A Bayesian Approach to Estimate OJD Prevalence From Pooled Fecal Samples of Variable Pool Size

Additive partially linear model for pooled biomonitoring data

Human biomonitoring involves monitoring human health by measuring the accumulation of harmful chemicals, typically in specimens like blood samples. The high cost of chemical analysis has led researchers to adopt a cost-effective approach. This approach physically combines specimens and subsequently analyzes the concentration of toxic substances within the merged pools. Consequently, there arises a need for innovative regression techniques to effectively interpret these aggregated measurements. To address this need, a new regression framework is proposed by extending the additive partially linear model (APLM) to accommodate the pooling context. The APLM is well-known for its versatility in capturing the complex association between outcomes and covariates, which is particularly valuable in assessing the complex interplay between chemical bioaccumulation and potential risk factors. Consistent estimators of the APLM are obtained through an iterative process that disaggregates information from the pooled observations. The performance is evaluated through simulations and an environmental health study focused on brominated flame retardants using data from the National Health and Nutrition Examination Survey.

Novel application of one-step pooled molecular testing and maximum likelihood approaches to estimate the prevalence of malaria parasitaemia among rapid diagnostic test negative samples in western Kenya

Background

Detection of malaria parasitaemia in samples that are negative by rapid diagnostic tests (RDTs) requires resource-intensive molecular tools. While pooled testing using a two-step strategy provides a cost-saving alternative to the gold standard of individual sample testing, statistical adjustments are needed to improve accuracy of prevalence estimates for a single step pooled testing strategy.

Methods

A random sample of 4670 malaria RDT negative dried blood spot samples were selected from a mass testing and treatment trial in Asembo, Gem, and Karemo, western Kenya. Samples were tested for malaria individually and in pools of five, 934 pools, by one-step quantitative polymerase chain reaction (qPCR). Maximum likelihood approaches were used to estimate subpatent parasitaemia (RDT-negative, qPCR-positive) prevalence by pooling, assuming poolwise sensitivity and specificity was either 100% (strategy A) or imperfect (strategy B). To improve and illustrate the practicality of this estimation approach, a validation study was constructed from pools allocated at random into main (734 pools) and validation (200 pools) subsets. Prevalence was estimated using strategies A and B and an inverse-variance weighted estimator and estimates were weighted to account for differential sampling rates by area.

Results

The prevalence of subpatent parasitaemia was 14.5% (95% CI 13.6–15.3%) by individual qPCR, 9.5% (95% CI (8.5–10.5%) by strategy A, and 13.9% (95% CI 12.6–15.2%) by strategy B. In the validation study, the prevalence by individual qPCR was 13.5% (95% CI 12.4–14.7%) in the main subset, 8.9% (95% CI 7.9–9.9%) by strategy A, 11.4% (95% CI 9.9–12.9%) by strategy B, and 12.8% (95% CI 11.2–14.3%) using inverse-variance weighted estimator from poolwise validation. Pooling, including a 20% validation subset, reduced costs by 52% compared to individual testing.

Conclusions

Compared to individual testing, a one-step pooled testing strategy with an internal validation subset can provide accurate prevalence estimates of PCR-positivity among RDT-negatives at a lower cost.

Generalized additive regression for group testing data

In screening applications involving low-prevalence diseases, pooling specimens (e.g., urine, blood, swabs, etc.) through group testing can be far more cost effective than testing specimens individually. Estimation is a common goal in such applications and typically involves modeling the probability of disease as a function of available covariates. In recent years, several authors have developed regression methods to accommodate the complex structure of group testing data but often under the assumption that covariate effects are linear. Although linearity is a reasonable assumption in some applications, it can lead to model misspecification and biased inference in others. To offer a more flexible framework, we propose a Bayesian generalized additive regression approach to model the individual-level probability of disease with potentially misclassified group testing data. Our approach can be used to analyze data arising from any group testing protocol with the goal of estimating multiple unknown smooth functions of covariates, standard linear effects for other covariates, and assay classification accuracy probabilities. We illustrate the methods in this article using group testing data on chlamydia infection in Iowa.

