of malaria and rotavirus vaccine candidates across a number of settings, including low and high resource settings, 6,17 provided data for assessing if and how FoI might be a determinant of VE.
Both the thought experiment of setting-dependent VE of a hypothetical vaccine and the retrospective analyses of rotavirus and malaria Phase 3 efficacy results make a multitude of assumptions that limit the robustness and soundness of any conclusions. For simplicity, factors previously shown or hypothesized to influence transmission, susceptibility, VE, and/or FoI, such as, country income status, age, underlying medical conditions, co-infections, access to healthcare, seasonality, NPI use, spreading events, and strain differences across different settings, were excluded from consideration in both the hypothetical VE or observed VE analyses.
Given these significant limitations in the analyses, the primary goal of the present study was not to provide a definitive answer to the questions of if and to what degree FoI determines VE in different settings. Rather the goal of these analyses was to continue to raise the awareness of the potential impact of FoI on VE, 8,18 and to prompt prospective studies designed to assess if and how NPIs might reduce FoI and enhance VE when vaccines are introduced and scaled up.
Ultimately well-designed studies that directly evaluate the potential relationship of FoI and . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted January 26, 2021. ; https://doi.org/10.1101/2021.01.21.21250235 doi: medRxiv preprint setting-dependent VE will provide the evidence needed for well-informed policy recommendations on the continued use or not of NPIs during vaccine introduction and scale-up.

Three scenarios of the potential mathematical consequences of force of infection on settingdependent vaccine efficacy
The potential effects of FoI on the level of VE were explored in three mathematical scenarios: 1) VE constant , where VE is independent of FoI; 2) VE linear , where VE decreases linearly as a function of increasing FoI; and, 3) VE natural log , where VE decreases logarithmically as FoI. As noted above, multiple simplifying assumptions were made when considering the mathematical consequences of FoI on VE, including homogeneity in the population with respect to a number of factors, including pathogen transmission, host susceptibility to infection and disease, FoI over time in a specific setting, and protective immunity as a result of vaccination across settings.
With these simplifying assumptions in mind, equations that define the three mathematical scenarios (see Box 2, Vaccine efficacy as a function of Force of infection) are shown graphically in Fig. 1, using the example of a hypothetical vaccine that has a maximum VE of 83% studied under conditions of FoI that vary across three orders of magnitude, from 0.03 to 3.50 infections/person-year. While other mathematical relationships between VE and FoI may be considered, these three equations seemed a reasonable starting point from which to interrogate observed data from Phase 3 VE studies conducted in multiple epidemiological settings.

Empiric evidence of force of infection on observed setting-dependent vaccine efficacy
. CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted January 26, 2021. ; https://doi.org/10.1101/2021.01.21.21250235 doi: medRxiv preprint Results from recent placebo-controlled Phase 3 studies of vaccine candidates for two diverse pathogens, Plasmodium falciparum and rotavirus, provided a database to determine which, if any, of the three mathematical scenarios best explained any setting-dependent differences in VE.
In addition to the assumptions mentioned above, several additional assumptions noted below facilitated the analyses of these multi-setting VE studies.
First and foremost, the analyses of both pathogens assumed that the intent-to-treat (ITT) incidence of the most sensitive definition of the mildest disease end point in the youngest age cohort in the placebo arm best served as an internal Phase 3 study surrogate of λ, the force of infection. The validity of this assumption relies upon several other assumptions, including the absence of any significant herd effect (see Box 1, Glossary of Key Terms) on the control from the vaccinated arm of the Phase 3 study. The rationale for making this herd effect assumption, typically also assumed for the control used in estimating VE in the context of Phase 3 efficacy studies, relies upon: 1) the relatively small proportion of the total population in the study setting enrolled in the vaccinated group in the Phase 3 study; and, 2) the timing of incident disease in the control group relative to eliciting herd immunity and reaching the herd immunity threshold (see Box 1, Glossary of Key Terms) in the study population.
A third key assumption relied upon a comparison of trendlines from the three mathematical scenarios described above to the closest fit trendline of observed VE (VE observed ) as a function of observed setting FoI (FoI observed , incidence in the placebo group) to determine if and how VE varied as a function of FoI. In this regard, because the Phase 3 VE results for both pathogens were known a priori to vary by epidemiologic setting, the posterior probability was low of selecting the VE constant mathematical scenario to categorize VE observed as a function of FoI observed .
As noted below for each specific analysis, the observed trendline may not necessarily reflect a . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted January 26, 2021. ; https://doi.org/10.1101/2021.01.21.21250235 doi: medRxiv preprint statistically significant association between VE observed and FoI observed , as assessed by a regression analysis. The best fit trendline analysis of VE observed as a function of FoI observed revealed a logarithmic relationship (Fig. 2, Observed VE) with an R 2 of 0.807. Regression analysis of VE observed as a function of ln FoI observed revealed a Significance F of 0.006. Using the VE natural log equation (Box 2), the observed VE max , VE min , FoI max , FOI min and the FoI observed from each site generated a . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted January 26, 2021. ; https://doi.org/10.1101/2021.01.21.21250235 doi: medRxiv preprint logarithmic relationship between the calculated site-specific VE and FoI observed (Fig 2, Calculated VE). These analyses suggest that FoI functions as a determinant of RTS,S/AS01 E VE.

