Estimating seroprevalence of human papillomavirus type 16 using a mixture model with smoothed age-dependent mixing proportions

Empirical sample-specific approaches to define HPV16 and HPV18 seropositivity in unvaccinated, young, sexually active women

Given low seroconversion rates following human papillomavirus (HPV) infection, fixed external cutoffs may lead to errors in estimating HPV seroprevalence. We evaluated finite mixture modeling (FMM) and group-based trajectory modeling (GBTM) among unvaccinated, sexually active, HPV-exposed women to determine study-specific HPV16 and HPV18 seropositivity thresholds. We included 399 women (aged 18-24 years) enrolled in the HPV Infection and Transmission Among Couples Through Heterosexual Activity (HITCH) cohort study between 2005 and 2011 in Montreal, Canada. Participants' blood samples from up to six visits spanning 2 years were tested by multiplex serology for antibodies [median fluorescence intensity (MFI)] specific to bacterially expressed HPV16 and HPV18 L1 glutathione S-transferase fusion proteins. We applied FMM and GBTM to baseline and longitudinal antibody titer measurements, respectively, to define HPV type-specific seronegative and seropositive distributions. Study-specific thresholds were generated as five standard deviations above the mean seronegative antibody titers, mimicking cutoffs (HPV16: 422 MFI; HPV18: 394 MFI) derived from an external population of sexually inactive, HPV DNA-negative Korean women (aged 15-29 years). Agreement (kappa) of study-specific thresholds was evaluated against external cutoffs. Seroprevalence estimates using FMM (HPV16: 27.5%-43.2%; HPV18: 21.7%-49.5%) and GBTM (HPV16: 11.8%-11.8%; HPV18: 9.9%-13.4%) thresholds exceeded those of external cutoffs (HPV: 10.2%; HPV18: 9.7%). FMM thresholds showed slight-to-moderate agreement with external cutoffs (HPV16: 0.26%-0.46%; HPV18: 0.20%-0.56%), while GBTM thresholds exhibited high agreement (HPV16: 0.92%-0.92%; HPV18: 0.82%-0.99%). Kappa values suggest that GBTM, used for longitudinal serological data, and otherwise FMM, for cross-sectional data, are robust methods for determining the HPV serostatus without prior classification rules.IMPORTANCEWhile human papillomavirus (HPV) seropositivity has been employed as an epidemiologic determinant of the natural history of genital HPV infections, only a fraction of women incidentally infected with HPV respond by developing significant antibody levels. HPV seropositivity is often determined by a dichotomous fixed cutoff based on the seroreactivity of an external population of women presumed as seronegative, given the lack of evidence of HPV exposure. However, considering the variable nature of seroreactivity upon HPV infection, which arguably varies across populations, such externally defined cutoffs may lack specificity to the population of interest, causing inappropriate assessment of HPV seroprevalence and related epidemiologic uses of that information. This study demonstrates that finite mixture modeling (FMM) and group-based trajectory modeling (GBTM) can be used to independently estimate seroprevalence or serve as the basis for defining study-specific seropositivity thresholds without requiring prior subjective assumptions, consequently providing a more apt internally valid discrimination of seropositive from seronegative individuals.

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 cutoff values for diagnostic tests to achieve target specificity using extreme value theory

BACKGROUND

Rapidly developing tests for emerging diseases is critical for early disease monitoring. In the early stages of an epidemic, when low prevalences are expected, high specificity tests are desired to avoid numerous false positives. Selecting a cutoff to classify positive and negative test results that has the desired operating characteristics, such as specificity, is challenging for new tests because of limited validation data with known disease status. While there is ample statistical literature on estimating quantiles of a distribution, there is limited evidence on estimating extreme quantiles from limited validation data and the resulting test characteristics in the disease testing context.

METHODS

We propose using extreme value theory to select a cutoff with predetermined specificity by fitting a Pareto distribution to the upper tail of the negative controls. We compared this method to five previously proposed cutoff selection methods in a data analysis and simulation study. We analyzed COVID-19 enzyme linked immunosorbent assay antibody test results from long-term care facilities and skilled nursing staff in Colorado between May and December of 2020.

RESULTS

We found the extreme value approach had minimal bias when targeting a specificity of 0.995. Using the empirical quantile of the negative controls performed well when targeting a specificity of 0.95. The higher target specificity is preferred for overall test accuracy when prevalence is low, whereas the lower target specificity is preferred when prevalence is higher and resulted in less variable prevalence estimation.

DISCUSSION

While commonly used, the normal based methods showed considerable bias compared to the empirical and extreme value theory-based methods.

CONCLUSIONS

When determining disease testing cutoffs from small training data samples, we recommend using the extreme value based-methods when targeting a high specificity and the empirical quantile when targeting a lower specificity.

