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.

Model Checking for ROC Regression Analysis

The Receiver Operating Characteristic (ROC) curve is a prominent tool for characterizing the accuracy of continuous diagnostic test. To account for factors that might invluence the test accuracy, various ROC regression methods have been proposed. However, as in any regression analysis, when the assumed models do not fit the data well, these methods may render invalid and misleading results. To date practical model checking techniques suitable for validating existing ROC regression models are not yet available. In this paper, we develop cumulative residual based procedures to graphically and numerically assess the goodness-of-fit for some commonly used ROC regression models, and show how specific components of these models can be examined within this framework. We derive asymptotic null distributions for the residual process and discuss resampling procedures to approximate these distributions in practice. We illustrate our methods with a dataset from the Cystic Fibrosis registry.

Semiparametric Estimation in General Repeated Measures Problems

This paper considers a wide class of semiparametric problems with a parametric part for some covariate effects and repeated evaluations of a nonparametric function. Special cases in our approach include marginal models for longitudinal/clustered data, conditional logistic regression for matched case-control studies, multivariate measurement error models, generalized linear mixed models with a semiparametric component, and many others. We propose profile-kernel and backfitting estimation methods for these problems, derive their asymptotic distributions, and show that in likelihood problems the methods are semiparametric efficient. While generally not true, with our methods profiling and backfitting are asymptotically equivalent. We also consider pseudolikelihood methods where some nuisance parameters are estimated from a different algorithm. The proposed methods are evaluated using simulation studies and applied to the Kenya hemoglobin data.

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.

Portfolio-optimization models for small investors

Since 2010, the client base of online-trading service providers has grown significantly. Such companies enable small investors to access the stock market at advantageous rates. Because small investors buy and sell stocks in moderate amounts, they should consider fixed transaction costs, integral transaction units, and dividends when selecting their portfolio. In this paper, we consider the small investor’s problem of investing capital in stocks in a way that maximizes the expected portfolio return and guarantees that the portfolio risk does not exceed a prescribed risk level. Portfolio-optimization models known from the literature are in general designed for institutional investors and do not consider the specific constraints of small investors. We therefore extend four well-known portfolio-optimization models to make them applicable for small investors. We consider one nonlinear model that uses variance as a risk measure and three linear models that use the mean absolute deviation from the portfolio return, the maximum loss, and the conditional value-at-risk as risk measures. We extend all models to consider piecewise-constant transaction costs, integral transaction units, and dividends. In an out-of-sample experiment based on Swiss stock-market data and the cost structure of the online-trading service provider Swissquote, we apply both the basic models and the extended models; the former represent the perspective of an institutional investor, and the latter the perspective of a small investor. The basic models compute portfolios that yield on average a slightly higher return than the portfolios computed with the extended models. However, all generated portfolios yield on average a higher return than the Swiss performance index. There are considerable differences between the four risk measures with respect to the mean realized portfolio return and the standard deviation of the realized portfolio return.

Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks.

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

Changes in the PQRST intervals and heart rate variability associated with rewarming in two newborns undergoing hypothermia therapy.

BACKGROUND: Little is known about the effects of hypothermia therapy and subsequent rewarming on the PQRST intervals and heart rate variability (HRV) in term newborns with hypoxic-ischemic encephalopathy (HIE). OBJECTIVES: This study describes the changes in the PQRST intervals and HRV during rewarming to normal core body temperature of 2 newborns with HIE after hypothermia therapy. METHODS: Within 6 h after birth, 2 newborns with HIE were cooled to a core body temperature of 33.5 degrees C for 72 h using a cooling blanket, followed by gradual rewarming (0.5 degrees C per hour) until the body temperature reached 36.5 degrees C. Custom instrumentation recorded the electrocardiogram from the leads used for clinical monitoring of vital signs. Generalized linear mixed models were calculated to estimate temperature-related changes in PQRST intervals and HRV. Results: For every 1 degrees C increase in body temperature, the heart rate increased by 9.2 bpm (95% CI 6.8-11.6), the QTc interval decreased by 21.6 ms (95% CI 17.3-25.9), and low and high frequency HRV decreased by 0.480 dB (95% CI 0.052-0.907) and 0.938 dB (95% CI 0.460-1.416), respectively. CONCLUSIONS: Hypothermia-induced changes in the electrocardiogram should be monitored carefully in future studies.

