Elastic analysis of irregularly or sparsely sampled curves.

We provide statistical analysis methods for samples of curves in two or more dimensions, where the image, but not the parameterization of the curves, is of interest and suitable alignment/registration is thus necessary. Examples are handwritten letters, movement paths, or object outlines. We focus in particular on the computation of (smooth) means and distances, allowing, for example, classification or clustering. Existing parameterization invariant analysis methods based on the elastic distance of the curves modulo parameterization, using the square-root-velocity framework, have limitations in common realistic settings where curves are irregularly and potentially sparsely observed. We propose using spline curves to model smooth or polygonal (Fréchet) means of open or closed curves with respect to the elastic distance and show identifiability of the spline model modulo parameterization. We further provide methods and algorithms to approximate the elastic distance for irregularly or sparsely observed curves, via interpreting them as polygons. We illustrate the usefulness of our methods on two datasets. The first application classifies irregularly sampled spirals drawn by Parkinson's patients and healthy controls, based on the elastic distance to a mean spiral curve computed using our approach. The second application clusters sparsely sampled GPS tracks based on the elastic distance and computes smooth cluster means to find new paths on the Tempelhof field in Berlin. All methods are implemented in the R-package "elasdics" and evaluated in simulations.

Nonlinear association structures in flexible Bayesian additive joint models.

Joint models of longitudinal and survival data have become an important tool for modeling associations between longitudinal biomarkers and event processes. The association between marker and log hazard is assumed to be linear in existing shared random effects models, with this assumption usually remaining unchecked. We present an extended framework of flexible additive joint models that allows the estimation of nonlinear covariate specific associations by making use of Bayesian P-splines. Our joint models are estimated in a Bayesian framework using structured additive predictors for all model components, allowing for great flexibility in the specification of smooth nonlinear, time-varying, and random effects terms for longitudinal submodel, survival submodel, and their association. The ability to capture truly linear and nonlinear associations is assessed in simulations and illustrated on the widely studied biomedical data on the rare fatal liver disease primary biliary cirrhosis. All methods are implemented in the R package bamlss to facilitate the application of this flexible joint model in practice.

The impact of model assumptions in scalar-on-image regression.

Complex statistical models such as scalar-on-image regression often require strong assumptions to overcome the issue of nonidentifiability. While in theory, it is well understood that model assumptions can strongly influence the results, this seems to be underappreciated, or played down, in practice. This article gives a systematic overview of the main approaches for scalar-on-image regression with a special focus on their assumptions. We categorize the assumptions and develop measures to quantify the degree to which they are met. The impact of model assumptions and the practical usage of the proposed measures are illustrated in a simulation study and in an application to neuroimaging data. The results show that different assumptions indeed lead to quite different estimates with similar predictive ability, raising the question of their interpretability. We give recommendations for making modeling and interpretation decisions in practice based on the new measures and simulations using hypothetic coefficient images and the observed data.

Mixed modeling for irregularly sampled and correlated functional data: Speech science applications.

The speech sciences often employ complex experimental designs requiring models with multiple covariates and crossed random effects. For curve-like data such as time-varying signals, single-time-point feature extraction is commonly used as data reduction technique to make the data amenable to statistical hypothesis testing, thereby discarding a wealth of information. The present paper discusses the application of functional linear mixed models, a functional analogue to linear mixed models. This type of model allows for the holistic evaluation of curve dynamics for data with complex correlation structures due to repeated measures on subjects and stimulus items. The nonparametric, spline-based estimation technique allows for correlated functional data to be observed irregularly, or even sparsely. This means that information on variation in the temporal domain is preserved. Functional principal component analysis is used for parsimonious data representation and variance decomposition. The basic functionality and usage of the model is illustrated based on several case studies with different data types and experimental designs. The statistical method is broadly applicable to any types of data that consist of groups of curves, whether they are articulatory or acoustic time series data, or generally any types of data suitably modeled based on penalized splines.

Flexible Bayesian additive joint models with an application to type 1 diabetes research.

