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.

High-molecular weight adiponectin is independently associated with the extent of coronary artery disease in men

OBJECTIVE: Adiponectin has anti-atherogenic properties and low circulating adiponectin has been linked to coronary atherosclerosis. Yet, there is considerable evidence that the high-molecular weight (HMW) complex of adiponectin is the major active form of this adipokine. We therefore investigated whether HMW adiponectin is associated with the extent of coronary artery disease (CAD) in men. RESEARCH DESIGN AND METHODS: Associations among CAD, HMW adiponectin and the HMW/total-adiponectin ratio were assessed in 240 male patients undergoing elective coronary angiography. Total adiponectin and HMW adiponectin was measured by enzyme-linked immunosorbent assay and serum levels were correlated with defined coronary scores and established cardiovascular risk factors. RESULTS: We found significant inverse correlations between angiographic scores and HMW adiponectin [Extent Score (ES): r=-0.39; Gensini Score (GS): r=-0.35; and Severity Score (SS): r=-0.40, all P<0.001], and the HMW/total-adiponectin ratio (ES: r=-0.49; GS: r=-0.46; SS: r=-0.46; all P<0.001). Multivariable regression analyses revealed that HMW adiponectin and the HMW/total-adiponectin ratio were significantly associated with the extent of CAD (both P<0.001). ROC analyses demonstrated that the predictive value of HMW adiponectin and the HMW/total-adiponectin ratio for the extent of coronary atherosclerosis significantly exceeded that of total adiponectin (P<0.001, P=0.010, respectively). CONCLUSIONS: HMW adiponectin and the HMW/total-adiponectin ratio inversely correlate with the extent of CAD. HMW adiponectin in particular seems to be a better marker for CAD extent than total adiponectin.

Osteoporosis case finding in the general practice: phalangeal radiographic absorptiometry with and without risk factors for osteoporosis to select postmenopausal women eligible for lumbar spine and hip densitometry

Mass screening for osteoporosis using DXA measurements at the spine and hip is presently not recommended by health authorities. Instead, risk factor questionnaires and peripheral bone measurements may facilitate the selection of women eligible for axial bone densitometry. The aim of this study was to validate a case finding strategy for postmenopausal women who would benefit most from subsequent DXA measurement by using phalangeal radiographic absorptiometry (RA) alone or in combination with risk factors in a general practice setting. The sensitivity and specificity of this strategy in detecting osteoporosis (T-score < or =2.5 SD at the spine and/or the hip) were compared with those of the current reimbursement criteria for DXA measurements in Switzerland. Four hundred and twenty-three postmenopausal women with one or more risk factors for osteoporosis were recruited by 90 primary care physicians who also performed the phalangeal RA measurements. All women underwent subsequent DXA measurement of the spine and the hip at the Osteoporosis Policlinic of the University Hospital of Berne. They were allocated to one of two groups depending on whether they matched with the Swiss reimbursement conditions for DXA measurement or not. Logistic regression models were used to predict the likelihood of osteoporosis versus "no osteoporosis" and to derive ROC curves for the various strategies. Differences in the areas under the ROC curves (AUC) were tested for significance. In women lacking reimbursement criteria, RA achieved a significantly larger AUC (0.81; 95% CI 0.72-0.89) than the risk factors associated with patients' age, height and weight (0.71; 95% C.I. 0.62-0.80). Furthermore, in this study, RA provided a better sensitivity and specificity in identifying women with underlying osteoporosis than the currently accepted criteria for reimbursement of DXA measurement. In the Swiss environment, RA is a valid case finding tool for patients with risk factors for osteoporosis, especially for those who do not qualify for DXA reimbursement.

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.

PROBABILISTIC MODELING OF RAINFALL INDUCED LANDSLIDE HAZARD ASSESSMENT IN SAN JUAN LA LAGUNA, SOLOLÁ, GUATEMALA

The municipality of San Juan La Laguna, Guatemala is home to approximately 5,200 people and located on the western side of the Lake Atitlán caldera. Steep slopes surround all but the eastern side of San Juan. The Lake Atitlán watershed is susceptible to many natural hazards, but most predictable are the landslides that can occur annually with each rainy season, especially during high-intensity events. Hurricane Stan hit Guatemala in October 2005; the resulting flooding and landslides devastated the Atitlán region. Locations of landslide and non-landslide points were obtained from field observations and orthophotos taken following Hurricane Stan. This study used data from multiple attributes, at every landslide and non-landslide point, and applied different multivariate analyses to optimize a model for landslides prediction during high-intensity precipitation events like Hurricane Stan. The attributes considered in this study are: geology, geomorphology, distance to faults and streams, land use, slope, aspect, curvature, plan curvature, profile curvature and topographic wetness index. The attributes were pre-evaluated for their ability to predict landslides using four different attribute evaluators, all available in the open source data mining software Weka: filtered subset, information gain, gain ratio and chi-squared. Three multivariate algorithms (decision tree J48, logistic regression and BayesNet) were optimized for landslide prediction using different attributes. The following statistical parameters were used to evaluate model accuracy: precision, recall, F measure and area under the receiver operating characteristic (ROC) curve. The algorithm BayesNet yielded the most accurate model and was used to build a probability map of landslide initiation points. The probability map developed in this study was also compared to the results of a bivariate landslide susceptibility analysis conducted for the watershed, encompassing Lake Atitlán and San Juan. Landslides from Tropical Storm Agatha 2010 were used to independently validate this study’s multivariate model and the bivariate model. The ultimate aim of this study is to share the methodology and results with municipal contacts from the author's time as a U.S. Peace Corps volunteer, to facilitate more effective future landslide hazard planning and mitigation.

