Influence diagnostics in Gaussian spatial linear models

Spatial linear models have been applied in numerous fields such as agriculture, geoscience and environmental sciences, among many others. Spatial dependence structure modelling, using a geostatistical approach, is an indispensable tool to estimate the parameters that define this structure. However, this estimation may be greatly affected by the presence of atypical observations in the sampled data. The purpose of this paper is to use diagnostic techniques to assess the sensitivity of the maximum-likelihood estimators, covariance functions and linear predictor to small perturbations in the data and/or the spatial linear model assumptions. The methodology is illustrated with two real data sets. The results allowed us to conclude that the presence of atypical values in the sample data have a strong influence on thematic maps, changing the spatial dependence structure.

The importance of plant life form on spatial associations along a subtropical coastal dune gradient

Questions Does the spatial association between isolated adult trees and understorey plants change along a gradient of sand dunes? Does this association depend on the life form of the understorey plant? Location Coastal sand dunes, southeast Brazil. Methods We recorded the occurrence of understorey plant species in 100 paired 0.25 m2 plots under adult trees and in adjacent treeless sites along an environmental gradient from beach to inland. Occurrence probabilities were modelled as a function of the fixed variables of the presence of a neighbour, distance from the seashore and life form, and a random variable, the block (i.e. the pair of plots). Generalized linear mixed models (GLMM) were fitted in a backward step-wise procedure using Akaike's information criterion (AIC) for model selection. Results The occurrence of understorey plants was affected by the presence of an adult tree neighbour, but the effect varied with the life form of the understorey species. Positive spatial association was found between isolated adult neighbour and young trees, whereas a negative association was found for shrubs. Moreover, a neutral association was found for lianas, whereas for herbs the effect of the presence of an adult neighbour ranged from neutral to negative, depended on the subgroup considered. The strength of the negative association with forbs increased with distance from the seashore. However, for the other life forms, the associational pattern with adult trees did not change along the gradient. Conclusions For most of the understorey life forms there is no evidence that the spatial association between isolated adult trees and understorey plants changes with the distance from the seashore, as predicted by the stress gradient hypothesis, a common hypothesis in the literature about facilitation in plant communities. Furthermore, the positive spatial association between isolated adult trees and young trees identified along the entire gradient studied indicates a positive feedback that explains the transition from open vegetation to forest in subtropical coastal dune environments.

Creep and damage models for the service behaviour of structural members

Deformability is often a crucial to the conception of many civil-engineering structural elements. Also, design is all the more burdensome if both long- and short-term deformability has to be considered. In this thesis, long- and short-term deformability has been studied from the material and the structural modelling point of view. Moreover, two materials have been handled: pultruded composites and concrete. A new finite element model for thin-walled beams has been introduced. As a main assumption, cross-sections rigid are considered rigid in their plane; this hypothesis replaces that of the classical beam theory of plane cross-sections in the deformed state. That also allows reducing the total number of degrees of freedom, and therefore making analysis faster compared with twodimensional finite elements. Longitudinal direction warping is left free, allowing describing phenomena such as the shear lag. The new finite-element model has been first applied to concrete thin-walled beams (such as roof high span girders or bridge girders) subject to instantaneous service loadings. Concrete in his cracked state has been considered through a smeared crack model for beams under bending. At a second stage, the FE-model has been extended to the viscoelastic field and applied to pultruded composite beams under sustained loadings. The generalized Maxwell model has been adopted. As far as materials are concerned, long-term creep tests have been carried out on pultruded specimens. Both tension and shear tests have been executed. Some specimen has been strengthened with carbon fibre plies to reduce short- and long- term deformability. Tests have been done in a climate room and specimens kept 2 years under constant load in time. As for concrete, a model for tertiary creep has been proposed. The basic idea is to couple the UMLV linear creep model with a damage model in order to describe nonlinearity. An effective strain tensor, weighting the total and the elasto-damaged strain tensors, controls damage evolution through the damage loading function. Creep strains are related to the effective stresses (defined by damage models) and so associated to the intact material.

