Finite mixture models with concomitant information: assessing diagnostic criteria for diabetes

Performance of the StaphGold ELISA test in determining subclinical Staphylococcus aureus infections in dairy cows using a Gaussian mixture model

Background

A novel ELISA test has been developed to detect antigen‐specific IgG in early and late lactation cows in New Zealand.

Objectives

This study was to evaluate the discriminatory ability of the ELISA based on the detection of S. aureus‐specific IgG as a screening test.

Methods

The ELISA was used for the composite milk samples taken during routine herd testing in 2018–2019 milking season in New Zealand. In the absence of a gold standard test, the diagnostic specificity and sensitivity was estimated using a Gaussian mixture model.

Results

The ELISA test had a high accuracy (AUC = 0.98) to detect antigen‐specific IgG in early and late lactation cows with high somatic cell count due to either subsequent to or contemporaneous with the S. aureus invasion. Using an S/P ratio = 0.3 as the cut‐off value, the ELISA test has sensitivity of 0.9 and specificity of 0.95, while the sensitivity increased to 0.94 at a cost of a decreased specificity of 0.9 at a lower cut‐off value 0.26.

Conclusions

The integration of the ELISA test as a screening tool into specific control programs may be useful to reduce the spread of S. aureus infections, to aid with treatment decisions, and to establish a correct milking order.

Dealing with highly skewed hospital length of stay distributions: The use of Gamma mixture models to study delivery hospitalizations

The increased focus on addressing severe maternal morbidity and maternal mortality has led to studies investigating patient and hospital characteristics associated with longer hospital stays. Length of stay (LOS) for delivery hospitalizations has a strongly skewed distribution with the vast majority of LOS lasting two to three days in the United States. Prior studies typically focused on common LOSs and dealt with the long LOS distribution tail in ways to fit conventional statistical analyses (e.g., log transformation, trimming). This study demonstrates the use of Gamma mixture models to analyze the skewed LOS distribution. Gamma mixture models are flexible and, do not require data transformation or removal of outliers to accommodate many outcome distribution shapes, these models allow for the analysis of patients staying in the hospital for a longer time, which often includes those women experiencing worse outcomes. Random effects are included in the model to account for patients being treated within the same hospitals. Further, the role and influence of differing placements of covariates on the results is discussed in the context of distinct model specifications of the Gamma mixture regression model. The application of these models shows that they are robust to the placement of covariates and random effects. Using New York State data, the models showed that longer LOS for childbirth hospitalizations were more common in hospitals designated to accept more complicated deliveries, across hospital types, and among Black women. Primary insurance also was associated with LOS. Substantial variation between hospitals suggests the need to investigate protocols to standardize evidence-based medical care.

Accounting for misclassification in electronic health records-derived exposures using generalized linear finite mixture models

Exposures derived from electronic health records (EHR) may be misclassified, leading to biased estimates of their association with outcomes of interest. An example of this problem arises in the context of cancer screening where test indication, the purpose for which a test was performed, is often unavailable. This poses a challenge to understanding the effectiveness of screening tests because estimates of screening test effectiveness are biased if some diagnostic tests are misclassified as screening. Prediction models have been developed for a variety of exposure variables that can be derived from EHR, but no previous research has investigated appropriate methods for obtaining unbiased association estimates using these predicted probabilities. The full likelihood incorporating information on both the predicted probability of exposure-class membership and the association between the exposure and outcome of interest can be expressed using a finite mixture model. When the regression model of interest is a generalized linear model (GLM), the expectation-maximization algorithm can be used to estimate the parameters using standard software for GLMs. Using simulation studies, we compared the bias and efficiency of this mixture model approach to alternative approaches including multiple imputation and dichotomization of the predicted probabilities to create a proxy for the missing predictor. The mixture model was the only approach that was unbiased across all scenarios investigated. Finally, we explored the performance of these alternatives in a study of colorectal cancer screening with colonoscopy. These findings have broad applicability in studies using EHR data where gold-standard exposures are unavailable and prediction models have been developed for estimating proxies.