A meta-analysis of cambium phenology and growth: linear and non-linear patterns in conifers of the northern hemisphere

Background and Aims Ongoing global warming has been implicated in shifting phenological patterns such as the timing and duration of the growing season across a wide variety of ecosystems. Linear models are routinely used to extrapolate these observed shifts in phenology into the future and to estimate changes in associated ecosystem properties such as net primary productivity. Yet, in nature, linear relationships may be special cases. Biological processes frequently follow more complex, non-linear patterns according to limiting factors that generate shifts and discontinuities, or contain thresholds beyond which responses change abruptly. This study investigates to what extent cambium phenology is associated with xylem growth and differentiation across conifer species of the northern hemisphere. Methods Xylem cell production is compared with the periods of cambial activity and cell differentiation assessed on a weekly time scale on histological sections of cambium and wood tissue collected from the stems of nine species in Canada and Europe over 1–9 years per site from 1998 to 2011. Key Results The dynamics of xylogenesis were surprisingly homogeneous among conifer species, although dispersions from the average were obviously observed. Within the range analysed, the relationships between the phenological timings were linear, with several slopes showing values close to or not statistically different from 1. The relationships between the phenological timings and cell production were distinctly non-linear, and involved an exponential pattern. Conclusions The trees adjust their phenological timings according to linear patterns. Thus, shifts of one phenological phase are associated with synchronous and comparable shifts of the successive phases. However, small increases in the duration of xylogenesis could correspond to a substantial increase in cell production. The findings suggest that the length of the growing season and the resulting amount of growth could respond differently to changes in environmental conditions.

An index to identify stroke-related vs incidental patent foramen ovale in cryptogenic stroke

OBJECTIVE We aimed to create an index to stratify cryptogenic stroke (CS) patients with patent foramen ovale (PFO) by their likelihood that the stroke was related to their PFO. METHODS Using data from 12 component studies, we used generalized linear mixed models to predict the presence of PFO among patients with CS, and derive a simple index to stratify patients with CS. We estimated the stratum-specific PFO-attributable fraction and stratum-specific stroke/TIA recurrence rates. RESULTS Variables associated with a PFO in CS patients included younger age, the presence of a cortical stroke on neuroimaging, and the absence of these factors: diabetes, hypertension, smoking, and prior stroke or TIA. The 10-point Risk of Paradoxical Embolism score is calculated from these variables so that the youngest patients with superficial strokes and without vascular risk factors have the highest score. PFO prevalence increased from 23% (95% confidence interval [CI]: 19%-26%) in those with 0 to 3 points to 73% (95% CI: 66%-79%) in those with 9 or 10 points, corresponding to attributable fraction estimates of approximately 0% to 90%. Kaplan-Meier estimated stroke/TIA 2-year recurrence rates decreased from 20% (95% CI: 12%-28%) in the lowest Risk of Paradoxical Embolism score stratum to 2% (95% CI: 0%-4%) in the highest. CONCLUSION Clinical characteristics identify CS patients who vary markedly in PFO prevalence, reflecting clinically important variation in the probability that a discovered PFO is likely to be stroke-related vs incidental. Patients in strata more likely to have stroke-related PFOs have lower recurrence risk.

Portfolio-optimization models for small investors

Since 2010, the client base of online-trading service providers has grown significantly. Such companies enable small investors to access the stock market at advantageous rates. Because small investors buy and sell stocks in moderate amounts, they should consider fixed transaction costs, integral transaction units, and dividends when selecting their portfolio. In this paper, we consider the small investor’s problem of investing capital in stocks in a way that maximizes the expected portfolio return and guarantees that the portfolio risk does not exceed a prescribed risk level. Portfolio-optimization models known from the literature are in general designed for institutional investors and do not consider the specific constraints of small investors. We therefore extend four well-known portfolio-optimization models to make them applicable for small investors. We consider one nonlinear model that uses variance as a risk measure and three linear models that use the mean absolute deviation from the portfolio return, the maximum loss, and the conditional value-at-risk as risk measures. We extend all models to consider piecewise-constant transaction costs, integral transaction units, and dividends. In an out-of-sample experiment based on Swiss stock-market data and the cost structure of the online-trading service provider Swissquote, we apply both the basic models and the extended models; the former represent the perspective of an institutional investor, and the latter the perspective of a small investor. The basic models compute portfolios that yield on average a slightly higher return than the portfolios computed with the extended models. However, all generated portfolios yield on average a higher return than the Swiss performance index. There are considerable differences between the four risk measures with respect to the mean realized portfolio return and the standard deviation of the realized portfolio return.