Numerical modelling of fluid-structure interaction with application in hemodynamics

The thesis deals with numerical algorithms for fluid-structure interaction problems with application in blood flow modelling. It starts with a short introduction on the mathematical description of incompressible viscous flow with non-Newtonian viscosity and a moving linear viscoelastic structure. The mathematical model consists of the generalized Navier-Stokes equation used for the description of fluid flow and the generalized string model for structure movement. The arbitrary Lagrangian-Eulerian approach is used in order to take into account moving computational domain. A part of the thesis is devoted to the discussion on the non-Newtonian behaviour of shear-thinning fluids, which is in our case blood, and derivation of two non-Newtonian models frequently used in the blood flow modelling. Further we give a brief overview on recent fluid-structure interaction schemes with discussion about the difficulties arising in numerical modelling of blood flow. Our main contribution lies in numerical and experimental study of a new loosely-coupled partitioned scheme called the kinematic splitting fluid-structure interaction algorithm. We present stability analysis for a coupled problem of non-Newtonian shear-dependent fluids in moving domains with viscoelastic boundaries. Here, we assume both, the nonlinearity in convective as well is diffusive term. We analyse the convergence of proposed numerical scheme for a simplified fluid model of the Oseen type. Moreover, we present series of experiments including numerical error analysis, comparison of hemodynamic parameters for the Newtonian and non-Newtonian fluids and comparison of several physiologically relevant computational geometries in terms of wall displacement and wall shear stress. Numerical analysis and extensive experimental study for several standard geometries confirm reliability and accuracy of the proposed kinematic splitting scheme in order to approximate fluid-structure interaction problems.

Body mass index, hormone replacement therapy, and endometrial cancer risk: a meta-analysis

Background: Body mass index (BMI) is a risk factor for endometrial cancer. We quantified the risk and investigated whether the association differed by use of hormone replacement therapy (HRT), menopausal status, and histologic type. Methods: We searched MEDLINE and EMBASE (1966 to December 2009) to identify prospective studies of BMI and incident endometrial cancer. We did random-effects meta-analyses, meta-regressions, and generalized least square regressions for trend estimations assuming linear, and piecewise linear, relationships. Results: Twenty-four studies (17,710 cases) were analyzed; 9 studies contributed to analyses by HRT, menopausal status, or histologic type, all published since 2003. In the linear model, the overall risk ratio (RR) per 5 kg/m2 increase in BMI was 1.60 (95% CI, 1.52–1.68), P < 0.0001. In the piecewise model, RRs compared with a normal BMI were 1.22 (1.19–1.24), 2.09 (1.94–2.26), 4.36 (3.75–5.10), and 9.11 (7.26–11.51) for BMIs of 27, 32, 37, and 42 kg/m2, respectively. The association was stronger in never HRT users than in ever users: RRs were 1.90 (1.57–2.31) and 1.18 (95% CI, 1.06–1.31) with P for interaction ¼ 0.003. In the piecewise model, the RR in never users was 20.70 (8.28–51.84) at BMI 42 kg/m2, compared with never users at normal BMI. The association was not affected by menopausal status (P ¼ 0.34) or histologic type (P ¼ 0.26). Conclusions: HRT use modifies the BMI-endometrial cancer risk association. Impact: These findings support the hypothesis that hyperestrogenia is an important mechanism underlying the BMI-endometrial cancer association, whilst the presence of residual risk in HRT users points to the role of additional systems. Cancer Epidemiol Biomarkers Prev; 19(12); 3119–30.

Coping personality type and environmental enrichment affect aggression at weaning in pigs

This study investigated the effects of different environmental treatments and personality types on aggression at mixing of newly weaned domestic piglets. From birth to weaning, 16 litters were housed with their dams in either barren (B) or larger, substrate-enriched (E) environments. At 15 days old, piglets were classified as 'high' (HR) or low resistant' (LR) in a manual restraint test (backtest), which is thought to identify proactive (HR) and reactive (LR) stress coping strategies that may reflect different personality types. At 30 days old, 128 piglets were weaned, relocated and mixed into 32 pens comprising two HR and two LR unfamiliar pigs, balanced for sex and weaning weight. Eight B and eight E groups changed environmental condition whereas the others remained in the same type of environment. Number and duration of fights. fight outcomes and unilateral fighting were scored for 5 h post-mixing and skin lesions were counted before and 5 h, 1 day and 2 days after mixing. On the day following weaning, fighting and also exploratory and oral manipulative behaviours were measured for 6 h. Generalized Linear Mixed Model analyses suggested interactions between pre-weaning environment, post-weaning environment and personality type. Overall, pre-weaning E pigs had longer fights at weaning and mixing (P=0.01) and fought for longer on the next day (P=0.02) than pre-weaning B pigs, and inflicted more skin lesions (P=0.02). Post-weaning enrichment did not affect fighting at mixing but reduced the time spent fighting the next day (P=0.03). Personality had subtle and environment-dependent effects on fighting, and influenced the "structure" rather than the amount of aggressive behaviour. HR pigs, for instance, bullied (i.e. chased surrendering pigs) more often (P=0.009) and their fighting behaviour was less affected by their relative body weight than that of LR pigs. Post-weaning E pigs showed relatively higher levels of exploratory behaviour (P=0.02) and less oral manipulative behaviour (P=0.04) than post-weaning B pigs. In particular, switching from a good quality environment (E) to a worse quality one (B) at weaning decreased exploratory behaviour on the next day, especially for LR pigs, who also tended to fight with and orally manipulate their pen mates more in that condition, and seemed to be more affected by a deterioration of the environment. Overall, pre-weaning enrichment increased aggression after weaning whereas post-weaning enrichment reduced it, and personality type related to some aspects of fighting behaviour. (C) 2011 Elsevier B.V. All rights reserved.

