Semiparametric Latent Variable Regression Models for Spatio-temporal Modeling of Mobile Source Particles in the Greater Boston Area

Traffic particle concentrations show considerable spatial variability within a metropolitan area. We consider latent variable semiparametric regression models for modeling the spatial and temporal variability of black carbon and elemental carbon concentrations in the greater Boston area. Measurements of these pollutants, which are markers of traffic particles, were obtained from several individual exposure studies conducted at specific household locations as well as 15 ambient monitoring sites in the city. The models allow for both flexible, nonlinear effects of covariates and for unexplained spatial and temporal variability in exposure. In addition, the different individual exposure studies recorded different surrogates of traffic particles, with some recording only outdoor concentrations of black or elemental carbon, some recording indoor concentrations of black carbon, and others recording both indoor and outdoor concentrations of black carbon. A joint model for outdoor and indoor exposure that specifies a spatially varying latent variable provides greater spatial coverage in the area of interest. We propose a penalised spline formation of the model that relates to generalised kringing of the latent traffic pollution variable and leads to a natural Bayesian Markov Chain Monte Carlo algorithm for model fitting. We propose methods that allow us to control the degress of freedom of the smoother in a Bayesian framework. Finally, we present results from an analysis that applies the model to data from summer and winter separately

DECOMPOSITION OF REGRESSION ESTIMATORS TO EXPLORE THE INFLUENCE OF "UNMEASURED" TIME-VARYING CONFOUNDERS

In environmental epidemiology, exposure X and health outcome Y vary in space and time. We present a method to diagnose the possible influence of unmeasured confounders U on the estimated effect of X on Y and to propose several approaches to robust estimation. The idea is to use space and time as proxy measures for the unmeasured factors U. We start with the time series case where X and Y are continuous variables at equally-spaced times and assume a linear model. We define matching estimator b(u)s that correspond to pairs of observations with specific lag u. Controlling for a smooth function of time, St, using a kernel estimator is roughly equivalent to estimating the association with a linear combination of the b(u)s with weights that involve two components: the assumptions about the smoothness of St and the normalized variogram of the X process. When an unmeasured confounder U exists, but the model otherwise correctly controls for measured confounders, the excess variation in b(u)s is evidence of confounding by U. We use the plot of b(u)s versus lag u, lagged-estimator-plot (LEP), to diagnose the influence of U on the effect of X on Y. We use appropriate linear combination of b(u)s or extrapolate to b(0) to obtain novel estimators that are more robust to the influence of smooth U. The methods are extended to time series log-linear models and to spatial analyses. The LEP plot gives us a direct view of the magnitude of the estimators for each lag u and provides evidence when models did not adequately describe the data.

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.

PENALIZED FUNCTIONAL REGRESSION

We develop fast fitting methods for generalized functional linear models. An undersmooth of the functional predictor is obtained by projecting on a large number of smooth eigenvectors and the coefficient function is estimated using penalized spline regression. Our method can be applied to many functional data designs including functions measured with and without error, sparsely or densely sampled. The methods also extend to the case of multiple functional predictors or functional predictors with a natural multilevel structure. Our approach can be implemented using standard mixed effects software and is computationally fast. Our methodology is motivated by a diffusion tensor imaging (DTI) study. The aim of this study is to analyze differences between various cerebral white matter tract property measurements of multiple sclerosis (MS) patients and controls. While the statistical developments proposed here were motivated by the DTI study, the methodology is designed and presented in generality and is applicable to many other areas of scientific research. An online appendix provides R implementations of all simulations.

Anemia is associated with abdominal aortic aneurysm (AAA) size and decreased long-term survival after endovascular AAA repair

