Bayesian Latent Class Models for the Multiple Imputation of Categorical Data

With great interest we read the article from Dramé et al1 “Should RT-PCR be considered as gold standard in the diagnosis of COVID-19” questioning the conclusions from Cassaniti et al.2 We agree with the argument that considering reverse transcription-polymerase chain reaction (RT-PCR) as gold standard when evaluating a new test will inevitably lead to biased test accuracy estimates of the new test.1 However, we disagree that it is impossible to “demonstrate that a new test might be better than the old-test” and propose using Bayesian latent class models (BLCMs) to estimate the sensitivity and specificity in the absence of a gold standard. “Latent” means here that the true disease/infection status is not observed, but can be estimated from the data. BLCMs have been applied widely, reporting guidelines have been developed,3 and currently an European Union-funded initiative aims to expand their application in the evaluation of diagnostic tests (www.harmony-net.eu). For showcasing BLCMs, we used the data from Cassaniti et al,2 although the keys to validity in diagnostic test studies are not respected, that is, “a consecutive series of patients suspected (but not known) to have the target disorder,”4 which precludes the generalizability of the findings. We considered a model with three tests for the diagnosis of coronavirus disease-2019 (COVID-19) in one population (110 patients), and extracted the following data of cross-classified test results (RT-PCR, IgG, and IgM)2: +++ 28, ++− 1, +−+ 3, +−− 36, −++ 0, −+− 0, −−+ 1, and −−− 41. We aim to estimate the prevalence, the sensitivities, and the specificities of three tests, and potential conditional dependencies (correlations) between tests. Since the maximum number of estimable parameters for three tests in one population is seven,5 this model is not identifiable. Therefore, in a Bayesian framework, we rely on prior information for the specificities of all three tests similar to a previous analysis with two tests and four populations.6 We assume that they are close to 100%. Further technical details about the model and Markov Chain Monte Carlo simulation, including the code to reproduce the results, are available on (https://github.com/shartn/BLCM-COVID19). In Table 1 the posteriors resulting from a model with conditional dependency between the IgG and IgM test sensitivities are displayed. In contrast to the previous analysis,2 which used the RT-PCR as a gold standard, implicitly assuming 100% sensitivity and specificity, the RT-PCR sensitivity based on our BLCM analysis is lower, while the specificity of all three tests is close to 100%. The estimated sensitivity of the combined IgM/IgG in the study from Cassaniti et al2 was 18.4%, being outside the 95% probability interval of our BLCM estimates for both the IgM and IgG. Although, based on our BLCM analysis, we cannot state “that the new test might be better,”1 we are confident that BLCMs allow estimation of sensitivities and specificities in an unbiased way without needing a gold standard. Since this data set—with the exception of the 50 emergency patients—does not comply with the key aspects of validity,4 it is not possible to generalize the results of our BLCM beyond the study population of the 110 patients. Despite enormous COVID-19 research activities, the application of BLCMs and suitable data sets are virtually absent. For the preparedness of future pandemics, we suggest to include the design of appropriate diagnostic test accuracy studies, which will also be suitable for BLCMs. We used for our BLCM analysis data which have been published by the journal, and extracted the data directly from this publication: https://doi.org/10.1002/jmv.25800.

In the assessment of the accuracy of diagnostic tests for infectious diseases, the true disease status of the subjects is often unknown due to the lack of a gold standard test. Latent class models with two latent classes, representing diseased and non-diseased subjects, are often used to analyze this type of data. In its basic format, latent class analysis requires the observed outcomes to be statistically independent conditional on the disease status. In most diagnostic settings, this assumption is highly questionable. During the last decade, several methods have been proposed to estimate latent class models with conditional dependence between the test results. A class of flexible fixed and random effects models were described by Dendukuri and Joseph in a Bayesian framework. We illustrate these models using the analysis of a diagnostic study of three field tests and an imperfect reference test for the diagnosis of visceral leishmaniasis. We show that, as observed earlier by Albert and Dodd, different dependence models may result in similar fits to the data while resulting in different inferences. Given this problem, selection of appropriate latent class models should be based on substantive subject matter knowledge. If several clinically plausible models are supported by the data, a sensitivity analysis should be performed by describing the results obtained from different models and using different priors.

