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.

Fixed-Width Output Analysis for Markov Chain Monte Carlo

Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a complicated target distribution via simple ergodic averages. A fundamental question in MCMC applications is when should the sampling stop? That is, when are the ergodic averages good estimates of the desired quantities? We consider a method that stops the MCMC sampling the first time the width of a confidence interval based on the ergodic averages is less than a user-specified value. Hence calculating Monte Carlo standard errors is a critical step in assessing the output of the simulation. In particular, we consider the regenerative simulation and batch means methods of estimating the variance of the asymptotic normal distribution. We describe sufficient conditions for the strong consistency and asymptotic normality of both methods and investigate their finite sample properties in a variety of examples.

A HIDDEN MARKOV MODEL FOR JOINT ESTIMATION OF GENOTYPE AND COPY NUMBER IN HIGH-THROUGHPUT SNP CHIPS

Amplifications and deletions of chromosomal DNA, as well as copy-neutral loss of heterozygosity have been associated with diseases processes. High-throughput single nucleotide polymorphism (SNP) arrays are useful for making genome-wide estimates of copy number and genotype calls. Because neighboring SNPs in high throughput SNP arrays are likely to have dependent copy number and genotype due to the underlying haplotype structure and linkage disequilibrium, hidden Markov models (HMM) may be useful for improving genotype calls and copy number estimates that do not incorporate information from nearby SNPs. We improve previous approaches that utilize a HMM framework for inference in high throughput SNP arrays by integrating copy number, genotype calls, and the corresponding confidence scores when available. Using simulated data, we demonstrate how confidence scores control smoothing in a probabilistic framework. Software for fitting HMMs to SNP array data is available in the R package ICE.

COVARIATE-ADJUSTED NONPARAMETRIC ANALYSIS OF MAGNETIC RESONANCE IMAGES USING MARKOV CHAIN MONTE CARLO

Permutation tests are useful for drawing inferences from imaging data because of their flexibility and ability to capture features of the brain that are difficult to capture parametrically. However, most implementations of permutation tests ignore important confounding covariates. To employ covariate control in a nonparametric setting we have developed a Markov chain Monte Carlo (MCMC) algorithm for conditional permutation testing using propensity scores. We present the first use of this methodology for imaging data. Our MCMC algorithm is an extension of algorithms developed to approximate exact conditional probabilities in contingency tables, logit, and log-linear models. An application of our non-parametric method to remove potential bias due to the observed covariates is presented.

Glycoprotein Ib cross-linking/ligation on echicetin-coated surfaces or echicetin-IgMkappa in stirred suspension activates platelets by cytoskeleton modulated calcium release

Cross-linking platelet GPIb with the snake C-type lectin echicetin provides a specific technique for activation via this receptor. This allows GPIb-dependent mechanisms to be studied without the necessity for shear stress-induced binding of von Willebrand factor or primary alpha(IIb)beta(3) involvement. We already showed that platelets are activated, including tyrosine phosphorylation, by echicetin-IgMkappa-induced GPIb cross-linking. We now investigate the mechanism further and demonstrate that platelets, without modulator reagents, spread directly on an echicetin-coated surface, by a GPIb-specific mechanism, causing exocytosis of alpha-granule markers (P-selectin) and activation of alpha(IIb)beta(3). This spreading requires actin polymerization and release of internal calcium stores but is not dependent on external calcium nor on src family tyrosine kinases. Cross-linking of GPIb complex molecules on platelets, either in suspension or via specific surface attachment, is sufficient to induce platelet activation.

Acute and late toxicity in prostate cancer patients treated by dose escalated intensity modulated radiation therapy and organ tracking

BACKGROUND: To report acute and late toxicity in prostate cancer patients treated by dose escalated intensity-modulated radiation therapy (IMRT) and organ tracking. METHODS: From 06/2004 to 12/2005 39 men were treated by 80 Gy IMRT along with organ tracking. Median age was 69 years, risk of recurrence was low 18%, intermediate 21% and high in 61% patients. Hormone therapy (HT) was received by 74% of patients. Toxicity was scored according to the CTC scale version 3.0. Median follow-up (FU) was 29 months. RESULTS: Acute and maximal late grade 2 gastrointestinal (GI) toxicity was 3% and 8%, late grade 2 GI toxicity dropped to 0% at the end of FU. No acute or late grade 3 GI toxicity was observed. Grade 2 and 3 pre-treatment genitourinary (GU) morbidity (PGUM) was 20% and 5%. Acute and maximal late grade 2 GU toxicity was 56% and 28% and late grade 2 GU toxicity decreased to 15% of patients at the end of FU. Acute and maximal late grade 3 GU toxicity was 8% and 3%, respectively. Decreased late > or = grade 2 GU toxicity free survival was associated with higher age (P = .025), absence of HT (P = .016) and higher PGUM (P < .001). DISCUSSION: GI toxicity rates after IMRT and organ tracking are excellent, GU toxicity rates are strongly related to PGUM.

Hierarchical Markov Random Fields Applied to Model Soft Tissue Deformations on Graphics Hardware

Many methodologies dealing with prediction or simulation of soft tissue deformations on medical image data require preprocessing of the data in order to produce a different shape representation that complies with standard methodologies, such as mass–spring networks, finite element method s (FEM). On the other hand, methodologies working directly on the image space normally do not take into account mechanical behavior of tissues and tend to lack physics foundations driving soft tissue deformations. This chapter presents a method to simulate soft tissue deformations based on coupled concepts from image analysis and mechanics theory. The proposed methodology is based on a robust stochastic approach that takes into account material properties retrieved directly from the image, concepts from continuum mechanics and FEM. The optimization framework is solved within a hierarchical Markov random field (HMRF) which is implemented on the graphics processor unit (GPU See Graphics processing unit ).

Association of urethral toxicity with dose exposure in combined high-dose-rate brachytherapy and intensity-modulated radiation therapy in intermediate- and high-risk prostate cancer

INTRODUCTION: To report acute and late toxicities in patients with intermediate- and high-risk prostate cancer treated with combined high-dose-rate brachytherapy (HDR-B) and intensity-modulated radiation therapy (IMRT). MATERIALS AND METHODS: From March 2003 to September 2005, 64 men were treated with a single implant HDR-B with 21 Gy given in three fractions, followed by 50 Gy IMRT along with organ tracking. Median age was 66.1 years, and risk of recurrence was intermediate in 47% of the patients or high in 53% of the patients. Androgen deprivation therapy was received by 69% of the patients. Toxicity was scored according to the CTCAE version 3.0. Median follow-up was 3.1 years. RESULTS: Acute grade 3 genitourinary (GU) toxicity was observed in 7.8% of the patients, and late grades 3 and 4 GU toxicity was observed in 10.9% and 1.6% of the patients. Acute grade 3 gastrointestinal (GI) toxicity was experienced by 1.6% of the patients, and late grade 3 GI toxicity was absent. The urethral V(120) (urethral volume receiving > or =120% of the prescribed HDR-B dose) was associated with acute (P=.047) and late > or = grade 2 GU toxicities (P=.049). CONCLUSIONS: Late grades 3 and 4GU toxicity occurred in 10.9% and 1.6% of the patients after HDR-B followed by IMRT in association with the irradiated urethral volume. The impact of V(120) on GU toxicity should be validated in further studies.