The joint modeling of longitudinal and time-to-event data is an important tool of growing popularity to gain insights into the association between a biomarker and an event process. We develop a general framework of flexible additive joint models that allows the specification of a variety of effects, such as smooth nonlinear, time-varying and random effects, in the longitudinal and survival parts of the models. Our extensions are motivated by the investigation of the relationship between fluctuating disease-specific markers, in this case autoantibodies, and the progression to the autoimmune disease type 1 diabetes. Using Bayesian P-splines, we are in particular able to capture highly nonlinear subject-specific marker trajectories as well as a time-varying association between the marker and event process allowing new insights into disease progression. The model is estimated within a Bayesian framework and implemented in the R-package bamlss.

Structured functional principal component analysis.

Motivated by modern observational studies, we introduce a class of functional models that expand nested and crossed designs. These models account for the natural inheritance of the correlation structures from sampling designs in studies where the fundamental unit is a function or image. Inference is based on functional quadratics and their relationship with the underlying covariance structure of the latent processes. A computationally fast and scalable estimation procedure is developed for high-dimensional data. Methods are used in applications including high-frequency accelerometer data for daily activity, pitch linguistic data for phonetic analysis, and EEG data for studying electrical brain activity during sleep.

Longitudinal scalar-on-functions regression with application to tractography data.

We propose a class of estimation techniques for scalar-on-function regression where both outcomes and functional predictors may be observed at multiple visits. Our methods are motivated by a longitudinal brain diffusion tensor imaging tractography study. One of the study's primary goals is to evaluate the contemporaneous association between human function and brain imaging over time. The complexity of the study requires the development of methods that can simultaneously incorporate: (1) multiple functional (and scalar) regressors; (2) longitudinal outcome and predictor measurements per patient; (3) Gaussian or non-Gaussian outcomes; and (4) missing values within functional predictors. We propose two versions of a new method, longitudinal functional principal components regression (PCR). These methods extend the well-known functional PCR and allow for different effects of subject-specific trends in curves and of visit-specific deviations from that trend. The new methods are compared with existing approaches, and the most promising techniques are used for analyzing the tractography data.

Privacy Attitudes toward Mouse-Tracking Paradata Collection.

Survey participants' mouse movements provide a rich, unobtrusive source of paradata, offering insight into the response process beyond the observed answers. However, the use of mouse tracking may require participants' explicit consent for their movements to be recorded and analyzed. Thus, the question arises of how its presence affects the willingness of participants to take part in a survey at all-if prospective respondents are reluctant to complete a survey if additional measures are recorded, collecting paradata may do more harm than good. Previous research has found that other paradata collection modes reduce the willingness to participate, and that this decrease may be influenced by the specific motivation provided to participants for collecting the data. However, the effects of mouse movement collection on survey consent and participation have not been addressed so far. In a vignette experiment, we show that reported willingness to participate in a survey decreased when mouse tracking was part of the overall consent. However, a larger proportion of the sample indicated willingness to both take part and provide mouse-tracking data when these decisions were combined, compared to an independent opt-in to paradata collection, separated from the decision to complete the study. This suggests that survey practitioners may face a trade-off between maximizing their overall participation rate and maximizing the number of participants who also provide mouse-tracking data. Explaining motivations for paradata collection did not have a positive effect and, in some cases, even reduced participants' reported willingness to take part in the survey.

Pedestrian exposure to black carbon and PM2.5 emissions in urban hot spots: new findings using mobile measurement techniques and flexible Bayesian regression models.

BACKGROUND: Data from extensive mobile measurements (MM) of air pollutants provide spatially resolved information on pedestrians' exposure to particulate matter (black carbon (BC) and PM2.5 mass concentrations). OBJECTIVE: We present a distributional regression model in a Bayesian framework that estimates the effects of spatiotemporal factors on the pollutant concentrations influencing pedestrian exposure. METHODS: We modeled the mean and variance of the pollutant concentrations obtained from MM in two cities and extended commonly used lognormal models with a lognormal-normal convolution (logNNC) extension for BC to account for instrument measurement error. RESULTS: The logNNC extension significantly improved the BC model. From these model results, we found local sources and, hence, local mitigation efforts to improve air quality, have more impact on the ambient levels of BC mass concentrations than on the regulated PM2.5. SIGNIFICANCE: Firstly, this model (logNNC in bamlss package available in R) could be used for the statistical analysis of MM data from various study areas and pollutants with the potential for predicting pollutant concentrations in urban areas. Secondly, with respect to pedestrian exposure, it is crucial for BC mass concentration to be monitored and regulated in areas dominated by traffic-related air pollution.