Comparison of the current abattoir surveillance system for detection of paratuberculosis in Australian sheep with quantitative PCR tissue strategies using simulation modelling

Abattoir surveillance for Johne's disease monitoring in Australia has provided valuable feedback to producers about their flock's disease status since its commencement in 1999. The current surveillance system relies on the identification of gross lesions in sheep carcases at an abattoir, followed by sampling and histopathology testing. This manual inspection system has not been adapted to meet the changing disease situation, as infection prevalence levels have declined over time due to vaccination. This simulation study compares the current system with two alternative approaches utilising a validated quantitative (q)PCR method for the detection of Mycobacterium avium subsp. paratuberculosis in tissues, with random systematic sampling either alone or in conjunction with sampling of a single carcass presenting gross lesions. Consigned sheep were randomly simulated as either infected or uninfected according to defined prevalence levels of infection, with varying histopathological lesion severity and the presence or absence of gross lesions. These sheep were then allocated into multiple 'lines' (group of sheep slaughtered together) within each consignment, with each line subjected to testing with the three sampling strategies for the estimation of line and flock (consignment) sensitivity. The line sensitivity described the proportion of infected lines that tested positive, whereas the flock sensitivity was the proportion of consignments from the simulated infected flocks that had one or more lines test positive for paratuberculosis infection. The tissue qPCR strategy with gross lesion detection achieved marginally higher line sensitivity than the current abattoir surveillance strategy. The simulation of unvaccinated infected flocks with low to moderate prevalence levels demonstrated similar flock sensitivity for all three sampling models. However, the current strategy had very low line sensitivity for the simulated vaccinated infected flocks when the infection prevalence level was <2%. There were substantial differences in flock sensitivity between the two tissue qPCR approaches and the current abattoir surveillance strategy for vaccinated infected flocks, whereas, only marginal differences in flock sensitivity were evident between the two tissue qPCR models. Our results demonstrate that the current strategy is not effective at identifying infected animals at very low infection prevalence levels. The tissue qPCR approach investigated in this study is better as it removes the reliance on meat inspectors to identify gross lesions and can also assist in identifying flocks that have subclinical infected sheep not displaying gross lesions. Therefore, the sheep industry may benefit from incorporating tissue qPCR for Johne's disease surveillance, however the logistics and costs of conducting this type of testing would need to be considered prior to implementing any changes.

Determination of the prevalence and intensity of Fasciola hepatica infection in dairy cattle from six irrigation regions of Victoria, South-eastern Australia, further identifying significant triclabendazole resistance on three properties

Fasciola hepatica (liver fluke) is a widespread parasite infection of livestock in Victoria, South-eastern Australia, where high rainfall and a mild climate is suitable for the main intermediate host Austropeplea tomentosa. The aims of this study were to quantify the prevalence and intensity of F. hepatica in dairy cattle in the irrigated dairy regions of Victoria and determine if triclabendazole resistance was present in infected herds. Cattle in 83 herds from the following six irrigation regions were tested for F. hepatica: Macalister Irrigation District (MID), Upper Murray (UM), Murray Valley (MV), Central Goulburn (CG), Torrumbarry (TIA) and Loddon Valley (LV). Twenty cattle from each herd were tested using the F. hepatica faecal egg count (FEC) as well as the coproantigen ELISA (cELISA). The mean individual animal true prevalence of F. hepatica across all regions was 39 % (95 % credible interval [CrI] 27%-51%) by FEC and 39 % (95 % CrI 27%-50%) by cELISA with the highest true prevalence (75-80 %) found in the MID. Our results show that 46 % of the herds that took part in this study were likely to experience fluke-associated production losses, based on observations that herd productivity is impaired when the true within-herd prevalence is > 25 %. Using the FEC and cELISA reduction tests, triclabendazole resistance was assessed on 3 herds in total (2 from the 83 in the study; and 1 separate herd that did not take part in the prevalence study) and resistance was confirmed in all 3 herds. This study has confirmed that F. hepatica is endemic in several dairy regions in Victoria: triclabendazole resistance may be contributing to the high prevalence in some herds. From our analysis, we estimate that the state-wide economic loss associated with fasciolosis is in the order of AUD 129 million (range AUD 38-193 million) per year or about AUD 50,000 (range AUD 15,000-75,000) per herd per year.

To pool or not to pool? Guidelines for pooling samples for use in surveillance testing of infectious diseases in aquatic animals

Samples from multiple animals may be pooled and tested to reduce costs of surveillance for infectious agents in aquatic animal populations. The primary advantage of pooling is increased population-level coverage when prevalence is low (<10%) and the number of tests is fixed, because of increased likelihood of including target analyte from at least one infected animal in a tested pool. Important questions and a priori design considerations need to be addressed. Unfortunately, pooling recommendations in disease-specific chapters of the 2018 OIE Aquatic Manual are incomplete and, except for amphibian chytrid fungus, are not supported by peer-reviewed research. A systematic review identified only 12 peer-reviewed aquatic diagnostic accuracy and surveillance studies using pooled samples. No clear patterns for pooling methods and characteristics were evident across reviewed studies, although most authors agreed there is a negative effect on detection. Therefore, our purpose was to review pooling procedures used in published aquatic infectious disease research, present evidence-based guidelines, and provide simulated data examples for white spot syndrome virus in shrimp. A decision tree of pooling guidelines was developed for use by peer-reviewed journals and research institutions for the design, statistical analysis and reporting of comparative accuracy studies of individual and pooled tests for surveillance purposes.