Rotavirus vaccine efficacy and force of infection
Multiple Phase 3 studies of two rotavirus vaccines, RV1 (Rotarix ® ) and RV5 (RotaTeq ® ), evaluated VE in diverse epidemiologic settings. 17 In comparison to the analyses conducted for malaria VE, the analyses of VE observed as a function of FoI observed for rotavirus vaccines was complicated by the evaluation of two different vaccine candidates, with two different regimens, in several different clinical protocols. Some of the Phase 3 studies conducted in low resource settings did not collect data on the incidence of rotavirus gastroenteritis (RVGE) of any severity.
The analyses excluded these studies due to the absence of an intent-to-treat incidence of any severity RVGE in the placebo group to serve as a surrogate of λ. The analyses also excluded data from countries in which the placebo group had no or just a single case of RVGE of any severity.
From those studies that collected sufficient incidence of any severity RVGE in the placebo group, an Analysis of Variance failed to detect a statistically significant difference (p-value = 0.749) when categorizing FoI observed by 2020 World Bank country income classifications (i.e., upper-v upper middle-v lower middle/lower-income country) 21 ( Table 1).
For RV1, results from 10 countries in five independent Phase 3 studies 17,22-26 (see Table 1  CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted January 26, 2021. ; https://doi.org/10.1101/2021.01.21.21250235 doi: medRxiv preprint 2), the observed VE max , VE min , FoI max , FOI min and the FoI observed from each of the 10 countries generated a linear relationship between the calculated site-specific VE and FoI observed (Fig. 3a lower line, Calculated VE). These analyses suggest that FoI may function as a determinant of RV1 VE.
For RV5, results from 5 settings in three independent Phase 3 studies 17,27-31 (see Table 1) met the above FoI observed criteria for interrogation. The best fit trendline analysis of VE observed as a function of FoI observed revealed an independent relationship (data not shown) with an R 2 of -0.215 and regression analysis Significance F of 0.9838. Interrogating results from 7 settings in five independent Phase 3 studies 17,27-32 (see Table 1) by using the incidence of SRVGE in the placebo group as the FoI observed and surrogate of λ in the analyses, the best fit trendline analysis of

Conclusion
Of the many proposed determinants of setting-dependent VE, FoI provides one of the most direct, mechanistically proximate potential determinants. For many but not all pathogens, modifying the FoI provides one of the most actionable interventions to enhance or sustain VE.
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The copyright holder for this preprint this version posted January 26, 2021. ; https://doi.org/10.1101/2021.01.21.21250235 doi: medRxiv preprint While improving indirect or distal VE determinants, such as poverty, gut pathology, coinfections, and malnutrition, could significantly enhance efforts to control and eliminate simultaneously many pathogens, implementing interventions that effectively mitigate these VE determinants is complex and not immediately achievable. In contrast, modifying the FoI through the concomitant use of affordable, accessible, available, acceptable, and sustainable NPIs provides a proximate and actionable approach to optimizing VE. Considering and then prospectively verifying the speculation that introduction or continued optimal use of NPIs in an effort to reduce the FoI and thereby enhance or sustain VE, respectively, upon vaccine rollout seems prudent and, in the context of a pandemic, quite urgent.
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The copyright holder for this preprint this version posted January 26, 2021. . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. Herd immunity threshold: The proportion of the population required to be immune in the population for the infection incidence to reach steady state, i.e., the infection level is neither growing nor declining. To eliminate an infection in the population, the proportion of the population that is immune to infection must exceed this threshold value. 33 Herd effect: The reduction in the rate of infection or disease in the unimmunized portion of a population as a result of immunizing a proportion of the population. 2 It is also known as indirect effect.
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Box 2. Vaccine efficacy as a function of Force of infection
The following equations define mathematical relationships between Vaccine Efficacy (VE) and Force of Infection (FOI) shown in Figure 1, when the relationship of VE is: 1) independent of FOI (VE constant ); 2) linear to FOI (VE linear ); or 3) logarithmic to FOI (VE natural log ): Where: VE S is the VE in setting S, VE max is the highest observed VE, and VE min is the lowest observed VE.
And, where FOI S is the FOI in setting S, FOI min is lowest observed FOI, and FOI max is the highest observed FOI.
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Fig 1. Vaccine Efficacy (VE) as a function of Force of Infection (FoI) for hypothetical vaccine
Equations that define three mathematical scenarios (see Box 2, Vaccine efficacy as a function of force of infection) are shown graphically, using as an example a hypothetical vaccine with a maximum vaccine efficacy (VE max ) of 83% and minimum VE (VE min ) of 44.0% studied under conditions of force of infection (FoI) that vary across three orders of magnitude, from a minimum FoI (FoI min ) 0.03 to a maximum FoI (FoI max ) of 3.50 infections/person-year.
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Fig 2. Vaccine Efficacy (VE) as a function of Force of Infection (FoI) for malaria vaccine
Best fit trendline analysis of observed vaccine efficacy (VE observed ) as a function of observed force of infection (FoI observed ) is shown as a logarithmic relationship (blue dotted line) with a R 2 of 0.807. Significance F of 0.006 from a regression analysis of VE observed as a function of ln FoI observed in the embedded table is shown. Using the VE natural log equation (see Box 2, Vaccine efficacy as a function of force of infection), the observed VE max , VE min , FoI max , FOI min and FoI observed were used to calculate the VE natural log in the embedded table and the calculated VE natural log shown graphically (orange dotted line).
. CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted January 26, 2021. ; https://doi.org/10.1101/2021.01.21.21250235 doi: medRxiv preprint is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted January 26, 2021. ; https://doi.org/10.1101/2021.01.21.21250235 doi: medRxiv preprint R 2 of 0.6692. Significance F of 0.081 from a regression analysis of VE observed as a function of FoI observed in the embedded table is shown. Using the VE natural log equation (see Box 2, Vaccine efficacy as a function of force of infection), the observed VE max , VE min , FoI max , FOI min and FoI observed were used to calculate the VE natural log in the embedded table and the calculated VE natural log shown graphically (orange dotted line).
. CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted January 26, 2021. ; https://doi.org/10.1101/2021.01.21.21250235 doi: medRxiv preprint