A Mixture Model for Estimating SARS-CoV-2 Seroprevalence in Chennai, India

Serological assays used to estimate the prevalence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) often rely on manufacturers' cutoffs established on the basis of severe cases. We conducted a household-based serosurvey of 4,677 individuals in Chennai, India, from January to May 2021. Samples were tested for SARS-CoV-2 immunoglobulin G (IgG) antibodies to the spike (S) and nucleocapsid (N) proteins. We calculated seroprevalence, defining seropositivity using manufacturer cutoffs and using a mixture model based on measured IgG level. Using manufacturer cutoffs, there was a 5-fold difference in seroprevalence estimated by each assay. This difference was largely reconciled using the mixture model, with estimated anti-S and anti-N IgG seroprevalence of 64.9% (95% credible interval (CrI): 63.8, 66.0) and 51.5% (95% CrI: 50.2, 52.9), respectively. Age and socioeconomic factors showed inconsistent relationships with anti-S and anti-N IgG seropositivity using manufacturer cutoffs. In the mixture model, age was not associated with seropositivity, and improved household ventilation was associated with lower seropositivity odds. With global vaccine scale-up, the utility of the more stable anti-S IgG assay may be limited due to the inclusion of the S protein in several vaccines. Estimates of SARS-CoV-2 seroprevalence using alternative targets must consider heterogeneity in seroresponse to ensure that seroprevalence is not underestimated and correlates are not misinterpreted.

Applying mixture model methods to SARS-CoV-2 serosurvey data from Geneva

Serosurveys are an important tool to estimate the true extent of the current SARS-CoV-2 pandemic. So far, most serosurvey data have been analyzed with cutoff-based methods, which dichotomize individual measurements into sero-positives or negatives based on a predefined cutoff. However, mixture model methods can gain additional information from the same serosurvey data. Such methods refrain from dichotomizing individual values and instead use the full distribution of the serological measurements from pre-pandemic and COVID-19 controls to estimate the cumulative incidence. This study presents an application of mixture model methods to SARS-CoV-2 serosurvey data from the SEROCoV-POP study from April and May 2020 in Geneva (2766 individuals). Besides estimating the total cumulative incidence in these data (8.1% (95% CI: 6.8%–9.9%)), we applied extended mixture model methods to estimate an indirect indicator of disease severity, which is the fraction of cases with a distribution of antibody levels similar to hospitalized COVID-19 patients. This fraction is 51.2% (95% CI: 15.2%–79.5%) across the full serosurvey, but differs between three age classes: 21.4% (95% CI: 0%–59.6%) for individuals between 5 and 40 years old, 60.2% (95% CI: 21.5%–100%) for individuals between 41 and 65 years old and 100% (95% CI: 20.1%–100%) for individuals between 66 and 90 years old. Additionally, we find a mismatch between the inferred negative distribution of the serosurvey and the validation data of pre-pandemic controls. Overall, this study illustrates that mixture model methods can provide additional insights from serosurvey data.

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.

Estimating prevalence from dried blood spots without using biological cut-offs: application of a novel approach to hepatitis C virus in drug users in France (ANRS-Coquelicot survey)

Seroprevalence estimation using cross-sectional serosurveys can be challenging due to inadequate or unknown biological cut-off limits of detection. In recent years, diagnostic assay cut-offs, fixed assay cut-offs and more flexible approaches as mixture modelling have been proposed to classify biological quantitative measurements into a positive or negative status. Our objective was to estimate the prevalence of anti-HCV antibodies among drug users (DU) in France in 2011 using a biological test performed on dried blood spots (DBS) collected during a cross-sectional serosurvey. However, in 2011, we did not have a cut-off value for DBS. We could not use the values for serum or plasma, knowing that the DBS value was not necessarily the same. Accordingly, we used a method which consisted of applying a two-component mixture model with age-dependent mixing proportions using penalised splines. The component densities were assumed to be log-normally distributed and were estimated in a Bayesian framework. Anti-HCV prevalence among DU was estimated at 43.3% in France and increased with age. Our method allowed us to provide estimates of age-dependent prevalence using DBS without having a specified biological cut-off value.

