A Bivariate Mixture Model for Natural Antibody Levels to Human Papillomavirus Types 16 and 18: Baseline Estimates for Monitoring the Herd Effects of Immunization

A Bayesian approach to estimating COVID-19 incidence and infection fatality rates

Naive estimates of incidence and infection fatality rates (IFR) of coronavirus disease 2019 suffer from a variety of biases, many of which relate to preferential testing. This has motivated epidemiologists from around the globe to conduct serosurveys that measure the immunity of individuals by testing for the presence of SARS-CoV-2 antibodies in the blood. These quantitative measures (titer values) are then used as a proxy for previous or current infection. However, statistical methods that use this data to its full potential have yet to be developed. Previous researchers have discretized these continuous values, discarding potentially useful information. In this article, we demonstrate how multivariate mixture models can be used in combination with post-stratification to estimate cumulative incidence and IFR in an approximate Bayesian framework without discretization. In doing so, we account for uncertainty from both the estimated number of infections and incomplete deaths data to provide estimates of IFR. This method is demonstrated using data from the Action to Beat Coronavirus erosurvey in Canada.

Estimation of the infection attack rate of mumps in an outbreak among college students using paired serology

Mumps virus is a highly transmissible pathogen that is effectively controlled in countries with high vaccination coverage. Nevertheless, outbreaks have occurred worldwide over the past decades in vaccinated populations. Here we analyse an outbreak of mumps virus genotype G among college students in the Netherlands over the period 2009-2012 using paired serological data. To identify infections in the presence of preexisting antibodies we compared mumps specific serum IgG concentrations in two consecutive samples (n=746), whereby the first sample was taken when students started their study prior to the outbreaks, and the second sample was taken 2-5 years later. We fit a binary mixture model to the data. The two mixing distributions represent uninfected and infected classes. Throughout we assume that the infection probability increases with the ratio of antibody concentrations of the second to first sample. The estimated infection attack rate in this study is higher than reported earlier (0.095 versus 0.042). The analyses yield probabilistic classifications of participants, which are mostly quite precise owing to the high intraclass correlation of samples in uninfected participants (0.85, 95%CrI: 0.82-0.87). The estimated probability of infection increases with decreasing antibody concentration in the pre-outbreak sample, such that the probability of infection is 0.12 (95%CrI: 0.10-0.13) for the lowest quartile of the pre-outbreak samples and 0.056 (95%CrI: 0.044-0.068) for the highest quartile. We discuss the implications of these insights for the design of booster vaccination strategies.

Estimating the cumulative incidence of SARS-CoV-2 with imperfect serological tests: Exploiting cutoff-free approaches

Large-scale serological testing in the population is essential to determine the true extent of the current SARS-CoV-2 pandemic. Serological tests measure antibody responses against pathogens and use predefined cutoff levels that dichotomize the quantitative test measures into sero-positives and negatives and use this as a proxy for past infection. With the imperfect assays that are currently available to test for past SARS-CoV-2 infection, the fraction of seropositive individuals in serosurveys is a biased estimator of the cumulative incidence and is usually corrected to account for the sensitivity and specificity. Here we use an inference method-referred to as mixture-model approach-for the estimation of the cumulative incidence that does not require to define cutoffs by integrating the quantitative test measures directly into the statistical inference procedure. We confirm that the mixture model outperforms the methods based on cutoffs, leading to less bias and error in estimates of the cumulative incidence. We illustrate how the mixture model can be used to optimize the design of serosurveys with imperfect serological tests. We also provide guidance on the number of control and case sera that are required to quantify the test's ambiguity sufficiently to enable the reliable estimation of the cumulative incidence. Lastly, we show how this approach can be used to estimate the cumulative incidence of classes of infections with an unknown distribution of quantitative test measures. This is a very promising application of the mixture-model approach that could identify the elusive fraction of asymptomatic SARS-CoV-2 infections. An R-package implementing the inference methods used in this paper is provided. Our study advocates using serological tests without cutoffs, especially if they are used to determine parameters characterizing populations rather than individuals. This approach circumvents some of the shortcomings of cutoff-based methods at exactly the low cumulative incidence levels and test accuracies that we are currently facing in SARS-CoV-2 serosurveys.

Capturing multiple-type interactions into practical predictors of type replacement following human papillomavirus vaccination

Current HPV vaccines target a subset of the oncogenic human papillomavirus (HPV) types. If HPV types compete during infection, vaccination may trigger replacement by the non-targeted types. Existing approaches to assess the risk of type replacement have focused on detecting competitive interactions between pairs of vaccine and non-vaccine types. However, methods to translate any inferred pairwise interactions into predictors of replacement have been lacking. In this paper, we develop practical predictors of type replacement in a multi-type setting, readily estimable from pre-vaccination longitudinal or cross-sectional prevalence data. The predictors we propose for replacement by individual non-targeted types take the form of weighted cross-hazard ratios of acquisition versus clearance, or aggregate odds ratios of coinfection with the vaccine types. We elucidate how the hazard-based predictors incorporate potentially heterogeneous direct and indirect type interactions by appropriately weighting type-specific hazards and show when they are equivalent to the odds-based predictors. Additionally, pooling type-specific predictors proves to be useful for predicting increase in the overall non-vaccine-type prevalence. Using simulations, we demonstrate good performance of the predictors under different interaction structures. We discuss potential applications and limitations of the proposed methodology in predicting type replacement, as compared to existing approaches. This article is part of the theme issue 'Silent cancer agents: multi-disciplinary modelling of human DNA oncoviruses'.