Cardiovascular events during World Cup soccer.

BACKGROUND: The Fédération Internationale de Football Association (FIFA) World Cup, held in Germany from June 9 to July 9, 2006, provided an opportunity to examine the relation between emotional stress and the incidence of cardiovascular events. METHODS: Cardiovascular events occurring in patients in the greater Munich area were prospectively assessed by emergency physicians during the World Cup. We compared those events with events that occurred during the control period: May 1 to June 8 and July 10 to July 31, 2006, and May 1 to July 31 in 2003 and 2005. RESULTS: Acute cardiovascular events were assessed in 4279 patients. On days of matches involving the German team, the incidence of cardiac emergencies was 2.66 times that during the control period (95% confidence interval [CI], 2.33 to 3.04; P<0.001); for men, the incidence was 3.26 times that during the control period (95% CI, 2.78 to 3.84; P<0.001), and for women, it was 1.82 times that during the control period (95% CI, 1.44 to 2.31; P<0.001). Among patients with coronary events on days when the German team played, the proportion with known coronary heart disease was 47.0%, as compared with 29.1% of patients with events during the control period. On those days, the highest average incidence of events was observed during the first 2 hours after the beginning of each match. A subanalysis of serious events during that period, as compared with the control period, showed an increase in the incidence of myocardial infarction with ST-segment elevation by a factor of 2.49 (95% CI, 1.47 to 4.23), of myocardial infarction without ST-segment elevation or unstable angina by a factor of 2.61 (95% CI, 2.22 to 3.08), and of cardiac arrhythmia causing major symptoms by a factor of 3.07 (95% CI, 2.32 to 4.06) (P<0.001 for all comparisons). CONCLUSIONS: Viewing a stressful soccer match more than doubles the risk of an acute cardiovascular event. In view of this excess risk, particularly in men with known coronary heart disease, preventive measures are urgently needed.

Reproducibility in serial C-reactive protein and interleukin-6 measurements in post-myocardial infarction patients: results from the AIRGENE study.

BACKGROUND: Among the numerous emerging biomarkers, high-sensitivity C-reactive protein (hsCRP) and interleukin-6 (IL-6) have received widespread interest, and a large database has been accumulated on their potential role as predictors of cardiovascular risk. The concentrations of inflammatory biomarkers, however, are influenced, among other things, by physiological variation, which is the natural within-individual variation occurring over time. Implementation of hsCRP and IL-6 measurement into clinical practice requires data on the reliability of such measurements. METHODS: We serially measured hsCRP and IL-6 concentrations in up to 6 blood samples taken at monthly intervals from 200 post-myocardial infarction patients who participated in the AIRGENE study. RESULTS: The mean (SD) of the ln-transformed plasma concentrations (in milligrams per liter for hsCRP and nanograms per liter for IL-6) for all participants over all samples was 0.16 (1.04) for hsCRP and 0.76 (0.57) for IL-6, with no significant differences between men and women. The within-individual and analytical variance component for the ln-transformed hsCRP data was 0.37, and the between-individual variance component was 0.73. For the ln-transformed IL-6 data, these values were 0.11 and 0.22, respectively. A substantial part of the total variation in plasma hsCRP and IL-6 concentrations was explained by the between-individual variation (as a percentage of the total variance, 66.1% for the ln-transformed hsCRP data and 66.2% for the ln-transformed IL-6 data). For both markers, 2 measurements were needed to reach a sufficient reliability. CONCLUSIONS: Our results demonstrate considerable stability and good reproducibility for serial hsCRP and IL-6 measurements. Thus, there should be no major concern about misclassification in clinical practice if at least 2 subsequent measurements are taken.

Fibrinogen genes modify the fibrinogen response to ambient particulate matter.