Currently, assessing the diagnostic performance of new laboratory tests assumes a perfect reference standard, which is rarely the case. Wrong classifications of the true disease status will inevitably lead to biased estimates of sensitivity and specificity. Using Bayesian' latent class models (BLCMs), an approach that does not assume a perfect reference standard, we re-analyzed data of a large prospective observational study assessing the diagnostic accuracy of an antigen test for the diagnosis of SARS-CoV-2 infection in clinical practice. A cohort of consecutive patients presenting to a COVID-19 testing facility affiliated with a Swiss University Hospital were recruited (n = 1465). Two real-time PCR tests were conducted in parallel with the Roche/SD Biosensor rapid antigen test on nasopharyngeal swabs. A two-test (PCR and antigen test), three-population BLCM was fitted to the frequencies of paired test results. Based on the BLCM, the sensitivities of the RT-PCR and the Roche/SD Biosensor rapid antigen test were 98.5% [95% CRI 94.8;100] and 82.7% [95% CRI 66.8;100]. The specificities were 97.7% [96.1;99.7] and 99.9% [95% CRI 99.6;100]. Applying the BLCM, the diagnostic accuracy of RT-PCR was high but not perfect. In contrast to previous results, the sensitivity of the antigen test was higher. Our results suggest that BLCMs are valuable tools for investigating the diagnostic performance of laboratory tests in the absence of perfect reference standard.

BackgroundLow malaria parasite densities in pregnancy are a diagnostic challenge. PCR provides high sensitivity and specificity in detecting low density of parasites, but cost and technical requirements limit its application in resources-limited settings. Pooling samples for PCR detection was explored to estimate prevalence of submicroscopic malaria infection in pregnant women at delivery. Previous work uses gold-standard based methods to calculate sensitivity and specificity of tests, creating a challenge when newer methodologies are substantially more sensitive than the gold standard. Thus prevalence was estimated using Bayesian latent class models (LCMs) in this study.MethodsNested PCR (nPCR) for the 18S rRNA gene subunit of Plasmodium falciparum was conducted to detect malaria infection in microscopy-negative Malawian women on IPTp. Two-step sample pooling used dried blood spot samples (DBSs) collected from placenta or periphery at delivery. Results from nPCR and histology as well as previously published data were used to construct LCMs to estimate assay sensitivity and specificity. Theoretical confidence intervals for prevalence of infection were calculated for two-step and one-step pooling strategies.ResultsOf 617 microscopy-negative Malawian women, 39 (6.3%) were identified as actively infected by histology while 52 (8.4%) were positive by nPCR. One hundred forty (22.7%) individuals had past infection assessed by histology. With histology as a reference, 72% of women in the active infection group, 7.1% in the past infection group and 3.2% in histology-negative group were nPCR positive. Using latent class models without a gold standard, histology had a median sensitivity of 49.7% and specificity of 97.6% for active infection while PCR had a median sensitivity of 96.0% and specificity of 99.1%. The true prevalence of active infection was estimated at 8.0% (CI: 5.8-10.5%) from PCR. PCR also had similar sensitivity for detecting either peripheral or placental malaria for submicroscopic infections. One-step pooling would give similar confidence intervals for pool sizes less than 20 while reducing the number of tests performed.ConclusionsPooled nPCR testing was a sensitive and resource-efficient strategy and LCMs provided precise prevalence estimates of submicroscopic infections. Compared to two-step pooling, one-step pooling could provide similar prevalence estimates at population levels with many fewer tests required.Electronic supplementary materialThe online version of this article (doi:10.1186/1475-2875-13-509) contains supplementary material, which is available to authorized users.

