Analyzing Vaccine Trials in Epidemics With Mild and Asymptomatic Infection

Abstract

Vaccine efficacy against susceptibility to infection (VES), regardless of symptoms, is an important endpoint of vaccine trials for pathogens with a high proportion of asymptomatic infection, because such infections may contribute to onward transmission and long-term sequelae, such as congenital Zika syndrome. However, estimating VES is resource-intensive. We aimed to identify approaches for accurately estimating VES when limited information is available and resources are constrained. We modeled an individually randomized vaccine trial by generating a network of individuals and simulating an epidemic. The disease natural history followed a "susceptible-exposed-infectious/symptomatic (or infectious/asymptomatic)-recovered" model. We then used 7 approaches to estimate VES, and we also estimated vaccine efficacy against progression to symptoms (VEP). A corrected relative risk and an interval-censored Cox model accurately estimate VES and only require serological testing of participants once, while a Cox model using only symptomatic infections returns biased estimates. Only acquiring serological endpoints in a 10% sample and imputing the remaining infection statuses yields unbiased VES estimates across values of the basic reproduction number (R0) and accurate estimates of VEP for higher R0 values. Identifying resource-preserving methods for accurately estimating VES and VEP is important in designing trials for diseases with a high proportion of asymptomatic infection.

Figure 1.

Differential misclassification of at-risk person-time. Panel A shows reality—who is truly infected and who is truly still at risk. Panel B shows who we perceive to be infected and still at risk when considering only symptomatic individuals. When considering only symptomatic events, presumed person-time at risk increases for both the vaccine group and the control group, because all persons with asymptomatic infections are now perceived to be uninfected and at risk for the entire period of the trial. In the vaccine group, 11 people are perceived to still be at risk (panel B), when in reality only 7 remain at risk (panel A), since 4 people are asymptomatically infected. In the control group, 10 people are perceived to be at risk (panel B), when in reality only 2 remain at risk (panel A). Because there are more people infected and therefore more people incorrectly still perceived to be at risk in the control group than in the vaccine group, apparent incidence is underestimated in the controls more so than in the vaccine group, leading to bias towards the null. This bias is exacerbated as R₀ increases and more people in the control group become infected but are still perceived to be at risk. At time t postrandomization, person-time at risk in the controls will be overestimated by a factor of $e^{\mathrm{\Lambda }\left(t\right)\left(1-{\mathrm{\Theta }}_{P}p\right)(1-{\mathrm{\Theta }}_S)}$ relative to the vaccine group, where $\mathrm{\Lambda }(t)$ is the cumulative hazard up to time t, p is the symptomatic proportion in controls, and $\mathrm{1}-{\mathrm{\theta }}_S$ and $\mathrm{1}-{\mathrm{\theta }}_P$ are the efficacy of the vaccine against infection and the efficacy of the vaccine against disease given infection, respectively (29). This will be greater than 1 for nonnegative VE_P and positive VE_S. VE_P, vaccine efficacy against progression to symptoms; VE_S, vaccine efficacy against susceptibility to infection.

Figure 2.

Estimates of vaccine efficacy against susceptibility to infection (VE_S) obtained using 7 different approaches for R₀ = 1 (A), R₀ = 1.25 (B), and R₀ = 1.5 (C) under the model’s baseline parameters in the 1-community network. The 7 approaches are: Cox—“perfect knowledge” (1), Cox—symptomatic only (2), relative risk estimate (3), corrected relative risk estimate (4), interval-censored Cox model (3 intervals) (5), interval-censored Cox model (1 interval) (6), and imputation (7).

Figure 3.

Statistical power of the Cox “perfect knowledge” approach (approach 1) and 2 interval-censored models (approaches 5 and 6) to estimate vaccine efficacy against susceptibility to infection in 1 community with 1,500 trial participants (baseline) and R₀ = 1 (A), R₀ = 1.25 (B), and R₀ = 1.5 (C) (first row); in 1 community with 250 trial participants and R₀ = 1 (D), R₀ = 1.25 (E), and R₀ = 1.5 (F) (second row); and in 1 community with 100 trial participants and R₀ = 1 (G), R₀ = 1.25 (H), and R₀ = 1.5 (I) (third row). The interval-censored models do not lead to a substantial loss of power, except in the trial with 100 participants enrolled when R₀ = 1. The dashed lines represent a power of 80%.

Figure 4.

Estimates of vaccine efficacy against susceptibility to infection (VE_S) obtained using 7 different approaches for a 5-community network analyzed as 1 large community for R₀ = 1 (A), R₀ = 1.25 (B), and R₀ = 1.5 (C) and with stratified and meta-analyses for R₀ = 1 (D), R₀ = 1.25 (E), and R₀ = 1.5 (F) under baseline parameters. The 7 approaches are: Cox—“perfect knowledge” (1), Cox—symptomatic only (2), relative risk estimate (3), corrected relative risk estimate (4), interval-censored Cox model (3 intervals) (5), interval-censored Cox model (1 interval) (6), and imputation (7).