Checking Assumptions in Latent Class Regression Models via a Markov Chain Monte Carlo Estimation Approach: An Application to Depression and Socio-Economic Status

Latent class regression models are useful tools for assessing associations between covariates and latent variables. However, evaluation of key model assumptions cannot be performed using methods from standard regression models due to the unobserved nature of latent outcome variables. This paper presents graphical diagnostic tools to evaluate whether or not latent class regression models adhere to standard assumptions of the model: conditional independence and non-differential measurement. An integral part of these methods is the use of a Markov Chain Monte Carlo estimation procedure. Unlike standard maximum likelihood implementations for latent class regression model estimation, the MCMC approach allows us to calculate posterior distributions and point estimates of any functions of parameters. It is this convenience that allows us to provide the diagnostic methods that we introduce. As a motivating example we present an analysis focusing on the association between depression and socioeconomic status, using data from the Epidemiologic Catchment Area study. We consider a latent class regression analysis investigating the association between depression and socioeconomic status measures, where the latent variable depression is regressed on education and income indicators, in addition to age, gender, and marital status variables. While the fitted latent class regression model yields interesting results, the model parameters are found to be invalid due to the violation of model assumptions. The violation of these assumptions is clearly identified by the presented diagnostic plots. These methods can be applied to standard latent class and latent class regression models, and the general principle can be extended to evaluate model assumptions in other types of models.

A Mechanistic Latent Variable Model for Estimating Drug Concentrations in the Male Genital Tract

The purpose of this study is to develop statistical methodology to facilitate indirect estimation of the concentration of antiretroviral drugs and viral loads in the prostate gland and the seminal vesicle. The differences in antiretroviral drug concentrations in these organs may lead to suboptimal concentrations in one gland compared to the other. Suboptimal levels of the antiretroviral drugs will not be able to fully suppress the virus in that gland, lead to a source of sexually transmissible virus and increase the chance of selecting for drug resistant virus. This information may be useful selecting antiretroviral drug regimen that will achieve optimal concentrations in most of male genital tract glands. Using fractionally collected semen ejaculates, Lundquist (1949) measured levels of surrogate markers in each fraction that are uniquely produced by specific male accessory glands. To determine the original glandular concentrations of the surrogate markers, Lundquist solved a simultaneous series of linear equations. This method has several limitations. In particular, it does not yield a unique solution, it does not address measurement error, and it disregards inter-subject variability in the parameters. To cope with these limitations, we developed a mechanistic latent variable model based on the physiology of the male genital tract and surrogate markers. We employ a Bayesian approach and perform a sensitivity analysis with regard to the distributional assumptions on the random effects and priors. The model and Bayesian approach is validated on experimental data where the concentration of a drug should be (biologically) differentially distributed between the two glands. In this example, the Bayesian model-based conclusions are found to be robust to model specification and this hierarchical approach leads to more scientifically valid conclusions than the original methodology. In particular, unlike existing methods, the proposed model based approach was not affected by a common form of outliers.

Multilevel Latent Class Models with Dirichlet Mixing Distribution

Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social sciences and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this paper, we develop multilevel latent class model, in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the Expectation-Maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. We also show that a simple latent class analysis, combined with robust standard errors, provides another consistent, robust, but less efficient inferential procedure. Simulation studies suggest that the three methods work well in finite samples, and that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the Obsessive Compulsive Disorder study. Our models' random effects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for latent class analysis of multilevel data.

Detection of latent tuberculosis in immunosuppressed patients with autoimmune diseases: performance of a Mycobacterium tuberculosis antigen-specific interferon gamma assay

