A Latent Class Model with Hidden Markov Dependence for Array CGH Data

Summary Array CGH is a high‐throughput technique designed to detect genomic alterations linked to the development and progression of cancer. The technique yields fluorescence ratios that characterize DNA copy number change in tumor versus healthy cells. Classification of tumors based on aCGH profiles is of scientific interest but the analysis of these data is complicated by the large number of highly correlated measures. In this article, we develop a supervised Bayesian latent class approach for classification that relies on a hidden Markov model to account for the dependence in the intensity ratios. Supervision means that classification is guided by a clinical endpoint. Posterior inferences are made about class‐specific copy number gains and losses. We demonstrate our technique on a study of brain tumors, for which our approach is capable of identifying subsets of tumors with different genomic profiles, and differentiates classes by survival much better than unsupervised methods.     

A Bayesian Two‐Part Latent Class Model for Longitudinal Medical Expenditure Data: Assessing the Impact of Mental Health and Substance Abuse Parity

Summary In 2001, the U.S. Office of Personnel Management required all health plans participating in the Federal Employees Health Benefits Program to offer mental health and substance abuse benefits on par with general medical benefits. The initial evaluation found that, on average, parity did not result in either large spending increases or increased service use over the four‐year observational period. However, some groups of enrollees may have benefited from parity more than others. To address this question, we propose a Bayesian two‐part latent class model to characterize the effect of parity on mental health use and expenditures. Within each class, we fit a two‐part random effects model to separately model the probability of mental health or substance abuse use and mean spending trajectories among those having used services. The regression coefficients and random effect covariances vary across classes, thus permitting class‐varying correlation structures between the two components of the model. Our analysis identified three classes of subjects: a group of low spenders that tended to be male, had relatively rare use of services, and decreased their spending pattern over time; a group of moderate spenders, primarily female, that had an increase in both use and mean spending after the introduction of parity; and a group of high spenders that tended to have chronic service use and constant spending patterns. By examining the joint 95% highest probability density regions of expected changes in use and spending for each class, we confirmed that parity had an impact only on the moderate spender class.     

A Semiparametric Joint Model for Longitudinal and Survival Data with Application to Hemodialysis Study

Summary .  In many longitudinal clinical studies, the level and progression rate of repeatedly measured biomarkers on each subject quantify the severity of the disease and that subject's susceptibility to progression of the disease. It is of scientific and clinical interest to relate such quantities to a later time-to-event clinical endpoint such as patient survival. This is usually done with a shared parameter model. In such models, the longitudinal biomarker data and the survival outcome of each subject are assumed to be conditionally independent given subject-level severity or susceptibility (also called frailty in statistical terms). In this article, we study the case where the conditional distribution of longitudinal data is modeled by a linear mixed-effect model, and the conditional distribution of the survival data is given by a Cox proportional hazard model. We allow unknown regression coefficients and time-dependent covariates in both models. The proposed estimators are maximizers of an exact correction to the joint log likelihood with the frailties eliminated as nuisance parameters, an idea that originated from correction of covariate measurement error in measurement error models. The corrected joint log likelihood is shown to be asymptotically concave and leads to consistent and asymptotically normal estimators. Unlike most published methods for joint modeling, the proposed estimation procedure does not rely on distributional assumptions of the frailties. The proposed method was studied in simulations and applied to a data set from the Hemodialysis Study.     

A Score Test for Association of a Longitudinal Marker and an Event with Missing Data

Summary : Often clinical studies periodically record information on disease progression as well as results from laboratory studies that are believed to reflect the progressing stages of the disease. A primary aim of such a study is to determine the relationship between the lab measurements and a disease progression. If there were no missing or censored data, these analyses would be straightforward. However, often patients miss visits, and return after their disease has progressed. In this case, not only is their progression time interval censored, but their lab test series is also incomplete. In this article, we propose a simple test for the association between a longitudinal marker and an event time from incomplete data. We derive the test using a very intuitive technique of calculating the expected complete data score conditional on the observed incomplete data (conditional expected score test, CEST). The problem was motivated by data from an observational study of patients with diabetes.     

Model for Heterogeneous Random Networks Using Continuous Latent Variables and an Application to a Tree–Fungus Network

Summary The mixture model is a method of choice for modeling heterogeneous random graphs, because it contains most of the known structures of heterogeneity: hubs, hierarchical structures, or community structure. One of the weaknesses of mixture models on random graphs is that, at the present time, there is no computationally feasible estimation method that is completely satisfying from a theoretical point of view. Moreover, mixture models assume that each vertex pertains to one group, so there is no place for vertices being at intermediate positions. The model proposed in this article is a grade of membership model for heterogeneous random graphs, which assumes that each vertex is a mixture of extremal hypothetical vertices. The connectivity properties of each vertex are deduced from those of the extreme vertices. In this new model, the vector of weights of each vertex are fixed continuous parameters. A model with a vector of parameters for each vertex is tractable because the number of observations is proportional to the square of the number of vertices of the network. The estimation of the parameters is given by the maximum likelihood procedure. The model is used to elucidate some of the processes shaping the heterogeneous structure of a well‐resolved network of host/parasite interactions.     

Bayesian Meta‐Analysis of the Accuracy of a Test for Tuberculous Pleuritis in the Absence of a Gold Standard Reference

Summary Absence of a perfect reference test is an acknowledged source of bias in diagnostic studies. In the case of tuberculous pleuritis, standard reference tests such as smear microscopy, culture and biopsy have poor sensitivity. Yet meta‐analyses of new tests for this disease have always assumed the reference standard is perfect, leading to biased estimates of the new test’s accuracy. We describe a method for joint meta‐analysis of sensitivity and specificity of the diagnostic test under evaluation, while considering the imperfect nature of the reference standard. We use a Bayesian hierarchical model that takes into account within‐ and between‐study variability. We show how to obtain pooled estimates of sensitivity and specificity, and how to plot a hierarchical summary receiver operating characteristic curve. We describe extensions of the model to situations where multiple reference tests are used, and where index and reference tests are conditionally dependent. The performance of the model is evaluated using simulations and illustrated using data from a meta‐analysis of nucleic acid amplification tests (NAATs) for tuberculous pleuritis. The estimate of NAAT specificity was higher and the sensitivity lower compared to a model that assumed that the reference test was perfect.     

Model selection and parameter estimation for ion channel recordings with an application to the K + outward-rectifier in barley leaf

We present a statistical method, and its accompanying algorithms, for the selection of a mathematical model of the gating mechanism of an ion channel and for the estimation of the parameters of this model. The method assumes a hidden Markov model that incorporates filtering, colored noise and state-dependent white excess noise for the recorded data. The model selection and parameter estimation are performed via a Bayesian approach using Markov chain Monte Carlo. The method is illustrated by its application to single-channel recordings of the K⁺ outward-rectifier in barley leaf.Acknowledgement The authors thank Sake Vogelzang, Bert van Duijn and Bert de Boer for their helpful advice and useful comments and suggestions.