Estimating the herd and cow level prevalence of bovine digital dermatitis on New Zealand dairy farms: A Bayesian superpopulation approach

A cross-sectional study of 127 dairy herds distributed across four regions of New Zealand (NZ) was conducted to estimate the regional herd-level prevalence of bovine digital dermatitis (BDD) and the prevalence of cows with BDD lesions within affected herds. Each herd was visited once during the 2016-2017 lactating season and the rear feet of all cows in the milking herd were examined to detect the presence of BDD lesions. Of the 127 herds examined, 63 had at least one cow with a detected BDD lesion. Of the 59 849 cows observed, 646 cows were observed with BDD lesions. All of the herds in which BBD was detected were located in three of the four regions (Waikato, Manawatu and South Canterbury). No convincing lesions were observed on the West Coast. The probability of BDD freedom on the West Coast was predicted to be 99.97% using a Bayesian latent class model. For the three regions where BDD lesions were observed, the true herd level and cow level prevalences were estimated using a Bayesian superpopulation approach which accounted for the imperfect diagnostic method. Based on priors obtained from previous research in another region of NZ (Taranaki), the true herd level prevalences in Waikato, Manawatu and South Canterbury were estimated to be 59.2% (95% probability interval [PI]: 44.3%-73.9%), 43.3% (95%PI: 29%-59%) and 65.9% (95%PI: 49.5%-79.9%), respectively, while the true median within-herd prevalences were estimated as 3.2% (95%PI: 2%-5%), 1.7% (95%PI: 0.9%-3.1%) and 3.7% (95%PI: 2.4%-5.5%), respectively. All of these estimates except for the true herd level prevalence in Manawatu were fairly robust to changes in the priors. For Manawatu region, changing from the prior obtained in Taranaki (the best estimate of the herd level prevalence = 60%, 95% sure > 40%) to one where the mode was 50% (95% sure < 80%) reduced the posterior from 43.3% to 35.2% (95%PI: 20.1%-53.5%). The marked variation in BDD prevalence between regions and between farms highlights the need for further exploration into risk factors for disease.

Bayesian regression for group testing data

Group testing involves pooling individual specimens (e.g., blood, urine, swabs, etc.) and testing the pools for the presence of a disease. When individual covariate information is available (e.g., age, gender, number of sexual partners, etc.), a common goal is to relate an individual's true disease status to the covariates in a regression model. Estimating this relationship is a nonstandard problem in group testing because true individual statuses are not observed and all testing responses (on pools and on individuals) are subject to misclassification arising from assay error. Previous regression methods for group testing data can be inefficient because they are restricted to using only initial pool responses and/or they make potentially unrealistic assumptions regarding the assay accuracy probabilities. To overcome these limitations, we propose a general Bayesian regression framework for modeling group testing data. The novelty of our approach is that it can be easily implemented with data from any group testing protocol. Furthermore, our approach will simultaneously estimate assay accuracy probabilities (along with the covariate effects) and can even be applied in screening situations where multiple assays are used. We apply our methods to group testing data collected in Iowa as part of statewide screening efforts for chlamydia, and we make user-friendly R code available to practitioners.

Group testing regression models with dilution submodels

Group testing, where specimens are tested initially in pools, is widely used to screen individuals for sexually transmitted diseases. However, a common problem encountered in practice is that group testing can increase the number of false negative test results. This occurs primarily when positive individual specimens within a pool are diluted by negative ones, resulting in positive pools testing negatively. If the goal is to estimate a population-level regression model relating individual disease status to observed covariates, severe bias can result if an adjustment for dilution is not made. Recognizing this as a critical issue, recent binary regression approaches in group testing have utilized continuous biomarker information to acknowledge the effect of dilution. In this paper, we have the same overall goal but take a different approach. We augment existing group testing regression models (that assume no dilution) with a parametric dilution submodel for pool-level sensitivity and estimate all parameters using maximum likelihood. An advantage of our approach is that it does not rely on external biomarker test data, which may not be available in surveillance studies. Furthermore, unlike previous approaches, our framework allows one to formally test whether dilution is present based on the observed group testing data. We use simulation to illustrate the performance of our estimation and inference methods, and we apply these methods to 2 infectious disease data sets.

