Bayesian calendar-time survival analysis with epidemic curve priors and variant-specific infection hazards

TL;DR

A Bayesian calendar-time survival model motivated by infectious disease prevention studies occurring during an epidemic, when the risk of infection can change rapidly as the epidemic curve shifts, is developed.

Abstract

In this paper, we develop a Bayesian calendar-time survival model motivated by infectious disease prevention studies occurring during an epidemic, when the risk of infection can change rapidly as the epidemic curve shifts. For studies in which a biomarker is the predictor of interest, we include the option to estimate a threshold of protection for the biomarker. If the intervention is hypothesized to have different associations with several circulating viral variants, or if the infectiousness of the dominant variant(s) changes over the course of the study, we treat infection from different variants as competing risks. We also introduce a novel method for incorporating existing epidemic curve estimates into an informative prior for the baseline hazard function, enabling estimation of the intervention's association with infection risk during periods of calendar time with minimal follow-up in one or more comparator groups. We demonstrate the strengths of this method via simulations, and we apply it to data from an observational COVID-19 vaccine study.

Figures (11)

• Figure 1: Simulation results for the calendar-time survival model. The top and bottom rows show posterior mean estimates and 95% posterior credible interval (CrI) coverage, respectively, for $\gamma$, the association between intervention group and the hazard of infection. Each column shows different simulated sample sizes. Different colors show different strengths of the baseline hazard prior used in fitting the model. The dashed lines shows the true value of $\gamma$ (above) and 95% coverage (below).
• Figure 2: Priors for the baseline hazard function used in the MOMI-Vax analysis. The solid lines show the means of each prior distribution, while the ribbons show the 95% quantiles of each prior distribution. The value of $h_{\text{ref}, s_i}$ (the baseline hazard during the reference interval of calendar time) is fixed at its mean in these plots in order to highlight the level of informativeness of the relative baseline hazard priors.
• Figure 3: Observed maternal antibodies at delivery in the MOMI-Vax study. The top row shows the distribution of maternal antibody titers among those above the lower limit of detection (LLOD) by dose group, while the bottom plot shows the number and proportion of infants in each dose group whose mothers had undetectable antibodies (below the LLOD) at delivery.
• Figure 4: Prior and posterior distributions for the threshold at which maternal antibody levels at delivery are associated with infants' risk of SARS-CoV-2 infection in the MOMI-Vax study. Below the threshold, the model assumes that the antibodies have no association with the risk of infection.
• Figure 5: Estimated association between maternal antibodies at delivery and infants' risk of SARS-CoV-2 infection with the Omicron variant in the MOMI-Vax study. Posterior means and 95% posterior credible intervals (CrIs) are shown for the percent reduction in risk of infection in infants compared to the minimum observed maternal antibody titers in the study (top row for each antibody) or compared to the estimated maternal antibody threshold (bottom row for each antibody), adjusted for the covariates included in $\bm{Z}$. All comparisons are among infants at the same site and at the same calendar time. Relative risk reduction is calculated as (1 -- hazard ratio) and is only shown for the observed range of maternal antibodies in the study. The faceting columns refer to the baseline hazard prior used in the model.