Statistical identifiability and sample size calculations for serial seroepidemiology

serosim: An R package for simulating serological data arising from vaccination, epidemiological and antibody kinetics processes

serosim is an open-source R package designed to aid inference from serological studies, by simulating data arising from user-specified vaccine and antibody kinetics processes using a random effects model. Serological data are used to assess population immunity by directly measuring individuals' antibody titers. They uncover locations and/or populations which are susceptible and provide evidence of past infection or vaccination to help inform public health measures and surveillance. Both serological data and new analytical techniques used to interpret them are increasingly widespread. This creates a need for tools to simulate serological studies and the processes underlying observed titer values, as this will enable researchers to identify best practices for serological study design, and provide a standardized framework to evaluate the performance of different inference methods. serosim allows users to specify and adjust model inputs representing underlying processes responsible for generating the observed titer values like time-varying patterns of infection and vaccination, population demography, immunity and antibody kinetics, and serological sampling design in order to best represent the population and disease system(s) of interest. This package will be useful for planning sampling design of future serological studies, understanding determinants of observed serological data, and validating the accuracy and power of new statistical methods.

Prevalence and predictors of anti-SARS-CoV-2 serology in a highly vulnerable population of Rio de Janeiro: A population-based serosurvey

Background

COVID-19 serosurveys allow for the monitoring of the level of SARS-CoV-2 transmission and support data-driven decisions. We estimated the seroprevalence of anti-SARS-CoV-2 antibodies in a large favela complex in Rio de Janeiro, Brazil.

Methods

A population-based panel study was conducted in Complexo de Manguinhos (16 favelas) with a probabilistic sampling of participants aged ≥1 year who were randomly selected from a census of individuals registered in primary health care clinics that serve the area. Participants answered a structured interview and provided blood samples for serology. Multilevel regression models (with random intercepts to account for participants’ favela of residence) were used to assess factors associated with having anti-S IgG antibodies. Secondary analyses estimated seroprevalence using an additional anti-N IgG assay.

Findings

4,033 participants were included (from Sep/2020 to Feb/2021, 22 epidemic weeks), the median age was 39·8 years (IQR:21·8-57·7), 61% were female, 41% were mixed-race (Pardo) and 23% Black. Overall prevalence was 49·0% (95%CI:46·8%-51·2%) which varied across favelas (from 68·3% to 31·4%). Lower prevalence estimates were found when using the anti-N IgG assay. Odds of having anti-S IgG antibodies were highest for young adults, and those reporting larger household size, poor adherence to social distancing and use of public transportation.

Interpretation

We found a significantly higher prevalence of anti-S IgG antibodies than initially anticipated. Disparities in estimates obtained using different serological assays highlight the need for cautious interpretation of serosurveys estimates given the heterogeneity of exposure in communities, loss of immunological biomarkers, serological antigen target, and variant-specific test affinity.

Funding

Fundação Oswaldo Cruz, Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Fundação de Amparo a Pesquisa do Estado do Rio de Janeiro (FAPERJ), the European Union's Horizon 2020 research and innovation programme, Royal Society, Serrapilheira Institute, and FAPESP.

Effects of Accounting for Interval-Censored Antibody Titer Decay on Seroincidence in a Longitudinal Cohort Study of Leptospirosis

Accurate measurements of seroincidence are critical for infections undercounted by reported cases, such as influenza, arboviral diseases, and leptospirosis. However, conventional methods of interpreting paired serological samples do not account for antibody titer decay, resulting in underestimated seroincidence rates. To improve interpretation of paired sera, we modeled exponential decay of interval-censored microscopic agglutination test titers using a historical data set of leptospirosis cases traced to a point source exposure in Italy in 1984. We then applied that decay rate to a longitudinal cohort study conducted in a high-transmission setting in Salvador, Brazil (2013-2015). We estimated a decay constant of 0.926 (95% confidence interval: 0.918, 0.934) titer dilutions per month. Accounting for decay in the cohort increased the mean infection rate to 1.21 times the conventionally defined rate over 6-month intervals (range, 1.10-1.36) and 1.82 times that rate over 12-month intervals (range, 1.65-2.07). Improved estimates of infection in longitudinal data have broad epidemiologic implications, including comparing studies with different sampling intervals, improving sample size estimation, and determining risk factors for infection and the role of acquired immunity. Our method of estimating and accounting for titer decay is generalizable to other infections defined using interval-censored serological assays.