RATIONALE: Ambient particulate matter has been associated with systemic inflammation indicated by blood markers such as fibrinogen, implicated in promoting atherothrombosis. OBJECTIVES: This study evaluated whether single-nucleotide polymorphisms (SNPs) within the fibrinogen genes modified the relationship between ambient particles and plasma fibrinogen. METHODS: In 854 myocardial infarction survivors from five European cities plasma fibrinogen levels were determined repeatedly (n = 5,082). City-specific analyses were conducted to assess the impact of particulate matter on fibrinogen levels, applying additive mixed models adjusting for patient characteristics, time trend, and weather. City-specific estimates were pooled by meta-analysis methodology. MEASUREMENTS AND MAIN RESULTS: Seven SNPs in the FGA and FGB genes shown to be associated with differences in fibrinogen levels were selected. Promoter SNPs within FGA and FGB were associated with modifications of the relationship between 5-day averages of particulate matter with an aerodynamic diameter below 10 microm (PM(10)) and plasma fibrinogen levels. The PM(10)-fibrinogen relationship for subjects with the homozygous minor allele genotype of FGB rs1800790 compared with subjects homozygous for the major allele was eightfold higher (P value for the interaction, 0.037). CONCLUSIONS: The data suggest that susceptibility to ambient particulate matter may be partly genetically determined by polymorphisms that alter early physiological responses such as transcription of fibrinogen. Subjects with variants of these frequent SNPs may have increased risks not only due to constitutionally higher fibrinogen concentrations, but also due to an augmented response to environmental inflammatory stimuli such as ambient particulate matter.

DNA variants, plasma levels and variability of C-reactive protein in myocardial infarction survivors: results from the AIRGENE study.

AIMS: C-reactive protein represents the classical acute-phase protein produced in the liver in response to inflammatory stimuli. This study evaluated the association of gene polymorphisms with differences in C-reactive protein concentrations and assessed its intra-individual variability as a marker of individual response. METHODS AND RESULTS: One thousand and three myocardial infarction (MI) survivors were recruited in six European cities, and C-reactive protein concentrations were measured repeatedly during a 6-month period. We investigated 114 polymorphisms in 13 genes, all involved in the innate inflammatory pathway. We found two polymorphisms within the C-reactive protein (CRP) gene rs1800947 and rs1205, of which the minor alleles were strongly associated with lower levels of C-reactive protein (P < 10(-6)). A haplotype, identified by those two polymorphisms, was associated with the lowest C-reactive protein concentrations (P < 10(-6)). Additionally, the minor alleles of several variants were significantly associated with greater individual variability of C-reactive protein concentrations (P < 10(-3)). CONCLUSION: The present study investigated the association of polymorphisms with inter- and intra-individual variability of C-reactive protein levels. Two minor alleles of C-reactive protein variants were associated with lower C-reactive protein concentrations. Regarding intra-individual variability, we observed associations with the minor alleles of several variants in selected candidate genes, including the CRP gene itself.

Serotonin Selective Reuptake Inhibitor Treatment Improves Cognition and Grey Matter Atrophy but not Amyloid Burden During Two-Year Follow-Up in Mild Cognitive Impairment and Alzheimer's Disease Patients with Depressive Symptoms.

Late-life depression, even when of subsyndromal severity, has shown strong associations with mild cognitive impairment (MCI) and Alzheimer's disease (AD). Preclinical studies have suggested that serotonin selective reuptake inhibitors (SSRIs) can attenuate amyloidogenesis. Therefore, we aimed to investigate the effect of SSRI medication on amyloidosis and grey matter volume in subsyndromal depressed subjects with MCI and AD during an interval of two years. 256 cognitively affected subjects (225 MCI/ 31 AD) undergoing [18F]-AV45-PET and MRI at baseline and 2-year follow-up were selected from the ADNI database. Subjects with a positive depression item (DEP(+); n = 73) in the Neuropsychiatric Inventory Questionnaire were subdivided to those receiving SSRI medication (SSRI(+); n = 24) and those without SSRI treatment (SSRI(-); n = 49). Longitudinal cognition (Δ-ADAS), amyloid deposition rate (standardized uptake value, using white matter as reference region (SUVRWM), and changes in grey matter volume were compared using common covariates. Analyses were performed separately in all subjects and in the subgroup of amyloid-positive subjects. Cognitive performance in DEP(+)/SSRI(+) subjects (Δ-ADAS: -5.0%) showed less deterioration with 2-year follow-up when compared to DEP(+)/SSRI(-) subjects (Δ-ADAS: +18.6%, p < 0.05), independent of amyloid SUVRWM at baseline. With SSRI treatment, the progression of grey matter atrophy was reduced (-0.9% versus -2.7%, p < 0.05), notably in fronto-temporal cortex. A slight trend towards lower amyloid deposition rate was observed in DEP(+)/SSRI(+) subjects versus DEP(+)/SSRI(-). Despite the lack of effect to amyloid PET, SSRI medication distinctly rescued the declining cognitive performance in cognitively affected patients with depressive symptoms, and likewise attenuated grey matter atrophy.