OBJECTIVE: To analyse the performance of a new M. tuberculosis-specific interferon gamma (IFNgamma) assay in patients with chronic inflammatory diseases who receive immunosuppressive drugs, including tumour necrosis factor alpha (TNFalpha) inhibitors. METHODS: Cellular immune responses to the M. tuberculosis-specific antigens ESAT-6, CFP-10, TB7.7 were prospectively studied in 142 consecutive patients treated for inflammatory rheumatic conditions. Results were compared with tuberculin skin tests (TSTs). Association of both tests with risk factors for latent M. tuberculosis infection (LTBI) and BCG vaccination were determined and the influence of TNFalpha inhibitors, corticosteroids, and disease modifying antirheumatic drugs (DMARDs) on antigen-specific and mitogen-induced IFNgamma secretion was analysed. RESULTS: 126/142 (89%) patients received immunosuppressive therapy. The IFNgamma assay was more closely associated with the presence of risk factors (odds ratio (OR) = 23.8 (95% CI 5.14 to 110) vs OR = 2.77 (1.22 to 6.27), respectively; p = 0.009), but less associated with BCG vaccination than the TST (OR = 0.47 (95% CI 0.15 to 1.47) vs OR = 2.44 (0.74 to (8.01), respectively; p = 0.025). Agreement between the IFNgamma assay and TST results was low (kappa = 0.17; 95% CI 0.02 to 0.32). The odds for a positive IFNgamma assay strongly increased with increasing prognostic relevance of LTBI risk factors. Neither corticosteroids nor conventional DMARDs significantly affected IFNgamma responses, but the odds for a positive IFNgamma assay were decreased in patients treated with TNFalpha inhibitors (OR = 0.21 (95% CI 0.07 to 0.63), respectively; p = 0.006). CONCLUSIONS: These results demonstrate that the performance of the M. tuberculosis antigen-specific IFNgamma ELISA is better than the classic TST for detection of LTBI in patients receiving immunosuppressive therapy for treatment of systemic autoimmune disorders.

Distinguishing phenotypes of childhood wheeze and cough using latent class analysis

Airway disease in childhood comprises a heterogeneous group of disorders. Attempts to distinguish different phenotypes have generally considered few disease dimensions. The present study examines phenotypes of childhood wheeze and chronic cough, by fitting a statistical model to data representing multiple disease dimensions. From a population-based, longitudinal cohort study of 1,650 preschool children, 319 with parent-reported wheeze or chronic cough were included. Phenotypes were identified by latent class analysis using data on symptoms, skin-prick tests, lung function and airway responsiveness from two preschool surveys. These phenotypes were then compared with respect to outcome at school age. The model distinguished three phenotypes of wheeze and two phenotypes of chronic cough. Subsequent wheeze, chronic cough and inhaler use at school age differed clearly between the five phenotypes. The wheeze phenotypes shared features with previously described entities and partly reconciled discrepancies between existing sets of phenotype labels. This novel, multidimensional approach has the potential to identify clinically relevant phenotypes, not only in paediatric disorders but also in adult obstructive airway diseases, where phenotype definition is an equally important issue.

Computational simulations of latent heat thermal energy storage systems - with innovative and first-principles based simulation for the underlying unsteady melting (and solidification) processes

This thesis develops an effective modeling and simulation procedure for a specific thermal energy storage system commonly used and recommended for various applications (such as an auxiliary energy storage system for solar heating based Rankine cycle power plant). This thermal energy storage system transfers heat from a hot fluid (termed as heat transfer fluid - HTF) flowing in a tube to the surrounding phase change material (PCM). Through unsteady melting or freezing process, the PCM absorbs or releases thermal energy in the form of latent heat. Both scientific and engineering information is obtained by the proposed first-principle based modeling and simulation procedure. On the scientific side, the approach accurately tracks the moving melt-front (modeled as a sharp liquid-solid interface) and provides all necessary information about the time-varying heat-flow rates, temperature profiles, stored thermal energy, etc. On the engineering side, the proposed approach is unique in its ability to accurately solve – both individually and collectively – all the conjugate unsteady heat transfer problems for each of the components of the thermal storage system. This yields critical system level information on the various time-varying effectiveness and efficiency parameters for the thermal storage system.

Multivariate modelling of responses to conditional items: New possibilities for latent class analysis

Questionnaire data may contain missing values because certain questions do not apply to all respondents. For instance, questions addressing particular attributes of a symptom, such as frequency, triggers or seasonality, are only applicable to those who have experienced the symptom, while for those who have not, responses to these items will be missing. This missing information does not fall into the category 'missing by design', rather the features of interest do not exist and cannot be measured regardless of survey design. Analysis of responses to such conditional items is therefore typically restricted to the subpopulation in which they apply. This article is concerned with joint multivariate modelling of responses to both unconditional and conditional items without restricting the analysis to this subpopulation. Such an approach is of interest when the distributions of both types of responses are thought to be determined by common parameters affecting the whole population. By integrating the conditional item structure into the model, inference can be based both on unconditional data from the entire population and on conditional data from subjects for whom they exist. This approach opens new possibilities for multivariate analysis of such data. We apply this approach to latent class modelling and provide an example using data on respiratory symptoms (wheeze and cough) in children. Conditional data structures such as that considered here are common in medical research settings and, although our focus is on latent class models, the approach can be applied to other multivariate models.