Background: Over the last two decades, latent class analysis (LCA) has been extensively used to statistically identify phenotypes of childhood wheeze; however, less has been discussed on the external factors affecting the outcomes of LCA models in phenotype identification research. Objective: To understand the potential cause of variability in the number/types of wheeze phenotypes identified by means of LCA and to assess the performance of these models under different conditions. Methods: Here, we examined the effects of several data characteristics (sample size, data collection age and intervals), and model dimensionality (number of latent classes) on the classification of wheeze phenotypes by means of latent class and transition analysis. We also identified critical and redundant data collection points in discriminating phenotypes of wheeze using two different variable selection methods, stepwise-backward elimination, and genetic algorithm. Results: Small sample sizes suggested fewer wheeze sub-groups as they were underpowered to detect less frequently observed wheeze phenotypes. There was a strong interplay between sample size, number of data collection points and the optimal number of wheeze phenotypes extracted. A variable selection algorithm applied to LCA resulted in the exclusion of 6 redundant/non-informative time points (Month 6, Month 30, Month 69, Month 91, Month 140 and Month 198) as they contained very little discriminative and/or extra information about the wheeze classes. Conclusions: Input data characteristics and model complexity were found to be very influential on the classification of wheeze phenotypes and prevalence of each class in the population.

A bootstrap procedure useful in latent class models has been developed to determine the sufficient number of latent classes required to account for systematic group differences in the data. The procedure is illustrated in the context of a multidimensional scaling latent class model, CLASCAL. Real and artficial data are presented. The bootstrap procedure for selecting a sufficient number of classes seems to correctly select the correct number of latent classes at both low and high error levels. At higher error levels it outperforms Hope’s (1968) procedure.

Bayesian diagnostic test evaluation and true prevalence estimation of mycoplasma bovis in dairy herds.

Evaluation of a multiplex immunoassay for bovine respiratory syncytial virus and bovine coronavirus antibodies in bulk tank milk against two indirect ELISAs using latent class analysis

There is a shortage of rapid, accurate, and low-cost assays for diagnosing enteric fever. The dual-path platform for typhoid (DPPT) assay had high accuracy in retrospective studies with banked plasma samples. We aimed to evaluate the diagnostic accuracy of the DPPT assay in a prospective study using fingerstick capillary blood. For this prospective diagnostic accuracy study, we enrolled children younger than 18years, who presented at the Bangladesh Shishu Hospital and Institute (Dhaka, Bangladesh) with at least 3days of fever. We collected blood and nasal swabs, and did the following assays to assess the accuracy of DPPT: blood culture, serological assays for typhoid fever (DPPT assay, Widal, and Test-it), and molecular assays to identify alternative aetiologies (eg, respiratory syncytial virus [RSV], influenza, dengue virus, and Rickettsia spp). The primary outcomes of the study were the sensitivity and specificity of the DPPT assay for diagnosis of enteric fever. We evaluated the accuracy of combined anti-haemolysin Eand anti-lipopolysaccharide IgA readings using the DPPT assay in distinguishing culture-confirmed enteric fever from alternative aetiologies using receiver operating characteristic area under the curve (AUC). Given the imperfect reference standard diagnostics for enteric fever, we used Bayesian latent class models, incorporating results from the typhoid and alternative aetiology diagnostics, to estimate the sensitivity and specificity of the DPPT assay. We also did subgroup analyses for the assay across multiple biological variables. Between Aug 17, 2021, and July 16, 2022, we enrolled 501participants who presented with at least 3days of fever. 223 (45%) of 501participants were female and 278 (55%) were male. 77participants had culture-confirmed enteric fever (62 Salmonella entericaserotype Typhi and 15 Salmonella entericaserotype Paratyphi A) and 70were culture-negative with PCR-confirmed alternative aetiology (34 influenza Aor B, 22dengue virus, seven Rickettsia spp, six RSV, and one participant co-infected with RSV and dengue virus). The AUC for DPPT on fingerstick capillary blood in distinguishing typhoid from alternative aetiologies was 0·969 (95% CI 0·943-0·994). In latent class analysis, the sensitivity of DPPT was 93%(95% credible interval [CrI] 87-97) and specificity was 89% (85-93). The balanced accuracy was higher for DPPT (91%, 95% CrI 87-94) than blood culture (81%, 78-85), Test-it (77%,74-79), or Widal (70%, 67-73). Assay performance did not vary by sex, age, duration of fever at presentation, antibiotic use before presentation, Salmonella serotype, or sample type. The point-of-care DPPT assay achieved high diagnostic accuracy for enteric fever in a highly endemic community. This assay has the potential to improve clinical outcomes for enteric fever, allowing rapid diagnosis and treatment, and could facilitate more appropriate antimicrobial use. National Institute of Health, Bill & Melinda Gates Foundation, and Child Health Research Foundation.