Air pollution and inflammation (interleukin-6, C-reactive protein, fibrinogen) in myocardial infarction survivors.

BACKGROUND: Numerous studies have found that ambient air pollution has been associated with cardiovascular disease exacerbation. OBJECTIVES: Given previous findings, we hypothesized that particulate air pollution might induce systemic inflammation in myocardial infarction (MI) survivors, contributing to an increased vulnerability to elevated concentrations of ambient particles. METHODS: A prospective longitudinal study of 1,003 MI survivors was performed in six European cities between May 2003 and July 2004. We compared repeated measurements of interleukin 6 (IL-6), fibrinogen, and C-reactive protein (CRP) with concurrent levels of air pollution. We collected hourly data on particle number concentrations (PNC), mass concentrations of particulate matter (PM) < 10 microm (PM(10)) and < 2.5 microm (PM(2.5)), gaseous pollutants, and meteorologic data at central monitoring sites in each city. City-specific confounder models were built for each blood marker separately, adjusting for meteorology and time-varying and time-invariant covariates. Data were analyzed with mixed-effects models. RESULTS: Pooled results show an increase in IL-6 when concentrations of PNC were elevated 12-17 hr before blood withdrawal [percent change of geometric mean, 2.7; 95% confidence interval (CI), 1.0-4.6]. Five day cumulative exposure to PM(10) was associated with increased fibrinogen concentrations (percent change of arithmetic mean, 0.6; 95% CI, 0.1-1.1). Results remained stable for smokers, diabetics, and patients with heart failure. No consistent associations were found for CRP. CONCLUSIONS: Results indicate an immediate response to PNC on the IL-6 level, possibly leading to the production of acute-phase proteins, as seen in increased fibrinogen levels. This might provide a link between air pollution and adverse cardiac events.

Air pollution and inflammatory response in myocardial infarction survivors: gene-environment interactions in a high-risk group.

Ambient air pollution has been associated with an increased risk of hospital admission and mortality in potentially susceptible subpopulations, including myocardial infarction (MI) survivors. The multicenter epidemiological study described in this report was set up to study the role of air pollution in eliciting inflammation in MI survivors in six European cities, Helsinki, Stockholm, Augsburg, Rome, Barcelona, and Athens. Outcomes of interest are plasma concentrations of the proinflammatory cytokine interleukin 6 (IL-6) and the acute-phase proteins C-reactive protein (CRP) and fibrinogen. In addition, the study was designed to assess the role of candidate gene polymorphisms hypothesized to lead to a modification of the short-term effects of ambient air pollution. In total, 1003 MI survivors were recruited and assessed with at least 2 repeated clinic visits without any signs of infections. In total, 5813 blood samples were collected, equivalent to an average of 5.8 repeated clinic visits per subject (97% of the scheduled 6 repeated visits). Subjects across the six cities varied with respect to risk factor profiles. Most of the subjects were nonsmokers, but light smokers were included in Rome, Barcelona, and Athens. Substantial inter- and intraindividual variability was observed for IL-6 and CRP. The study will permit assessing the role of cardiovascular disease risk factors, including ambient air pollution and genetic polymorphisms in candidate genes, in determining the inter- and the intraindividual variability in plasma IL-6, CRP, and fibrinogen concentrations in MI survivors.

Modelling a response as a function of high-frequency count data: The association between physical activity and fat mass.

