To make informative public policy decisions in battling the ongoing COVID-19 pandemic, it is important to know the disease prevalence in a population. There are two intertwined difficulties in estimating this prevalence based on testing results from a group of subjects. First, the test is prone to measurement error with unknown sensitivity and specificity. Second, the prevalence tends to be low at the initial stage of the pandemic and we may not be able to determine if a positive test result is a false positive due to the imperfect specificity of the test. The statistical inference based on large sample approximation or conventional bootstrap may not be sufficiently reliable and yield confidence intervals that do not cover the true prevalence at the nominal level. In this paper, we have proposed a set of 95% confidence intervals, whose validity is guaranteed and doesn't depend on the sample size in the unweighted setting. For the weighted setting, the proposed inference is equivalent to a class of hybrid bootstrap methods, whose performance is also more robust to the sample size than those based on asymptotic approximations. The methods are used to reanalyze data from a study investigating the antibody prevalence in Santa Clara county, California, which was the motivating example of this research, in addition to several other seroprevalence studies where authors had tried to correct their estimates for test performance. Extensive simulation studies have been conducted to examine the finite-sample performance of the proposed confidence intervals.
We present several related methods for creating confidence intervals to assess disease prevalence in variety of survey sampling settings. These include simple random samples with imperfect tests, weighted sampling with perfect tests, and weighted sampling with imperfect tests, with the first two settings considered special cases of the third. Our methods use survey results and measurements of test sensitivity and specificity to construct melded confidence intervals. We demonstrate that our methods appear to guarantee coverage in simulated settings, while competing methods are shown to achieve …
For many diseases, logistic and other constraints often render large incidence studies difficult, if not impossible, to carry out. This becomes a drawback, particularly when a new incidence study is needed each time the disease incidence rate is investigated in a different population. However, by carrying out a prevalent cohort study with follow-up it is possible to estimate the incidence rate if it is constant. In this paper we derive the maximum likelihood estimator (MLE) of the overall incidence rate, $λ$, as well as age-specific incidence rates, by exploiting the well known epidemiologic r…
Countries officially record the number of COVID-19 cases based on medical tests of a subset of the population with unknown participation bias. For prevalence estimation, the official information is typically discarded and, instead, small random survey samples are taken. We derive (maximum likelihood and method of moment) prevalence estimators, based on a survey sample, that additionally utilize the official information, and that are substantially more accurate than the simple sample proportion of positive cases. Put differently, using our estimators, the same level of precision can be obtained…
Continuous biomarkers are common for disease screening and diagnosis. To reach a dichotomous clinical decision, a threshold would be imposed to distinguish subjects with disease from non-diseased individuals. Among various performance metrics for a continuous biomarker, specificity at a controlled sensitivity level (or vice versa) is often desirable for clinical utility since it directly targets where the clinical test is intended to operate. Covariates, such as age, race, and sample collection, could impact the controlled sensitivity level in subpopulations and may also confound the associati…
A bivariate copula mixed model has been recently proposed to synthesize diagnostic test accuracy studies and it has been shown that is superior to the standard generalized linear mixed model (GLMM) in this context. Here we call trivariate vine copulas to extend the bivariate meta-analysis of diagnostic test accuracy studies by accounting for disease prevalence. Our vine copula mixed model includes the trivariate GLMM as a special case and can also operate on the original scale of sensitivity, specificity, and disease prevalence. Our general methodology is illustrated by re-analysing the data o…
A Counterfactual Framework for Estimating Infectious Disease Prevalence under Repeated Testing with Symptomatic and Contact-Tracing Components
Division of Biostatistics, College of Public Health, The Ohio State University（俄亥俄州立大学公共卫生学院生物统计系）；Department of Medical Epidemiology and Biostatistics, Karolinska Institutet（卡罗林斯卡医学院医学流行病学与生物统计系）
PathCheck Foundation（PathCheck基金会）；Stony Brook Medicine（石溪医学中心）；MIT Media Lab（麻省理工学院媒体实验室）；University of California San Francisco（加州大学旧金山分校）
It is crucial for policymakers to understand the community prevalence of COVID-19 so combative resources can be effectively allocated and prioritized during the COVID-19 pandemic. Traditionally, community prevalence has been assessed through diagnostic and antibody testing data. However, despite the increasing availability of COVID-19 testing, the required level has not been met in most parts of the globe, introducing a need for an alternative method for communities to determine disease prevalence. This is further complicated by the observation that COVID-19 prevalence and spread varies across…
We study the relation between the age-specific prevalence, incidence and mortality in an illness-death model consisting of the three states Healthy, Ill, Dead. The dependency on three different time scales (age, calendar time, disease duration) is considered. It is shown that Keiding's equation published in 1991 is a generalisation of the solution of Brunet and Struchiner's partial differential equation from 1999. In a special case, we propose a particularly simple estimate of the incidence from prevalence data.