O(N) Models with Topological Lattice Actions

A variety of lattice discretisations of continuum actions has been considered, usually requiring the correct classical continuum limit. Here we discuss “weird” lattice formulations without that property, namely lattice actions that are invariant under most continuous deformations of the field configuration, in one version even without any coupling constants. It turns out that universality is powerful enough to still provide the correct quantum continuum limit, despite the absence of a classical limit, or a perturbative expansion. We demonstrate this for a set of O(N) models (or non-linear σ-models). Amazingly, such “weird” lattice actions are not only in the right universality class, but some of them even have practical benefits, in particular an excellent scaling behaviour.

Determinants of antithrombotic choice for patent foramen ovale in cryptogenic stroke

Objective: We examined the influence of clinical, radiologic, and echocardiographic characteristics on antithrombotic choice in patients with cryptogenic stroke (CS) and patent foramen ovale (PFO), hypothesizing that features suggestive of paradoxical embolism might lead to greater use of anticoagulation. Methods: The Risk of Paradoxical Embolism Study combined 12 databases to create the largest dataset of patients with CS and known PFO status. We used generalized linear mixed models with a random effect of component study to explore whether anticoagulation was preferentially selected based on the following: (1) younger age and absence of vascular risk factors, (2) “high-risk” echocardiographic features, and (3) neuroradiologic findings. Results: A total of 1,132 patients with CS and PFO treated with anticoagulation or antiplatelets were included. Overall, 438 participants (39%) were treated with anticoagulation with a range (by database) of 22% to 54%. Treatment choice was not influenced by age or vascular risk factors. However, neuroradiologic findings (superficial or multiple infarcts) and high-risk echocardiographic features (large shunts, shunt at rest, and septal hypermobility) were predictors of anticoagulation use. Conclusion: Both antithrombotic regimens are widely used for secondary stroke prevention in patients with CS and PFO. Radiologic and echocardiographic features were strongly associated with treatment choice, whereas conventional vascular risk factors were not. Prior observational studies are likely to be biased by confounding by indication.

Serum Testosterone Levels and Symptom-Based Depression Subtypes in Men

The main objective of this preliminary study was to further clarify the association between testosterone (T) levels and depression by investigating symptom-based depression subtypes in a sample of 64 men. The data were taken from the ZInEP epidemiology survey. Gonadal hormones of a melancholic (n  = 25) and an atypical (n = 14) depression subtype, derived from latent class analysis, were compared with those of healthy controls (n  = 18). Serum T was assayed using an enzyme-linked immunosorbent assay procedure. Analysis of variance, analysis of covariance, non-parametrical tests, and generalized linear regression models were performed to examine group differences. The atypical depressive subtype showed significantly lower T levels compared with the melancholic depressives. While accumulative evidence indicates that, beyond psychosocial characteristics, the melancholic and atypical depressive subtypes are also distinguishable by biological correlates, the current study expanded this knowledge to include gonadal hormones. Further longitudinal research is warranted to disclose causality by linking the multiple processes in pathogenesis of depression.

Empirical Analysis of Credit Risk Regime Switching and Temporal Conditional Default Correlation in Credit Default Swap Valuation: The Market liquidity effect

In this paper, we extend the debate concerning Credit Default Swap valuation to include time varying correlation and co-variances. Traditional multi-variate techniques treat the correlations between covariates as constant over time; however, this view is not supported by the data. Secondly, since financial data does not follow a normal distribution because of its heavy tails, modeling the data using a Generalized Linear model (GLM) incorporating copulas emerge as a more robust technique over traditional approaches. This paper also includes an empirical analysis of the regime switching dynamics of credit risk in the presence of liquidity by following the general practice of assuming that credit and market risk follow a Markov process. The study was based on Credit Default Swap data obtained from Bloomberg that spanned the period January 1st 2004 to August 08th 2006. The empirical examination of the regime switching tendencies provided quantitative support to the anecdotal view that liquidity decreases as credit quality deteriorates. The analysis also examined the joint probability distribution of the credit risk determinants across credit quality through the use of a copula function which disaggregates the behavior embedded in the marginal gamma distributions, so as to isolate the level of dependence which is captured in the copula function. The results suggest that the time varying joint correlation matrix performed far superior as compared to the constant correlation matrix; the centerpiece of linear regression models.