Beyond Vaccination Rates: A Synthetic Random Proxy Metric of Total SARS-CoV-2 Immunity Seroprevalence in the Community (preprint)

Explicit knowledge of total community-level immune seroprevalence is critical to developing policies to mitigate the social and clinical impact of SARS-CoV-2. Publicly available vaccination data are frequently cited as a proxy for population immunity, but this metric ignores the effects of naturally-acquired immunity, which varies broadly throughout the country and world. Without broad or random sampling of the population, accurate measurement of persistent immunity post natural infection is generally unavailable. To enable tracking of both naturally-acquired and vaccine-induced immunity, we set up a synthetic random proxy based on routine hospital testing for estimating total Immunoglobulin G (IgG) prevalence in the sampled community. Our approach analyzes viral IgG testing data of asymptomatic patients who present for elective procedures within a hospital system. We apply multilevel regression and poststratification to adjust for demographic and geographic discrepancies between the sample and the community population. We then apply state-based vaccination data to categorize immune status as driven by natural infection or by vaccine. We have validated the model using verified clinical metrics of viral and symptomatic disease incidence to show the expected biological correlation of these entities with the timing, rate, and magnitude of seroprevalence. In mid-July 2021, the estimated immunity level was 74% with the administered vaccination rate of 45% in the two counties. The metric improves real-time understanding of immunity to COVID-19 as it evolves and the coordination of policy responses to the disease, toward an inexpensive and easily operational surveillance system that transcends the limits of vaccination datasets alone.

Fast methods for posterior inference of two-group normal-normal models (preprint)

We describe a class of algorithms for evaluating posterior moments of certain Bayesian linear regression models with a normal likelihood and a normal prior on the regression coefficients. The proposed methods can be used for hierarchical mixed effects models with partial pooling over one group of predictors, as well as random effects models with partial pooling over two groups of predictors. We demonstrate the performance of the methods on two applications, one involving U.S. opinion polls and one involving the modeling of COVID-19 outbreaks in Israel using survey data. The algorithms involve analytical marginalization of regression coefficients followed by numerical integration of the remaining low-dimensional density. The dominant cost of the algorithms is an eigendecomposition computed once for each value of the outside parameter of integration. Our approach drastically reduces run times compared to state-of-the-art Markov chain Monte Carlo (MCMC) algorithms. The latter, in addition to being computationally expensive, can also be difficult to tune when applied to hierarchical models.

Routine Hospital-based SARS-CoV-2 Testing Outperforms State-based Data in Predicting Clinical Burden (preprint)

Throughout the COVID-19 pandemic, government policy and healthcare implementation responses have been guided by reported positivity rates and counts of positive cases in the community. The selection bias of these data calls into question their validity as measures of the actual viral incidence in the community and as predictors of clinical burden. In the absence of any successful public or academic campaign for comprehensive or random testing, we have developed a proxy method for synthetic random sampling, based on viral RNA testing of patients who present for elective procedures within a hospital system. We present here an approach under multilevel regression and poststratification (MRP) to collecting and analyzing data on viral exposure among patients in a hospital system and performing statistical adjustment that has been made publicly available to estimate true viral incidence and trends in the community. We apply our MRP method to track viral behavior in a mixed urban-suburban-rural setting in Indiana. This method can be easily implemented in a wide variety of hospital settings. Finally, we provide evidence that this model predicts the clinical burden of SARS-CoV-2 earlier and more accurately than currently accepted metrics.

Community prevalence of SARS-CoV-2 in England during April to September 2020: Results from the ONS Coronavirus Infection Survey (preprint)

Background: Decisions regarding the continued need for control measures to contain the spread of SARS-CoV-2 rely on accurate and up-to-date information about the number of people and risk factors for testing positive. Existing surveillance systems are not based on population samples and are generally not longitudinal in design. Methods: From 26 April to 19 September2020, 514,794 samples from 123,497 individuals were collected from individuals aged 2 years and over from a representative sample of private households from England. Participants completed a questionnaire and nose and throat swab were taken. The percentage of individuals testing positive for SARS-CoV-2 RNA was estimated over time using dynamic multilevel regression and post-stratification, to account for potential residual non-representativeness. Potential changes in risk factors for testing positive over time were also evaluated using multilevel regression models. Findings: Between 26 April and 19 September 2020, in total, results were available from 514,794 samples from 123,497 individuals, of which 489 were positive overall from 398 individuals. The percentage of people testing positive for SARS-CoV-2 changed substantially over time, with an initial decrease between end of April and June, followed by low levels during the summer, before marked increases end of August and September 2020. Having a patient-facing role and working outside your home were important risk factors for testing positive in the first period but not (yet) in the second period of increased positivity rates, and age (young adults) being an important driver of the second period of increased positivity rates. A substantial proportion of infections were in individuals not reporting symptoms (53%-70%, dependent on calendar time). Interpretation: Important risk factors for testing positive varied substantially between the initial and second periods of higher positivity rates, and a substantial proportion of infections were in individuals not reporting symptoms, indicating that continued monitoring for SARS-CoV-2 in the community will be important for managing the epidemic moving forwards.

Accounting for Uncertainty During a Pandemic (preprint)

We discuss several issues of statistical design, data collection, analysis, communication, and decision making that have arisen in recent and ongoing coronavirus studies, focusing on tools for assessment and propagation of uncertainty. This paper does not purport to be a comprehensive survey of the research literature; rather, we use examples to illustrate statistical points that we think are important.

Bayesian analysis of tests with unknown specificity and sensitivity (preprint)

When testing for a rare disease, prevalence estimates can be highly sensitive to uncertainty in the specificity and sensitivity of the test. Bayesian inference is a natural way to propagate these uncertainties, with hierarchical modeling capturing variation in these parameters across experiments. Another concern is the people in the sample not being representative of the general population. Statistical adjustment cannot with- out strong assumptions correct for selection bias in an opt-in sample, but multilevel regression and poststratification can at least adjust for known differences between the sample and the population. We demonstrate hierarchical regression and poststratification models with code in Stan and discuss their application to a controversial recent study of SARS-CoV-2 antibodies in a sample of people from the Stanford University area. Wide posterior intervals make it impossible to evaluate the quantitative claims of that study regarding the number of unreported infections. For future studies, the methods described here should facilitate more accurate estimates of disease prevalence from imperfect tests performed on non-representative samples.