Linking longitudinal and cross-sectional biomarker data to understand host-pathogen dynamics: Leptospira in California sea lions (Zalophus californianus) as a case study

Confronted with the challenge of understanding population-level processes, disease ecologists and epidemiologists often simplify quantitative data into distinct physiological states (e.g. susceptible, exposed, infected, recovered). However, data defining these states often fall along a spectrum rather than into clear categories. Hence, the host-pathogen relationship is more accurately defined using quantitative data, often integrating multiple diagnostic measures, just as clinicians do to assess their patients. We use quantitative data on a major neglected tropical disease (Leptospira interrogans) in California sea lions (Zalophus californianus) to improve individual-level and population-level understanding of this Leptospira reservoir system. We create a "host-pathogen space" by mapping multiple biomarkers of infection (e.g. serum antibodies, pathogen DNA) and disease state (e.g. serum chemistry values) from 13 longitudinally sampled, severely ill individuals to characterize changes in these values through time. Data from these individuals describe a clear, unidirectional trajectory of disease and recovery within this host-pathogen space. Remarkably, this trajectory also captures the broad patterns in larger cross-sectional datasets of 1456 wild sea lions in all states of health but sampled only once. Our framework enables us to determine an individual's location in their time-course since initial infection, and to visualize the full range of clinical states and antibody responses induced by pathogen exposure. We identify predictive relationships between biomarkers and outcomes such as survival and pathogen shedding, and use these to impute values for missing data, thus increasing the size of the useable dataset. Mapping the host-pathogen space using quantitative biomarker data enables more nuanced understanding of an individual's time course of infection, duration of immunity, and probability of being infectious. Such maps also make efficient use of limited data for rare or poorly understood diseases, by providing a means to rapidly assess the range and extent of potential clinical and immunological profiles. These approaches yield benefits for clinicians needing to triage patients, prevent transmission, and assess immunity, and for disease ecologists or epidemiologists working to develop appropriate risk management strategies to reduce transmission risk on a population scale (e.g. model parameterization using more accurate estimates of duration of immunity and infectiousness) and to assess health impacts on a population scale.

Sample size calculation for estimating key epidemiological parameters using serological data and mathematical modelling

Background

Our work was motivated by the need to, given serum availability and/or financial resources, decide on which samples to test in a serum bank for different pathogens. Simulation-based sample size calculations were performed to determine the age-based sampling structures and optimal allocation of a given number of samples for testing across various age groups best suited to estimate key epidemiological parameters (e.g., seroprevalence or force of infection) with acceptable precision levels in a cross-sectional seroprevalence survey.

Methods

Statistical and mathematical models and three age-based sampling structures (survey-based structure, population-based structure, uniform structure) were used. Our calculations are based on Belgian serological survey data collected in 2001–2003 where testing was done, amongst others, for the presence of Immunoglobulin G antibodies against measles, mumps, and rubella, for which a national mass immunisation programme was introduced in 1985 in Belgium, and against varicella-zoster virus and parvovirus B19 for which the endemic equilibrium assumption is tenable in Belgium.

Results

The optimal age-based sampling structure to use in the sampling of a serological survey as well as the optimal allocation distribution varied depending on the epidemiological parameter of interest for a given infection and between infections.

Conclusions

When estimating epidemiological parameters with acceptable levels of precision within the context of a single cross-sectional serological survey, attention should be given to the age-based sampling structure. Simulation-based sample size calculations in combination with mathematical modelling can be utilised for choosing the optimal allocation of a given number of samples over various age groups.