In this paper we set out general principles and develop geostatistical methods for the analysis of data from spatio-temporally referenced prevalence surveys. Our objective is to provide a tutorial guide that can be used in order to identify parsimonious geostatistical models for prevalence mapping. A general variogram-based Monte Carlo procedure is proposed to check the validity of the modelling assumptions. We describe and contrast likelihood-based and Bayesian methods of inference, showing how to account for parameter uncertainty under each of the two paradigms. We also describe extensions o…
Aggregated health data such as claims data from health insurances become more and more available for research purposes. Estimates of excess mortality from prevalence and incidence of a chronic condition have only been possible for ages 50 years and older and have shown to be unstable in younger ages. The aim of this article is to explore the reasons why estimates of excess mortality for younger ages are prone to bias and what can be done to extend the age range to ages below 50 years.
Bayes' Theorem confers inherent limitations on the accuracy of screening tests as a function of disease prevalence. We have shown in previous work that a testing system can tolerate significant drops in prevalence, up until a certain well-defined point known as the $prevalence$ $threshold$, below which the reliability of a positive screening test drops precipitously. Herein, we establish a mathematical model to determine whether sequential testing overcomes the aforementioned Bayesian limitations and thus improves the reliability of screening tests. We show that for a desired positive predicti…
Infectious diseases remain one of the major causes of human mortality and suffering. Mathematical models have been established as an important tool for capturing the features that drive the spread of the disease, predicting the progression of an epidemic and hence guiding the development of strategies to control it. Another important area of epidemiological interest is the development of geostatistical methods for the analysis of data from spatially referenced prevalence surveys. Maps of prevalence are useful, not only for enabling a more precise disease risk stratification, but also for guidi…
Recently, we have shown that the age-specific prevalence of a disease can be related to the transition rates in the illness-death model via a partial differential equation (PDE). In case of a chronic disease, we show that the PDE can be used to estimate excess mortality from prevalence and incidence. Applicability of the new method is demonstrated in a simulation and claims data about diabetes in German men.
Diagnosis is often based on the exceedance or not of continuous health indicators of a predefined cut-off value, so as to classify patients into positives and negatives for the disease under investigation. In this paper, we investigate the effects of dichotomization of spatially-referenced continuous outcome variables on geostatistical inference. Although this issue has been extensively studied in other fields, dichotomization is still a common practice in epidemiological studies. Furthermore, the effects of this practice in the context of prevalence mapping have not been fully understood. Her…
Prevalence estimation in infectious diseases with imperfect tests: A comparison of Frequentist and Bayesian Logistic Regression methods with misclassification correction
The relationship between a screening tests' positive predictive value, $ρ$, and its target prevalence, $ϕ$, is proportional - though not linear in all but a special case. In consequence, there is a point of local extrema of curvature defined only as a function of the sensitivity $a$ and specificity $b$ beyond which the rate of change of a test's $ρ$ drops precipitously relative to $ϕ$. Herein, we show the mathematical model exploring this phenomenon and define the $prevalence$ $threshold$ ($ϕ_e$) point where this change occurs as: $ϕ_e=\frac{\sqrt{a\left(-b+1\right)}+b-1}{(\varepsilon-1)}$ whe…
The prevalence of common chronic non-communicable diseases (CNCDs) far overshadows the prevalence of both monogenic and infectious diseases combined. All CNCDs, also called complex genetic diseases, have a heritable genetic component that can be used for pre-symptomatic risk assessment. Common single nucleotide polymorphisms (SNPs) that tag risk haplotypes across the genome currently account for a non-trivial portion of the germ-line genetic risk and we will likely continue to identify the remaining missing heritability in the form of rare variants, copy number variants and epigenetic modifica…
Pooled testing (also known as group testing), where diagnostic tests are performed on pooled samples, has broad applications in the surveillance of diseases in animals and humans. An increasingly common use case is molecular xenomonitoring (MX), where surveillance of vector-borne diseases is conducted by capturing and testing large numbers of vectors (e.g. mosquitoes). The R package PoolTestR was developed to meet the needs of increasingly large and complex molecular xenomonitoring surveys but can be applied to analyse any data involving pooled testing. PoolTestR includes simple and flexible t…
We propose a partial identification method for estimating disease prevalence from serology studies. Our data are results from antibody tests in some population sample, where the test parameters, such as the true/false positive rates, are unknown. Our method scans the entire parameter space, and rejects parameter values using the joint data density as the test statistic. The proposed method is conservative for marginal inference, in general, but its key advantage over more standard approaches is that it is valid in finite samples even when the underlying model is not point identified. Moreover,…
Bayes' Theorem imposes inevitable limitations on the accuracy of screening tests by tying the test's predictive value to the disease prevalence. The aforementioned limitation is independent of the adequacy and make-up of the test and thus implies inherent Bayesian limitations to the screening process itself. As per the WHO's $Wilson-Jungner$ criteria, one of the prerequisite steps before undertaking screening is to ensure that a treatment for the condition screened exists. However, in so doing, a paradox, henceforth termed the screening paradox, ensues. If a disease process is screened for and…