OBJECTIVE: Anemia is a common comorbid condition in various inflammatory states and an established predictor of mortality in patients with chronic heart failure, ischemic heart disease, and end-stage renal disease. The present study of patients with abdominal aortic aneurysm (AAA) undergoing endovascular repair (EVAR) assessed the relationships between baseline hemoglobin concentration and AAA size, as well as anemia and long-term survival. METHODS: Between March 1994 and November 2006, 711 patients (65 women, mean age 75.8 +/- 7.8 years) underwent elective EVAR. Anemia was defined as a hemoglobin level <13 g/dL in men and <12 g/dL in women. Post-EVAR mean follow-up was 48.3 +/- 32.0 months. Association of hemoglobin level with AAA size was assessed with multiple linear regression. Mortality was determined with use of the internet-based Social Security Death Index and the electronic hospital record. Kaplan-Meier survival curves of anemic and nonanemic patient groups were compared by the log-rank method. Multivariable logistic regression models were used to determine the influence of anemia on vital status after EVAR. RESULTS: A total of 218/711 (30.7%) of AAA patients undergoing EVAR had anemia at baseline. After adjustment for various risk factors, hemoglobin level was inversely related to maximum AAA diameter (beta: - .144, 95%-CI: -1.482 - .322, P = .002). Post-EVAR survival was 65.5% at 5 years and 44.4% at 10 years. In long-term follow-up, survival was significantly lower in patients with anemia as compared to patients without anemia (P < .0001 by log-rank). Baseline hemoglobin levels were independently related to long-term mortality in multivariable Cox regression analysis adjusted for various risk factors (adjusted HR: 0.866, 95% CI: .783 to .958, P = .005). Within this model, statin use (adjusted HR: .517, 95% CI: .308 to .868, P = .013) was independently related to long-term survival, whereas baseline AAA diameter (adjusted HR: 1.022, 95% CI: 1.009 to 1.036, P = .001) was an independently associated with increased mortality. CONCLUSIONS: Baseline hemoglobin concentration is independently associated with AAA size and reduced long-term survival following EVAR. Thus, the presence or absence of anemia offers a potential refinement of existing risk stratification instruments.

Statins are associated with decreased mortality in abdominal, but not in thoracic aortic aneurysm patients undergoing endovascular repair: propensity score-adjusted analysis

BACKGROUND: Purpose of this study was to compare the correlation of statin use with long-term mortality in patients with abdominal (AAA) and thoracic aortic aneurysm (TAA). PATIENTS AND METHODS: We compared long-term survival of 731 AAA and 59 TAA patients undergoing elective endovascular repair (EVAR). Kaplan-Meier survival curves were compared by the log-rank method. Propensity score-adjusted multivariable logistic regression models were used to determine independent associations of statin use on vital status after EVAR. RESULTS: Statin use was associated with decreased long-term mortality in AAA patients in bivariate and multivariable regression analysis, in which the effect of propensity to receive a statin was considered (adjusted HR: .613, 95%-CI: .379- .993, p = .047) whereas mortality of TAA patients was not associated with use of statins (adjusted HR: 1.795, 95%-CI: .147 -21.942, p = .647). CONCLUSIONS: Use of statins is an independent predictor of decreased mortality after elective EVAR in AAA, but not in TAA patients. These findings indirectly support the concept of a distinct pathogenesis of AAA and TAA.

Towards greater accuracy in individual-tree mortality regression

Background mortality is an essential component of any forest growth and yield model. Forecasts of mortality contribute largely to the variability and accuracy of model predictions at the tree, stand and forest level. In the present study, I implement and evaluate state-of-the-art techniques to increase the accuracy of individual tree mortality models, similar to those used in many of the current variants of the Forest Vegetation Simulator, using data from North Idaho and Montana. The first technique addresses methods to correct for bias induced by measurement error typically present in competition variables. The second implements survival regression and evaluates its performance against the traditional logistic regression approach. I selected the regression calibration (RC) algorithm as a good candidate for addressing the measurement error problem. Two logistic regression models for each species were fitted, one ignoring the measurement error, which is the “naïve” approach, and the other applying RC. The models fitted with RC outperformed the naïve models in terms of discrimination when the competition variable was found to be statistically significant. The effect of RC was more obvious where measurement error variance was large and for more shade-intolerant species. The process of model fitting and variable selection revealed that past emphasis on DBH as a predictor variable for mortality, while producing models with strong metrics of fit, may make models less generalizable. The evaluation of the error variance estimator developed by Stage and Wykoff (1998), and core to the implementation of RC, in different spatial patterns and diameter distributions, revealed that the Stage and Wykoff estimate notably overestimated the true variance in all simulated stands, but those that are clustered. Results show a systematic bias even when all the assumptions made by the authors are guaranteed. I argue that this is the result of the Poisson-based estimate ignoring the overlapping area of potential plots around a tree. Effects, especially in the application phase, of the variance estimate justify suggested future efforts of improving the accuracy of the variance estimate. The second technique implemented and evaluated is a survival regression model that accounts for the time dependent nature of variables, such as diameter and competition variables, and the interval-censored nature of data collected from remeasured plots. The performance of the model is compared with the traditional logistic regression model as a tool to predict individual tree mortality. Validation of both approaches shows that the survival regression approach discriminates better between dead and alive trees for all species. In conclusion, I showed that the proposed techniques do increase the accuracy of individual tree mortality models, and are a promising first step towards the next generation of background mortality models. I have also identified the next steps to undertake in order to advance mortality models further.