Robust Inferences For Covariate Effects On Survival Time With Censored Linear Regression Models

Various inference procedures for linear regression models with censored failure times have been studied extensively. Recent developments on efficient algorithms to implement these procedures enhance the practical usage of such models in survival analysis. In this article, we present robust inferences for certain covariate effects on the failure time in the presence of "nuisance" confounders under a semiparametric, partial linear regression setting. Specifically, the estimation procedures for the regression coefficients of interest are derived from a working linear model and are valid even when the function of the confounders in the model is not correctly specified. The new proposals are illustrated with two examples and their validity for cases with practical sample sizes is demonstrated via a simulation study.

Computational Techniques for Spatial Logistic Regression with Large Datasets

In epidemiological work, outcomes are frequently non-normal, sample sizes may be large, and effects are often small. To relate health outcomes to geographic risk factors, fast and powerful methods for fitting spatial models, particularly for non-normal data, are required. We focus on binary outcomes, with the risk surface a smooth function of space. We compare penalized likelihood models, including the penalized quasi-likelihood (PQL) approach, and Bayesian models based on fit, speed, and ease of implementation. A Bayesian model using a spectral basis representation of the spatial surface provides the best tradeoff of sensitivity and specificity in simulations, detecting real spatial features while limiting overfitting and being more efficient computationally than other Bayesian approaches. One of the contributions of this work is further development of this underused representation. The spectral basis model outperforms the penalized likelihood methods, which are prone to overfitting, but is slower to fit and not as easily implemented. Conclusions based on a real dataset of cancer cases in Taiwan are similar albeit less conclusive with respect to comparing the approaches. The success of the spectral basis with binary data and similar results with count data suggest that it may be generally useful in spatial models and more complicated hierarchical models.

ON MARGINALIZED MULTILEVEL MODELS AND THEIR COMPUTATION

Clustered data analysis is characterized by the need to describe both systematic variation in a mean model and cluster-dependent random variation in an association model. Marginalized multilevel models embrace the robustness and interpretations of a marginal mean model, while retaining the likelihood inference capabilities and flexible dependence structures of a conditional association model. Although there has been increasing recognition of the attractiveness of marginalized multilevel models, there has been a gap in their practical application arising from a lack of readily available estimation procedures. We extend the marginalized multilevel model to allow for nonlinear functions in both the mean and association aspects. We then formulate marginal models through conditional specifications to facilitate estimation with mixed model computational solutions already in place. We illustrate this approach on a cerebrovascular deficiency crossover trial.

RANDOM EFFECTS MODELS IN A META-ANALYSIS OF THE ACCURACY OF DIAGNOSTIC TESTS WITHIN A GOLD STANDARD IN THE PRESENCE OF MISSING DATA

In evaluating the accuracy of diagnosis tests, it is common to apply two imperfect tests jointly or sequentially to a study population. In a recent meta-analysis of the accuracy of microsatellite instability testing (MSI) and traditional mutation analysis (MUT) in predicting germline mutations of the mismatch repair (MMR) genes, a Bayesian approach (Chen, Watson, and Parmigiani 2005) was proposed to handle missing data resulting from partial testing and the lack of a gold standard. In this paper, we demonstrate an improved estimation of the sensitivities and specificities of MSI and MUT by using a nonlinear mixed model and a Bayesian hierarchical model, both of which account for the heterogeneity across studies through study-specific random effects. The methods can be used to estimate the accuracy of two imperfect diagnostic tests in other meta-analyses when the prevalence of disease, the sensitivities and/or the specificities of diagnostic tests are heterogeneous among studies. Furthermore, simulation studies have demonstrated the importance of carefully selecting appropriate random effects on the estimation of diagnostic accuracy measurements in this scenario.

