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.

Truncated recombinant human SP-D attenuates emphysema and type II cell changes in SP-D deficient mice

BACKGROUND: Surfactant protein D (SP-D) deficient mice develop emphysema-like pathology associated with focal accumulations of foamy alveolar macrophages, an excess of surfactant phospholipids in the alveolar space and both hypertrophy and hyperplasia of alveolar type II cells. These findings are associated with a chronic inflammatory state. Treatment of SP-D deficient mice with a truncated recombinant fragment of human SP-D (rfhSP-D) has been shown to decrease the lipidosis and alveolar macrophage accumulation as well as production of proinflammatory chemokines. The aim of this study was to investigate if rfhSP-D treatment reduces the structural abnormalities in parenchymal architecture and type II cells characteristic of SP-D deficiency. METHODS: SP-D knock-out mice, aged 3 weeks, 6 weeks and 9 weeks were treated with rfhSP-D for 9, 6 and 3 weeks, respectively. All mice were sacrificed at age 12 weeks and compared to both PBS treated SP-D deficient and wild-type groups. Lung structure was quantified by design-based stereology at the light and electron microscopic level. Emphasis was put on quantification of emphysema, type II cell changes and intracellular surfactant. Data were analysed with two sided non-parametric Mann-Whitney U-test. MAIN RESULTS: After 3 weeks of treatment, alveolar number was higher and mean alveolar size was smaller compared to saline-treated SP-D knock-out controls. There was no significant difference concerning these indices of pulmonary emphysema within rfhSP-D treated groups. Type II cell number and size were smaller as a consequence of treatment. The total volume of lamellar bodies per type II cell and per lung was smaller after 6 weeks of treatment. CONCLUSION: Treatment of SP-D deficient mice with rfhSP-D leads to a reduction in the degree of emphysema and a correction of type II cell hyperplasia and hypertrophy. This supports the concept that rfhSP-D might become a therapeutic option in diseases that are characterized by decreased SP-D levels in the lung.

Combined treatment with zidovudine and lymphoblast interferon-alpha in patients with HIV-related Kaposi's sarcoma

A combination of oral zidovudine (250 mg twice daily) and subcutaneous interferon-alpha (10 x 10(6) units daily) was evaluated for clinical, antiretroviral, and immunological efficacy and for side effects in 17 patients with AIDS-related Kaposi's sarcoma. Fifteen patients were evaluable. During the study period of 12 weeks, tumor responses were complete in two patients and partial in two patients (27% major response rate). Minimal responses were seen in two patients (40% overall response rate). An anti-HIV effect (reduction of serum p24 antigen by 70% or more) was observed in seven of ten evaluable patients who were initially antigenemic. CD4 lymphocyte counts remained unchanged. In six patients who had either a tumor response or a marked decline of HIV antigenemia, the treatment was continued between 12 and 59 weeks beyond the study period. Two of four patients with tumor regression at 12 weeks had an additional tumor response in this period despite prior dose reduction of interferon due to toxicity. Late progression of KS was eventually observed in four of six patients on prolonged treatment. The responsiveness of Kaposi's sarcoma seen in this study in patients with low CD4 counts and prior constitutional symptoms (fever, weight loss) was unexpected and needs further confirmation by larger patient groups. Dose-limiting toxicities were bone marrow depression (severe anemia in four and neutropenia with anemia in two patients), subjective adverse experiences (fever, fatigue, myalgia; four patients) and both (two patients).(ABSTRACT TRUNCATED AT 250 WORDS)

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.