Finding vulnerable subpopulations in the Seychelles Child Development Study: effect modification with latent groups

The Seychelles Child Development Study is a research project with the objective of examining associations between prenatal exposure to low doses of methylmercury from maternal fish consumption and children's developmental outcomes. Whether methylmercury has neurotoxic effects at low doses remains unclear and recommendations for pregnant women and children to reduce fish intake may prevent a substantial number of people from receiving sufficient nutrients that are abundant in fish. The primary findings of the Seychelles Child Development Study are inconsistent with adverse associations between methylmercury from fish consumption and neurodevelopmental outcomes. However, whether there are subpopulations of children who are particularly sensitive to this diet is an open question. Secondary analysis from this study found significant interactions between prenatal methylmercury levels and both caregiver IQ and income on 19-month IQ. These results are sensitive to the categories chosen for these covariates and are difficult to interpret collectively. In this paper, we estimate effect modification of the association between prenatal methylmercury exposure and 19-month IQ using a general formulation of mixture regression. Our mixture regression model creates a latent categorical group membership variable which interacts with methylmercury in predicting the outcome. We also fit the same outcome model when in addition the latent variable is assumed to be a parametric function of three distinct socioeconomic measures. Bayesian methods allow group membership and the regression coefficients to be estimated simultaneously and our approach yields a principled choice of the number of distinct subpopulations. The results show three groups with different response patterns between prenatal methylmercury exposure and 19-month IQ in this population.

Two-stage hierarchical modeling for analysis of subpopulations in conditional distributions

In this work, we develop modeling and estimation approach for the analysis of cross-sectional clustered data with multimodal conditional distributions where the main interest is in analysis of subpopulations. It is proposed to model such data in a hierarchical model with conditional distributions viewed as finite mixtures of normal components. With a large number of observations in the lowest level clusters, a two-stage estimation approach is used. In the first stage, the normal mixture parameters in each lowest level cluster are estimated using robust methods. Robust alternatives to the maximum likelihood estimation are used to provide stable results even for data with conditional distributions such that their components may not quite meet normality assumptions. Then the lowest level cluster-specific means and standard deviations are modeled in a mixed effects model in the second stage. A small simulation study was conducted to compare performance of finite normal mixture population parameter estimates based on robust and maximum likelihood estimation in stage 1. The proposed modeling approach is illustrated through the analysis of mice tendon fibril diameters data. Analyses results address genotype differences between corresponding components in the mixtures and demonstrate advantages of robust estimation in stage 1.

Bimodal distribution of glucose is not universally useful for diagnosing diabetes

OBJECTIVE

Bimodality in the distribution of glucose has been used to define the cut point for the diagnosis of diabetes. Previous studies on bimodality have primarily been in populations with a high prevalence of type 2 diabetes, including one study in a white Caucasian population. All studies included participants with known diabetes. The aim of this study was to assess whether a bimodal structure is a general phenomenon in fasting plasma glucose (FPG) and 2-h plasma glucose that is useful for deriving a common cut point for diabetes in populations of different origin, both including and excluding known diabetes.

RESEARCH DESIGN AND METHODS

The Evaluation of Screening and Early Detection Strategies for Type 2 Diabetes and Impaired Glucose Tolerance (DETECT-2) project is an international collaboration pooling surveys from all continents. These studies include surveys in which plasma glucose was measured during an oral glucose tolerance test; in total, 43 studies (135,383 participants) from 27 countries were included. A mixture of two normal distributions was fitted to plasma glucose levels, and a cut point for normal glycemia was estimated as their intersection. In populations with a biologically meaningful cut point, bimodality was tested for significance.

RESULTS

Distributions of FPG and 2-h plasma glucose did not, in general, produce bimodal structures useful for deriving cut points for diabetes. When present, the cut points produced were inconsistent over geographical regions.

CONCLUSIONS

Deriving cut points for normal glycemia from distributions of FPG and 2-h plasma glucose does not appear to be suitable for defining diagnostic cut points for diabetes.