The state of the practice in black spot identification uses safety performance functions based on total crash counts to identify high-risk crash sites. This paper postulates that total crash count is a result of multiple distinct risk-generating processes (RGPs), including geometric characteristics of the road, spatial features of the surrounding environment, and driver behavior factors. However, these multiple sources are ignored in current modeling methodologies that try to explain or predict crash frequencies across sites. Instead, current practice uses models that imply that a single RGP exists. This misspecification may lead to correlation of crashes with incorrect sources of contributing factors (e.g., concluding a crash is predominately caused by a geometric feature when the cause is a behavioral issue), which may ultimately lead to inefficient use of public funds and misidentification of true black spots. This study proposes a latent class model consistent with a multiple risk process theory and investigates the influence this model has on correctly identifying crash black spots. The paper presents the theoretical and corresponding methodological approach in which a Bayesian latent class model is estimated with the assumption that crashes arise from two distinct RGPs, including engineering and unobserved spatial factors. The methodology was applied to state-controlled roads in Queensland, Australia. The results were compared with an empirical Bayesian negative binomial (EB-NB) model. A comparison of goodness-of-fit measures illustrated superiority of the proposed model compared with the NB model. The detection of black spots was improved compared with the EB-NB model. In addition, modeling crashes as the result of two fundamentally separate RGPs reveals more detailed information about unobserved crash causes.

BackgroundThe physicians’ competency is an important public health issue around the world. Several international organizations have taken the lead in examining the competencies required to be a physician. The purpose of this study is to identify subgroups of physicians’ competency based upon the importance results of competency evaluation and provide a scientific basis for the qualitative research of the competency of physicians.MethodsA cross-sectional study was conducted on a large population-based sample in 31 provinces, autonomous regions and municipalities directly under the central government in China. The latent class analysis was performed to identify patterns of physicians’ competency using M-plus software.ResultsIn this study, the latent class analysis was adopted to identify the appropriate number of distinct latent classes of physicians’ competency based on eight competency dimensions, and a four-class model best fit the data, which are excellent competency group, lack of professionalism competency group, individual competency driven group, and lack of competency cognitive group. Therefore, 6247 physicians can be divided into four latent classes based on the importance results of competency evaluation, and the number of each class is 5684, 284, 215 and 64, respectively.ConclusionThese findings suggested that latent class analysis can be used to study the competency of physicians, and four distinct subgroups were identified. Therefore, we can effectively understand the patterns of physicians’ competency, and the health administrative departments could utilize more specific measures according to their different competency subgroups, and providing individualized training schemes in the future training and management of physicians.

SUMMARYPneumonia is a leading cause of mortality and morbidity worldwide with radiographically confirmed pneumonia a key disease burden indicator. This is usually determined by a radiology panel which is assumed to be the best available standard; however, this assumption may introduce bias into pneumonia incidence estimates. To improve estimates of radiographic pneumonia incidence, we applied Bayesian latent class modelling (BLCM) to a large database of hospitalized patients with acute lower respiratory tract illness in Sa Kaeo and Nakhon Phanom provinces, Thailand from 2005 to 2010 with chest radiographs read by both a radiology panel and a clinician. We compared these estimates to those from conventional analysis. For children aged <5 years, estimated radiographically confirmed pneumonia incidence by BLCM was 2394/100 000 person-years (95% credible interval 2185–2574) vs. 1736/100 000 person-years (95% confidence interval 1706–1766) from conventional analysis. For persons aged ≥5 years, estimated radiographically confirmed pneumonia incidence was similar between BLCM and conventional analysis (235 vs. 215/100 000 person-years). BLCM suggests the incidence of radiographically confirmed pneumonia in young children is substantially larger than estimated from the conventional approach using radiology panels as the reference standard.