Integrating measures of viral prevalence and seroprevalence: a mechanistic modelling approach to explaining cohort patterns of human papillomavirus in women in the USA

Incidence of human papillomavirus (HPV) related cancers is increasing, generating substantial interest in understanding how trends in population prevalence of HPV infection are changing. However, there are no direct, population-scale measurements of HPV prevalence prior to 2003. Previous work using models to reconstruct historical trends have focused only on genital infection or seroprevalence (prevalence of antibodies) separately, and the results of these single-measure studies have been hard to reconcile. Here, we develop a mechanistic disease model fit jointly to cervicogential prevalence and seroprevalence in unvaccinated women in the USA using National Health and Nutrition Examination Survey data (2003-2010) and compare it to fits of statistical age-cohort models. We find that including a latent HPV state in our model significantly improves model fit and that antibody waning may be an important contributor to observed patterns of seroprevalence. Moreover, we find that the mechanistic model outperforms the statistical model and that the joint analysis prevents the inconsistencies that arise when estimating historical cohort trends in infection from genital prevalence and seroprevalence separately. Our analysis suggests that while there is substantial uncertainty associated with the estimation of historic HPV trends, there has likely been an increase in the force of infection for more recent birth cohorts. This article is part of the theme issue 'Silent cancer agents: multi-disciplinary modelling of human DNA oncoviruses'.

Estimating the incidence of rotavirus infection in children from India and Malawi from serial anti-rotavirus IgA titres

Accurate estimates of rotavirus incidence in infants are crucial given disparities in rotavirus vaccine effectiveness from low-income settings. Sero-surveys are a pragmatic means of estimating incidence however serological data is prone to misclassification. This study used mixture models to estimate incidence of rotavirus infection from anti-rotavirus immunoglobulin A (IgA) titres in infants from Vellore, India, and Karonga, Malawi. IgA titres were measured using serum samples collected at 6 month intervals for 36 months from 373 infants from Vellore and 12 months from 66 infants from Karonga. Mixture models (two component Gaussian mixture distributions) were fit to the difference in titres between time points to estimate risk of sero-positivity and derive incidence estimates. A peak incidence of 1.05(95% confidence interval [CI]: 0.64, 1.64) infections per child-year was observed in the first 6 months of life in Vellore. This declined incrementally with each subsequent time interval. Contrastingly in Karonga incidence was greatest in the second 6 months of life (1.41 infections per child year [95% CI: 0.79, 2.29]). This study demonstrates that infants from Vellore experience peak rotavirus incidence earlier than those from Karonga. Identifying such differences in transmission patterns is important in informing vaccine strategy, particularly where vaccine effectiveness is modest.

Inferring infection hazard in wildlife populations by linking data across individual and population scales

Our ability to infer unobservable disease-dynamic processes such as force of infection (infection hazard for susceptible hosts) has transformed our understanding of disease transmission mechanisms and capacity to predict disease dynamics. Conventional methods for inferring FOI estimate a time-averaged value and are based on population-level processes. Because many pathogens exhibit epidemic cycling and FOI is the result of processes acting across the scales of individuals and populations, a flexible framework that extends to epidemic dynamics and links within-host processes to FOI is needed. Specifically, within-host antibody kinetics in wildlife hosts can be short-lived and produce patterns that are repeatable across individuals, suggesting individual-level antibody concentrations could be used to infer time since infection and hence FOI. Using simulations and case studies (influenza A in lesser snow geese and Yersinia pestis in coyotes), we argue that with careful experimental and surveillance design, the population-level FOI signal can be recovered from individual-level antibody kinetics, despite substantial individual-level variation. In addition to improving inference, the cross-scale quantitative antibody approach we describe can reveal insights into drivers of individual-based variation in disease response, and the role of poorly understood processes such as secondary infections, in population-level dynamics of disease.

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

Post-vaccine monitoring programs for human papillomavirus (HPV) have been introduced in many countries, but HPV serology is still an underutilized tool, partly owing to the weak antibody response to HPV infection. Changes in antibody levels among non-vaccinated individuals could be employed to monitor herd effects of immunization against HPV vaccine types 16 and 18, but inference requires an appropriate statistical model. The authors developed a four-component bivariate mixture model for jointly estimating vaccine-type seroprevalence from correlated antibody responses against HPV16 and -18 infections. This model takes account of the correlation between HPV16 and -18 antibody concentrations within subjects, caused e.g. by heterogeneity in exposure level and immune response. The model was fitted to HPV16 and -18 antibody concentrations as measured by a multiplex immunoassay in a large serological survey (3,875 females) carried out in the Netherlands in 2006/2007, before the introduction of mass immunization. Parameters were estimated by Bayesian analysis. We used the deviance information criterion for model selection; performance of the preferred model was assessed through simulation. Our analysis uncovered elevated antibody concentrations in doubly as compared to singly seropositive individuals, and a strong clustering of HPV16 and -18 seropositivity, particularly around the age of sexual debut. The bivariate model resulted in a more reliable classification of singly and doubly seropositive individuals than achieved by a combination of two univariate models, and suggested a higher pre-vaccine HPV16 seroprevalence than previously estimated. The bivariate mixture model provides valuable baseline estimates of vaccine-type seroprevalence and may prove useful in seroepidemiologic assessment of the herd effects of HPV vaccination.