Monte Carlo source model for photon beam radiotherapy: photon source characteristics

A major barrier to widespread clinical implementation of Monte Carlo dose calculation is the difficulty in characterizing the radiation source within a generalized source model. This work aims to develop a generalized three-component source model (target, primary collimator, flattening filter) for 6- and 18-MV photon beams that match full phase-space data (PSD). Subsource by subsource comparison of dose distributions, using either source PSD or the source model as input, allows accurate source characterization and has the potential to ease the commissioning procedure, since it is possible to obtain information about which subsource needs to be tuned. This source model is unique in that, compared to previous source models, it retains additional correlations among PS variables, which improves accuracy at nonstandard source-to-surface distances (SSDs). In our study, three-dimensional (3D) dose calculations were performed for SSDs ranging from 50 to 200 cm and for field sizes from 1 x 1 to 30 x 30 cm2 as well as a 10 x 10 cm2 field 5 cm off axis in each direction. The 3D dose distributions, using either full PSD or the source model as input, were compared in terms of dose-difference and distance-to-agreement. With this model, over 99% of the voxels agreed within +/-1% or 1 mm for the target, within 2% or 2 mm for the primary collimator, and within +/-2.5% or 2 mm for the flattening filter in all cases studied. For the dose distributions, 99% of the dose voxels agreed within 1% or 1 mm when the combined source model-including a charged particle source and the full PSD as input-was used. The accurate and general characterization of each photon source and knowledge of the subsource dose distributions should facilitate source model commissioning procedures by allowing scaling the histogram distributions representing the subsources to be tuned.

Estimating the prevalence of comorbid conditions and their effect on health care costs in patients with diabetes mellitus in Switzerland.

BACKGROUND Estimating the prevalence of comorbidities and their associated costs in patients with diabetes is fundamental to optimizing health care management. This study assesses the prevalence and health care costs of comorbid conditions among patients with diabetes compared with patients without diabetes. Distinguishing potentially diabetes- and nondiabetes-related comorbidities in patients with diabetes, we also determined the most frequent chronic conditions and estimated their effect on costs across different health care settings in Switzerland. METHODS Using health care claims data from 2011, we calculated the prevalence and average health care costs of comorbidities among patients with and without diabetes in inpatient and outpatient settings. Patients with diabetes and comorbid conditions were identified using pharmacy-based cost groups. Generalized linear models with negative binomial distribution were used to analyze the effect of comorbidities on health care costs. RESULTS A total of 932,612 persons, including 50,751 patients with diabetes, were enrolled. The most frequent potentially diabetes- and nondiabetes-related comorbidities in patients older than 64 years were cardiovascular diseases (91%), rheumatologic conditions (55%), and hyperlipidemia (53%). The mean total health care costs for diabetes patients varied substantially by comorbidity status (US$3,203-$14,223). Patients with diabetes and more than two comorbidities incurred US$10,584 higher total costs than patients without comorbidity. Costs were significantly higher in patients with diabetes and comorbid cardiovascular disease (US$4,788), hyperlipidemia (US$2,163), hyperacidity disorders (US$8,753), and pain (US$8,324) compared with in those without the given disease. CONCLUSION Comorbidities in patients with diabetes are highly prevalent and have substantial consequences for medical expenditures. Interestingly, hyperacidity disorders and pain were the most costly conditions. Our findings highlight the importance of developing strategies that meet the needs of patients with diabetes and comorbidities. Integrated diabetes care such as used in the Chronic Care Model may represent a useful strategy.

Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

Using spatial linear models with SAR and CAR structure to examine Texas lung cancer incidence rates

Scholars have found that socioeconomic status was one of the key factors that influenced early-stage lung cancer incidence rates in a variety of regions. This thesis examined the association between median household income and lung cancer incidence rates in Texas counties. A total of 254 individual counties in Texas with corresponding lung cancer incidence rates from 2004 to 2008 and median household incomes in 2006 were collected from the National Cancer Institute Surveillance System. A simple linear model and spatial linear models with two structures, Simultaneous Autoregressive Structure (SAR) and Conditional Autoregressive Structure (CAR), were used to link median household income and lung cancer incidence rates in Texas. The residuals of the spatial linear models were analyzed with Moran's I and Geary's C statistics, and the statistical results were used to detect similar lung cancer incidence rate clusters and disease patterns in Texas.^