We propose using latent class analysis as an alternative to log-linear analysis for the multiple imputation of incomplete categorical data. Similar to log-linear models, latent class models can be used to describe complex association structures between the variables used in the imputation model. However, unlike log-linear models, latent class models can be used to build large imputation models containing more than a few categorical variables. To obtain imputations reflecting uncertainty about the unknown model parameters, we use a nonparametric bootstrap procedure as an alternative to the more common full Bayesian approach. The proposed multiple imputation method, which is implemented in Latent GOLD software for latent class analysis, is illustrated with two examples. In a simulated data example, we compare the new method to well-established methods such as maximum likelihood estimation with incomplete data and multiple imputation using a saturated log-linear model. This example shows that the proposed method yields unbiased parameter estimates and standard errors. The second example concerns an application using a typical social sciences data set. It contains 79 variables that are all included in the imputation model. The proposed method is especially useful for such large data sets because standard methods for dealing with missing data in categorical variables break down when the number of variables is so large.

Bovine besnoitiosis, a disease caused by the tissue cyst-forming apicomplexan Besnoitia besnoiti, is re-emerging in Europe, leading to significant impairment of health and production, as well as economic losses. The early detection of the disease is of the utmost importance for the implementation of effective control measures, yet this is a challenge due to the lack of specific early clinical signs. The objectives of our study were 1) to estimate the diagnostic accuracy of three tests to detect B. besnoiti in naturally exposed cattle (histopathology-skin (HIS-SK); PCR-skin (PCR-SK); and parallel PCR of nasal and scleroconjunctival swabs (PCR-NS-SC)) using a Bayesian latent class model (BLCM) and 2) to describe the clinical presentation of besnoitiosis in the studied animals. The study involved 54 adult Limousin cattle. Biosecurity measures were assessed and scored as medium. At clinical examination, a sire was diagnosed with a form of besnoitiosis between the end of the acute phase and the beginning of the chronic phase. Furthermore, 29 animals displaying a subclinical infection, characterized by the presence of scleroconjunctival cysts, were identified. The PCR-SK and PCR-NS-SC were able to detect B. besnoitia. The diagnostic performance of PCR-SK, PCR-NS-SC and HIS-SK was evaluated. The BLCM indicated that HIS-SK had the highest specificity (99.1 %, 95 % posterior probability interval PI: 96-100 %), while PCR-SK and PCR-NS-SC demonstrated higher sensitivities (91.0 %, 95 % PI: 68-100 %, and 85.0 %, 95 % PI: 67-100 %, respectively). The study concludes that the use of a parallel PCR-NS-SC could represent a viable alternative for the early detection of B. besnoiti, providing a less invasive method to monitor and control bovine besnoitiosis at the herd level.

Pregnancy diagnosis using pregnancy-associated glycoprotein (PAG) ELISA technology in blood or milk samples is validated from 28 d after insemination in dairy cows. The objective of this study was to estimate the sensitivity (Se) and specificity (Sp) of a commercial milk PAG-based ELISA in Holstein dairy cows between 23 and 27 d after insemination. Milk samples (n = 268) from 257 Holstein dairy cows 23 to 27 d after AI were submitted for PAG ELISA testing. Pregnancy status was confirmed by either a second milk PAG ELISA test conducted between 28 and 50 d after insemination (n = 200) or transrectal ultrasonography performed between 28 and 59 d after insemination (n = 68). A Bayesian latent class model was used to compare the paired results from the test at 23 to 27 d after AI test to the reference test. The latent class model typically used for comparing 2 or more imperfect tests was extended to include the possibility of pregnancy loss between the 23 to 27 d test and the reference test. Informative priors for the probability of pregnancy loss, and for the Se and Sp of the PAG and ultrasonography reference tests were obtained from the scientific literature. Estimated median Se and Sp of the PAG ELISA test conducted between 23 and 27 d after AI were 0.98 (95% credible interval 0.93 to 1.0) and 0.98 (0.89 to 1.0), respectively, when using a standardized corrected optical density threshold of 0.15. Although the accuracy of the test under investigation was excellent, more data will be needed to confirm the optimal diagnostic cut point for PAG in milk for early pregnancy diagnosis in this time window. The optimal timing of pregnancy diagnosis will depend on herd-specific logistics and the action to be taken to re-inseminate nonpregnant cows.