Bayesian change-point analysis in linear regression model with scale mixtures of normal distributions

In this thesis, we consider Bayesian inference on the detection of variance change-point models with scale mixtures of normal (for short SMN) distributions. This class of distributions is symmetric and thick-tailed and includes as special cases: Gaussian, Student-t, contaminated normal, and slash distributions. The proposed models provide greater flexibility to analyze a lot of practical data, which often show heavy-tail and may not satisfy the normal assumption. As to the Bayesian analysis, we specify some prior distributions for the unknown parameters in the variance change-point models with the SMN distributions. Due to the complexity of the joint posterior distribution, we propose an efficient Gibbs-type with Metropolis- Hastings sampling algorithm for posterior Bayesian inference. Thereafter, following the idea of [1], we consider the problems of the single and multiple change-point detections. The performance of the proposed procedures is illustrated and analyzed by simulation studies. A real application to the closing price data of U.S. stock market has been analyzed for illustrative purposes.

Descriptive Statistics and Linear Regression

This morning Dr. Battle will introduce descriptive statistics and linear regression and how to apply these concepts in mathematical modeling. You will also learn how to use a spreadsheet to help with statistical analysis and to create graphs.

On Graphically Checking Goodness-of-fit of Binary Logistic Regression Models

OBJECTIVES: This paper is concerned with checking goodness-of-fit of binary logistic regression models. For the practitioners of data analysis, the broad classes of procedures for checking goodness-of-fit available in the literature are described. The challenges of model checking in the context of binary logistic regression are reviewed. As a viable solution, a simple graphical procedure for checking goodness-of-fit is proposed. METHODS: The graphical procedure proposed relies on pieces of information available from any logistic analysis; the focus is on combining and presenting these in an informative way. RESULTS: The information gained using this approach is presented with three examples. In the discussion, the proposed method is put into context and compared with other graphical procedures for checking goodness-of-fit of binary logistic models available in the literature. CONCLUSION: A simple graphical method can significantly improve the understanding of any logistic regression analysis and help to prevent faulty conclusions.

Immunohistochemical localization of RANK, RANKL and OPG in healthy and arthritic canine elbow joints

OBJECTIVE: To determine if the receptor activator of nuclear factor-kappaB-receptor activator of nuclear factor-kappaB ligand-osteoprotegerin (RANK-RANKL-OPG) system is active in bone remodeling in dogs and, if so, whether differences in expression of these mediators occur in healthy and arthritic joints. STUDY DESIGN: Experimental study. SAMPLE POPULATION: Fragmented processus coronoidei (n=20) were surgically removed from dogs with elbow arthritis and 5 corresponding healthy samples from dogs euthanatized for reasons other than elbow joint disease. METHODS: Bright-field immunohistochemistry and high-resolution fluorescence microscopy were used to investigate the distribution of RANK, RANKL, and OPG in healthy and arthritic joints. RESULTS: All 3 molecules were identified by immunostaining of canine bone tissue. In elbow dysplasia, the number of RANK-positive osteoclasts was increased. In their vicinity, cells expressing RANKL, a mediator of osteoclast activation, were abundant whereas the number of osteoblasts having the potential to limit osteoclastogenesis and bone resorption via OPG was few. CONCLUSIONS: The RANK-RANKL-OPG system is active in bone remodeling in dogs. In elbow dysplasia, a surplus of molecules promoting osteoclastogenesis was evident and is indicative of an imbalance between the mediators regulating bone resorption and bone formation. Both OPG and neutralizing antibodies against RANKL have the potential to counterbalance bone resorption. CLINICAL RELEVANCE: Therapeutic use of neutralizing antibodies against RANKL to inhibit osteoclast activation warrants further investigation.