How Is Vaccine Effectiveness Scaled by the Transmission Dynamics of Interacting Pathogen Strains with Cross-Protective Immunity?

<div><h3>Background</h3><p>Many novel vaccines can cover only a fraction of all antigenic types of a pathogen. Vaccine effectiveness (VE) in the presence of interactions between vaccine strains and others is complicated by the interacting transmission dynamics among all strains. The present study investigated how the VE estimates measured in the field, based on estimated odds ratio or relative risks, are scaled by vaccination coverage and the transmission dynamics in the presence of cross-protective immunity between two strains, i.e. vaccine and non-vaccine strains.</p> <h3>Methodology/Principal Findings</h3><p>Two different types of epidemiological models, i.e. with and without re-infection by the same antigenic type, were investigated. We computed the relative risk of infection and the odds ratio of vaccination, the latter of which has been measured by indirect cohort method as applied to vaccine effectiveness study of <em>Streptococcus pneumoniae</em>. The VE based on the relative risk was less sensitive to epidemiological dynamics such as cross-protective immunity and vaccination coverage than the VE calculated from the odds ratio, and this was especially the case for the model without re-infection. Vaccine-induced (cross-protective) immunity against a non-vaccine strain appeared to yield the highest impact on the VE estimate calculated from the odds ratio of vaccination.</p> <h3>Conclusion</h3><p>It is essential to understand the transmission dynamics of non-vaccine strains so that epidemiological methods can appropriately measure both the direct and indirect population impact of vaccination. For pathogens with interacting antigenic types, the most valid estimates of VE, that are unlikely to be biased by the transmission dynamics, may be obtained from longitudinal prospective studies that permit estimation of the VE based on the relative risk of infection among vaccinated compared to unvaccinated individuals.</p> </div

Vaccine effectiveness in the SIS (Susceptible-Infected-Susceptible) model.

<p>Field estimate (vertical axis) represents the vaccine effectiveness estimate derived from empirical observation in the field. Solid line represents vaccine effectiveness based on odds ratio, VE_O, while broken line represents that based on relative risk, VE_R. Assumed vaccine efficacy against VT (vaccine type) is shown at the right end of each line. Vaccine-induced immunity was dealt with as in two different ways, (i) all-or-nothing type or (ii) leaky type. (a)-(d) show the effectiveness of all-or-nothing vaccine (i.e. perfect protection given successful immunization and no protection for unsuccessful vaccination), whereas (e)-(h) show the effectiveness of leaky vaccine (i.e. imperfect protection for all vaccinated individuals).</p

Sample size per arm and total budget needed to achieve 80% power for differing methods of identification of influenza infections for both short (2 months) and long (6 months) influenza seasons.

<p>Sample size per arm and total budget needed to achieve 80% power for differing methods of identification of influenza infections for both short (2 months) and long (6 months) influenza seasons.</p

Transmission dynamics of two-strain disease in the presence of cross-protective immunity.

<p>(a) Model without re-infection with an identical antigenic type (SIR-type; susceptible-infectious-recovered) and (b) model with re-infections by an identical antigenic type (SIS-type; susceptible-infected-susceptible). SIR model is intended to capture the epidemiological dynamics of EV71, while SIS model is applied to pneumococcus. [Compartments] Variable <i>u</i> represents unvaccinated. Two subscripts represent the state of infection (or carriage) with respect to VT and NVT, respectively. For example, <i>u</i>_si represents unvaccinated host who is susceptible to VT but is infected with NVT. [Parameters] <i>c</i>, vaccination coverage; <i>μ</i>, background birth and death rates of human host; <i>λ</i>_A and <i>λ</i>_B, the rates of infection with VT (vaccine type) and NVT (non-vaccine type), respectively; <i>γ</i>_A and <i>γ</i>_B, recovery rates from infection with VT and NVT, respectively; <i>σ</i>, the relative reduction of the risk of infection upon exposure by cross-protective immunity in the SIR model; <i>σ</i>_A and <i>σ</i>_B, the relative reduction of the risk of carriage acquisition upon exposure to VT and NVT by competition, respectively, in the SIS model. For simplicity, both panels represent the population dynamics of unvaccinated population alone. In case no vaccination takes place, <i>c</i> is equal to 0.</p

Parameter values for the SIR (Susceptible-Infectious-Recovered) model as applied to the epidemiological dynamics of enterovirus 71.

<p>Parameter values for the SIR (Susceptible-Infectious-Recovered) model as applied to the epidemiological dynamics of enterovirus 71.</p

Comparison of alternative study designs.

<p>In the plot, the three rows indicate: (A) power, (B) total sample size per arm, and (C) estimated cumulative incidence of influenza in the control arm. Scenario I assumes the unbiased control non-influenza attack ARI and FARI rates are 0.4 and 0.1 respectively which exactly correspond to estimates made in advance of the study. Scenario II assumes the unbiased control non-influenza attack ARI and FARI rates are 0.4 and 0.1 but are underestimated at 0.2 and 0.06 when planning the study. Scenario III assumes the unbiased control non-influenza attack ARI and FARI rates are 0.4 and 0.1 and but are overestimated at 0.6 and 0.14 when planning the study. Control arm cumulative incidence proportion refers to the expected proportion of participants identified as having influenza infection among the control arm. “Combined” refers to paired serology analyzed by HAI plus RT-PCR upon ARI trigger. Black lines are used to denote design variants using RT-PCR confirmation. Grey lines are used to denote design variants using serologic confirmation or serologic plus RT-PCR confirmation.</p

Vaccine effectiveness in the SIR (Susceptible-Infectious-Recovered) model.

<p>Field estimate (vertical axis) represents the vaccine effectiveness estimate derived from empirical observation in the field. Solid line represents vaccine effectiveness based on odds ratio, VE_O, while broken line represents that based on relative risk, VE_R. Assumed vaccine efficacy against VT (vaccine type) is shown at the right end of each line. Cross-protective immunity is expressed as perfect protection with a probability <i>σ</i> for an all-or-nothing type vaccine, and expressed as the relative reduction in the instantaneous risk of infection upon exposure against a serotype among those who have already experienced infection with the other serotype for a leaky type vaccine. (a)-(c) show the effectiveness of all-or-nothing vaccine (i.e. perfect protection given successful immunization and no protection for unsuccessful vaccination), whereas (d)-(f) show the effectiveness of leaky vaccine (i.e. imperfect protection for all vaccinated individuals).</p

The relationship between vaccine effectiveness against VT (vaccine type) and assortativity coefficient <i>θ</i>.

<p>Solid line represents vaccine effectiveness based on odds ratio, VE_O, while broken line represents that based on relative risk, VE_R. Vaccine efficacy against VT is shown at the right end of lines. (a) and (c) show the result from SIR model, while (b) and (d) are from SIS model for <i>Streptococcus pneumoniae</i>. (a) and (b) show the effectiveness of all-or-nothing vaccine (i.e. perfect protection given successful immunization and no protection for unsuccessful vaccination), whereas (c) and (d) show the effectiveness of leaky vaccine (i.e. imperfect protection for all vaccinated individuals).</p

One-tailed test results of the basic reproduction number based on one-to-one transmission experiment.

†<p>The basic reproduction number, estimated from the one-to-one transmission experiment. ^‡CI, confidence intervals.^¶<i>R</i>₀ is significantly greater than 1 by one-sample Fisher's exact test.</p

Parameter values and ranges of the input values in sensitivity analysis.

<p>Parameter values and ranges of the input values in sensitivity analysis.</p