STARD-BLCM: Standards for the Reporting of Diagnostic accuracy studies that use Bayesian Latent Class Models

The Standards for the Reporting of Diagnostic Accuracy (STARD) statement, which was recently updated to the STARD2015 statement, was developed to encourage complete and transparent reporting of test accuracy studies. Although STARD principles apply broadly, the checklist is limited to studies designed to evaluate the accuracy of tests when the disease status is determined from a perfect reference procedure or an imperfect one with known measures of test accuracy. However, a reference standard does not always exist, especially in the case of infectious diseases with a long latent period. In such cases, a valid alternative to classical test evaluation involves the use of latent class models that do not require a priori knowledge of disease status. Latent class models have been successfully implemented in a Bayesian framework for over 20 years. The objective of this work was to identify the STARD items that require modification and develop a modified version of STARD for studies that use Bayesian latent class analysis to estimate diagnostic test accuracy in the absence of a reference standard. Examples and elaborations for each of the modified items are provided. The new guidelines, termed STARD-BLCM (Standards for Reporting of Diagnostic accuracy studies that use Bayesian Latent Class Models), will facilitate improved quality of reporting on the design, conduct and results of diagnostic accuracy studies that use Bayesian latent class models.

Misclassified group-tested current status data

Group testing, introduced by Dorfman (1943), has been used to reduce costs when estimating the prevalence of a binary characteristic based on a screening test of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$k$\end{document} groups that include \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$n$\end{document} independent individuals in total. If the unknown prevalence is low and the screening test suffers from misclassification, it is also possible to obtain more precise prevalence estimates than those obtained from testing all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$n$\end{document} samples separately (Tu et al., 1994). In some applications, the individual binary response corresponds to whether an underlying time-to-event variable \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$T$\end{document} is less than an observed screening time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$C$\end{document}, a data structure known as current status data. Given sufficient variation in the observed \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$C$\end{document} values, it is possible to estimate the distribution function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$F$\end{document} of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$T$\end{document} nonparametrically, at least at some points in its support, using the pool-adjacent-violators algorithm (Ayer et al., 1955). Here, we consider nonparametric estimation of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$F$\end{document} based on group-tested current status data for groups of size \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$k$\end{document} where the group tests positive if and only if any individual’s unobserved \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$T$\end{document} is less than the corresponding observed \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$C$\end{document}. We investigate the performance of the group-based estimator as compared to the individual test nonparametric maximum likelihood estimator, and show that the former can be more precise in the presence of misclassification for low values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$F(t)$\end{document}. Potential applications include testing for the presence of various diseases in pooled samples where interest focuses on the age-at-incidence distribution rather than overall prevalence. We apply this estimator to the age-at-incidence curve for hepatitis C infection in a sample of U.S. women who gave birth to a child in 2014, where group assignment is done at random and based on maternal age. We discuss connections to other work in the literature, as well as potential extensions.

Estimating the prevalence of multiple diseases from two-stage hierarchical pooling

Testing protocols in large-scale sexually transmitted disease screening applications often involve pooling biospecimens (e.g., blood, urine, and swabs) to lower costs and to increase the number of individuals who can be tested. With the recent development of assays that detect multiple diseases, it is now common to test biospecimen pools for multiple infections simultaneously. Recent work has developed an expectation-maximization algorithm to estimate the prevalence of two infections using a two-stage, Dorfman-type testing algorithm motivated by current screening practices for chlamydia and gonorrhea in the USA. In this article, we have the same goal but instead take a more flexible Bayesian approach. Doing so allows us to incorporate information about assay uncertainty during the testing process, which involves testing both pools and individuals, and also to update information as individuals are tested. Overall, our approach provides reliable inference for disease probabilities and accurately estimates assay sensitivity and specificity even when little or no information is provided in the prior distributions. We illustrate the performance of our estimation methods using simulation and by applying them to chlamydia and gonorrhea data collected in Nebraska. Copyright © 2016 John Wiley & Sons, Ltd.

Regression analysis for multiple-disease group testing data

Group testing, where individual specimens are composited into groups to test for the presence of a disease (or other binary characteristic), is a procedure commonly used to reduce the costs of screening a large number of individuals. Group testing data are unique in that only group responses may be available, but inferences are needed at the individual level. A further methodological challenge arises when individuals are tested in groups for multiple diseases simultaneously, because unobserved individual disease statuses are likely correlated. In this paper, we propose new regression techniques for multiple-disease group testing data. We develop an expectation-solution based algorithm that provides consistent parameter estimates and natural large-sample inference procedures. We apply our proposed methodology to chlamydia and gonorrhea screening data collected in Nebraska as part of the Infertility Prevention Project and to prenatal infectious disease screening data from Kenya.