Electronic supplementary material

The online version of this article (10.1186/s12874-019-0692-1) contains supplementary material, which is available to authorized users.

Timescales of influenza A/H3N2 antibody dynamics

Human immunity influences the evolution and impact of influenza strains. Because individuals are infected with multiple influenza strains during their lifetime, and each virus can generate a cross-reactive antibody response, it is challenging to quantify the processes that shape observed immune responses or to reliably detect recent infection from serological samples. Using a Bayesian model of antibody dynamics at multiple timescales, we explain complex cross-reactive antibody landscapes by inferring participants' histories of infection with serological data from cross-sectional and longitudinal studies of influenza A/H3N2 in southern China and Vietnam. We find that individual-level influenza antibody profiles can be explained by a short-lived, broadly cross-reactive response that decays within a year to leave a smaller long-term response acting against a narrower range of strains. We also demonstrate that accounting for dynamic immune responses alongside infection history can provide a more accurate alternative to traditional definitions of seroconversion for the estimation of infection attack rates. Our work provides a general model for quantifying aspects of influenza immunity acting at multiple timescales based on contemporary serological data and suggests a two-armed immune response to influenza infection consistent with competitive dynamics between B cell populations. This approach to analysing multiple timescales for antigenic responses could also be applied to other multistrain pathogens such as dengue and related flaviviruses.

Mathematical models used to inform study design or surveillance systems in infectious diseases: a systematic review

BACKGROUND

Mathematical models offer the possibility to investigate the infectious disease dynamics over time and may help in informing design of studies. A systematic review was performed in order to determine to what extent mathematical models have been incorporated into the process of planning studies and hence inform study design for infectious diseases transmitted between humans and/or animals.

METHODS

We searched Ovid Medline and two trial registry platforms (Cochrane, WHO) using search terms related to infection, mathematical model, and study design from the earliest dates to October 2016. Eligible publications and registered trials included mathematical models (compartmental, individual-based, or Markov) which were described and used to inform the design of infectious disease studies. We extracted information about the investigated infection, population, model characteristics, and study design.

RESULTS

We identified 28 unique publications but no registered trials. Focusing on compartmental and individual-based models we found 12 observational/surveillance studies and 11 clinical trials. Infections studied were equally animal and human infectious diseases for the observational/surveillance studies, while all but one between humans for clinical trials. The mathematical models were used to inform, amongst other things, the required sample size (n = 16), the statistical power (n = 9), the frequency at which samples should be taken (n = 6), and from whom (n = 6).

CONCLUSIONS

Despite the fact that mathematical models have been advocated to be used at the planning stage of studies or surveillance systems, they are used scarcely. With only one exception, the publications described theoretical studies, hence, not being utilised in real studies.

Structure of general-population antibody titer distributions to influenza A virus

Seroepidemiological studies aim to understand population-level exposure and immunity to infectious diseases. Their results are normally presented as binary outcomes describing the presence or absence of pathogen-specific antibody, despite the fact that many assays measure continuous quantities. A population's natural distribution of antibody titers to an endemic infectious disease may include information on multiple serological states - naiveté, recent infection, non-recent infection, childhood infection - depending on the disease in question and the acquisition and waning patterns of immunity. In this study, we investigate 20,152 general-population serum samples from southern Vietnam collected between 2009 and 2013 from which we report antibody titers to the influenza virus HA1 protein using a continuous titer measurement from a protein microarray assay. We describe the distributions of antibody titers to subtypes 2009 H1N1 and H3N2. Using a model selection approach to fit mixture distributions, we show that 2009 H1N1 antibody titers fall into four titer subgroups and that H3N2 titers fall into three subgroups. For H1N1, our interpretation is that the two highest-titer subgroups correspond to recent and historical infection, which is consistent with 2009 pandemic attack rates. Similar interpretations are available for H3N2, but right-censoring of titers makes these interpretations difficult to validate.

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.