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.

Arterial blood pressure during early sepsis and outcome

OBJECTIVE: To evaluate the association between arterial blood pressure (ABP) during the first 24 h and mortality in sepsis. DESIGN: Retrospective cohort study. SETTING: Multidisciplinary intensive care unit (ICU). PATIENTS AND PARTICIPANTS: A total of 274 septic patients. INTERVENTIONS: None. MEASUREMENTS AND RESULTS: Hemodynamic, and laboratory parameters were extracted from a PDMS database. The hourly time integral of ABP drops below clinically relevant systolic arterial pressure (SAP), mean arterial pressure (MAP), and mean perfusion pressure (MPP = MAP - central venous pressure) levels was calculated for the first 24 h after ICU admission and compared with 28-day-mortality. Binary and linear regression models (adjusted for SAPS II as a measure of disease severity), and a receiver operating characteristic (ROC) analysis were applied. The areas under the ROC curve were largest for the hourly time integrals of ABP drops below MAP 60 mmHg (0.779 vs. 0.764 for ABP drops below MAP 55 mmHg; P < or = 0.01) and MPP 45 mmHg. No association between the hourly time integrals of ABP drops below certain SAP levels and mortality was detected. One or more episodes of MAP < 60 mmHg increased the risk of death by 2.96 (CI 95%, 1.06-10.36, P = 0.04). The area under the ROC curve to predict the need for renal replacement therapy was highest for the hourly time integral of ABP drops below MAP 75 mmHg. CONCLUSIONS: A MAP level > or = 60 mmHg may be as safe as higher MAP levels during the first 24 h of ICU therapy in septic patients. A higher MAP may be required to maintain kidney function.

Validation of the estimation of physiologic ability and surgical stress (E-PASS) score in liver surgery

BACKGROUND: The estimation of physiologic ability and surgical stress (E-PASS) has been used to produce a numerical estimate of expected mortality and morbidity after elective gastrointestinal surgery. The aim of this study was to validate E-PASS in a selected cohort of patients requiring liver resections (LR). METHODS: In this retrospective study, E-PASS predictor equations for morbidity and mortality were applied to the prospective data from 243 patients requiring LR. The observed rates were compared with predicted rates using Fisher's exact test. The discriminative capability of E-PASS was evaluated using receiver-operating characteristic (ROC) curve analysis. RESULTS: The observed and predicted overall mortality rates were both 3.3% and the morbidity rates were 31.3 and 26.9%, respectively. There was a significant difference in the comprehensive risk scores for deceased and surviving patients (p = 0.043). However, the scores for patients with or without complications were not significantly different (p = 0.120). Subsequent ROC curve analysis revealed a poor predictive accuracy for morbidity. CONCLUSIONS: The E-PASS score seems to effectively predict mortality in this specific group of patients but is a poor predictor of complications. A new modified logistic regression might be required for LR in order to better predict the postoperative outcome.

A Combinatorial Approach to the Variable Selection in Multiple Linear Regression: Analysis of Selwood et al Data set -A Case Study.

A combinatorial protocol (CP) is introduced here to interface it with the multiple linear regression (MLR) for variable selection. The efficiency of CP-MLR is primarily based on the restriction of entry of correlated variables to the model development stage. It has been used for the analysis of Selwood et al data set [16], and the obtained models are compared with those reported from GFA [8] and MUSEUM [9] approaches. For this data set CP-MLR could identify three highly independent models (27, 28 and 31) with Q2 value in the range of 0.632-0.518. Also, these models are divergent and unique. Even though, the present study does not share any models with GFA [8], and MUSEUM [9] results, there are several descriptors common to all these studies, including the present one. Also a simulation is carried out on the same data set to explain the model formation in CP-MLR. The results demonstrate that the proposed method should be able to offer solutions to data sets with 50 to 60 descriptors in reasonable time frame. By carefully selecting the inter-parameter correlation cutoff values in CP-MLR one can identify divergent models and handle data sets larger than the present one without involving excessive computer time.