Accelerometers are widely used in health sciences, ecology and other application areas. They quantify the intensity of physical activity as counts per epoch over a given period of time. Currently, health scientists use very lossy summaries of the accelerometer time series, some of which are based on coarse discretisation of activity levels, and make certain implicit assumptions, including linear or constant effects of physical activity. We propose the histogram as a functional summary for achieving a near lossless dimension reduction, comparability between individual time series and easy interpretability. Using the histogram as a functional summary avoids registration of accelerometer counts in time. In our novel method, a scalar response is regressed on additive multi-dimensional functional predictors, including the histogram of the high-frequency counts, and additive non-linear predictors for other continuous covariates. The method improves on the current state-of-the art, as it can deal with high-frequency time series of different lengths and missing values and yields a flexible way to model the physical activity effect with fewer assumptions. It also allows the commonly made modelling assumptions to be tested. We investigate the relationship between the response fat mass and physical activity measured by accelerometer, in data from the Avon Longitudinal Study of Parents and Children. Our method allows testing of whether the effect of physical activity varies over its intensity by gender, by time of day or by day of the week. We show that meaningful interpretation requires careful treatment of identifiability constraints in the light of the sum-to-one property of a histogram. We find that the (not necessarily causal) effect of physical activity on kg fat mass is not linear and not constant over the activity intensity.

Joint modeling of longitudinal autoantibody patterns and progression to type 1 diabetes: results from the TEDDY study.

AIMS: The onset of clinical type 1 diabetes (T1D) is preceded by the occurrence of disease-specific autoantibodies. The level of autoantibody titers is known to be associated with progression time from the first emergence of autoantibodies to the onset of clinical symptoms, but detailed analyses of this complex relationship are lacking. We aimed to fill this gap by applying advanced statistical models. METHODS: We investigated data of 613 children from the prospective TEDDY study who were persistent positive for IAA, GADA and/or IA2A autoantibodies. We used a novel approach of Bayesian joint modeling of longitudinal and survival data to assess the potentially time- and covariate-dependent association between the longitudinal autoantibody titers and progression time to T1D. RESULTS: For all autoantibodies we observed a positive association between the titers and the T1D progression risk. This association was estimated as time-constant for IA2A, but decreased over time for IAA and GADA. For example the hazard ratio [95% credibility interval] for IAA (per transformed unit) was 3.38 [2.66, 4.38] at 6 months after seroconversion, and 2.02 [1.55, 2.68] at 36 months after seroconversion. CONCLUSIONS: These findings indicate that T1D progression risk stratification based on autoantibody titers should focus on time points early after seroconversion. Joint modeling techniques allow for new insights into these associations.

Functional Additive Mixed Models.

We propose an extensive framework for additive regression models for correlated functional responses, allowing for multiple partially nested or crossed functional random effects with flexible correlation structures for, e.g., spatial, temporal, or longitudinal functional data. Additionally, our framework includes linear and nonlinear effects of functional and scalar covariates that may vary smoothly over the index of the functional response. It accommodates densely or sparsely observed functional responses and predictors which may be observed with additional error and includes both spline-based and functional principal component-based terms. Estimation and inference in this framework is based on standard additive mixed models, allowing us to take advantage of established methods and robust, flexible algorithms. We provide easy-to-use open source software in the pffr() function for the R-package refund. Simulations show that the proposed method recovers relevant effects reliably, handles small sample sizes well and also scales to larger data sets. Applications with spatially and longitudinally observed functional data demonstrate the flexibility in modeling and interpretability of results of our approach.

Longitudinal High-Dimensional Principal Components Analysis with Application to Diffusion Tensor Imaging of Multiple Sclerosis.

We develop a flexible framework for modeling high-dimensional imaging data observed longitudinally. The approach decomposes the observed variability of repeatedly measured high-dimensional observations into three additive components: a subject-specific imaging random intercept that quantifies the cross-sectional variability, a subject-specific imaging slope that quantifies the dynamic irreversible deformation over multiple realizations, and a subject-visit specific imaging deviation that quantifies exchangeable effects between visits. The proposed method is very fast, scalable to studies including ultra-high dimensional data, and can easily be adapted to and executed on modest computing infrastructures. The method is applied to the longitudinal analysis of diffusion tensor imaging (DTI) data of the corpus callosum of multiple sclerosis (MS) subjects. The study includes 176 subjects observed at 466 visits. For each subject and visit the study contains a registered DTI scan of the corpus callosum at roughly 30,000 voxels.