Novel screening tools for latent tuberculosis: time to leave an old friend?

PURPOSE OF REVIEW: Therapeutic inhibition of tumour necrosis factor-alpha strongly increases the risk of reactivation in latent tuberculosis infection. Recent blood tests based on antigen-specific T cell response and measuring production of interferon-gamma, so called interferon-gamma release assays (IGRAs), are promising novel tools to identify infected patients. The performance of diagnostic testing for latent tuberculosis infection in patients with rheumatic diseases will be discussed. RECENT FINDINGS: In patients with rheumatoid arthritis, IGRAs are more sensitive and more specific than traditional tuberculin skin testing. They are unaffected by Bacillus-Calmette-Guérin vaccination and most nontuberculous mycobacteria. Most comparative studies show a better performance of the IGRAs than tuberculin skin testing in terms of a higher specificity. The rate of indeterminate results may be affected by glucocorticoids and the underlying disease but appears independent of disease-modifying antirheumatic drugs. Despite using identical Mycobacterium tuberculosis antigens, the two commercially available tests show differences in clinical performance. SUMMARY: The current information about the performance of the tuberculin skin testing and the IGRAs in the detection of latent tuberculosis infection in patients with rheumatic diseases strongly suggest a clinically relevant advantage of the IGRAs. Their use will help to reduce overuse and underuse of preventive treatment in tumour necrosis factor inhibition.

Incorporating Latent Variables into Discrete Choice Models - A Simultaneous Estimation Approach Using SEM Software

Integrated choice and latent variable (ICLV) models represent a promising new class of models which merge classic choice models with the structural equation approach (SEM) for latent variables. Despite their conceptual appeal, applications of ICLV models in marketing remain rare. We extend previous ICLV applications by first estimating a multinomial choice model and, second, by estimating hierarchical relations between latent variables. An empirical study on travel mode choice clearly demonstrates the value of ICLV models to enhance the understanding of choice processes. In addition to the usually studied directly observable variables such as travel time, we show how abstract motivations such as power and hedonism as well as attitudes such as a desire for flexibility impact on travel mode choice. Furthermore, we show that it is possible to estimate such a complex ICLV model with the widely available structural equation modeling package Mplus. This finding is likely to encourage more widespread application of this appealing model class in the marketing field.

Social Meets Molecular: Combining Phylogenetic and Latent Class Analyses to Understand HIV-1 Transmission in Switzerland

Switzerland has a complex human immunodeficiency virus (HIV) epidemic involving several populations. We examined transmission of HIV type 1 (HIV-1) in a national cohort study. Latent class analysis was used to identify socioeconomic and behavioral groups among 6,027 patients enrolled in the Swiss HIV Cohort Study between 2000 and 2011. Phylogenetic analysis of sequence data, available for 4,013 patients, was used to identify transmission clusters. Concordance between sociobehavioral groups and transmission clusters was assessed in correlation and multiple correspondence analyses. A total of 2,696 patients were infected with subtype B, 203 with subtype C, 196 with subtype A, and 733 with recombinant subtypes (mainly CRF02_AG and CRF01_AE). Latent class analysis identified 8 patient groups. Most transmission clusters of subtype B were shared between groups of gay men (groups 1-3) or between the heterosexual groups "heterosexual people of lower socioeconomic position" (group 4) and "injection drug users" (group 8). Clusters linking homosexual and heterosexual groups were associated with "older heterosexual and gay people on welfare" (group 5). "Migrant women in heterosexual partnerships" (group 6) and "heterosexual migrants on welfare" (group 7) shared non-B clusters with groups 4 and 5. Combining approaches from social and molecular epidemiology can provide insights into HIV-1 transmission and inform the design of prevention strategies.