MODELING FUNCTIONAL DATA WITH SPATIALLY HETEROGENEOUS SHAPE CHARACTERISTICS

We propose a novel class of models for functional data exhibiting skewness or other shape characteristics that vary with spatial or temporal location. We use copulas so that the marginal distributions and the dependence structure can be modeled independently. Dependence is modeled with a Gaussian or t-copula, so that there is an underlying latent Gaussian process. We model the marginal distributions using the skew t family. The mean, variance, and shape parameters are modeled nonparametrically as functions of location. A computationally tractable inferential framework for estimating heterogeneous asymmetric or heavy-tailed marginal distributions is introduced. This framework provides a new set of tools for increasingly complex data collected in medical and public health studies. Our methods were motivated by and are illustrated with a state-of-the-art study of neuronal tracts in multiple sclerosis patients and healthy controls. Using the tools we have developed, we were able to find those locations along the tract most affected by the disease. However, our methods are general and highly relevant to many functional data sets. In addition to the application to one-dimensional tract profiles illustrated here, higher-dimensional extensions of the methodology could have direct applications to other biological data including functional and structural MRI.

Sequential updating via dynamic hierarchical models: A Bayesian approach to longitudinal data analysis

Most statistical analysis, theory and practice, is concerned with static models; models with a proposed set of parameters whose values are fixed across observational units. Static models implicitly assume that the quantified relationships remain the same across the design space of the data. While this is reasonable under many circumstances this can be a dangerous assumption when dealing with sequentially ordered data. The mere passage of time always brings fresh considerations and the interrelationships among parameters, or subsets of parameters, may need to be continually revised. ^ When data are gathered sequentially dynamic interim monitoring may be useful as new subject-specific parameters are introduced with each new observational unit. Sequential imputation via dynamic hierarchical models is an efficient strategy for handling missing data and analyzing longitudinal studies. Dynamic conditional independence models offers a flexible framework that exploits the Bayesian updating scheme for capturing the evolution of both the population and individual effects over time. While static models often describe aggregate information well they often do not reflect conflicts in the information at the individual level. Dynamic models prove advantageous over static models in capturing both individual and aggregate trends. Computations for such models can be carried out via the Gibbs sampler. An application using a small sample repeated measures normally distributed growth curve data is presented. ^

Differences in coronary risk factors, procedural characteristics, mortality and stent thrombosis between two all-comers percutaneous coronary intervention registries from Europe and Japan: a patient-level data analysis of the Bern-Rotterdam and j-Cypher registries

Aims: The reported rate of stent thrombosis (ST) after drug-eluting stent (DES) implantation varies among registries. To investigate differences in baseline characteristics and clinical outcome in European and Japanese all-comers registries, we performed a pooled analysis of patient-level data. Methods and results: The j-Cypher registry (JC) is a multicentre observational study conducted in Japan, including 12,824 patients undergoing SES implantation. From the Bern-Rotterdam registry (BR) enrolled at two academic hospitals in Switzerland and the Netherlands, 3,823 patients with SES were included in the current analysis. Patients in BR were younger, more frequently smokers and presented more frequently with ST-elevation myocardial infarction (MI). Conversely, JC patients more frequently had diabetes and hypertension. At five years, the definite ST rate was significantly lower in JC than BR (JC 1.6% vs. BR 3.3%, p<0.001), while the unadjusted mortality tended to be lower in BR than in JC (BR 13.2% vs. JC 14.4%, log-rank p=0.052). After adjustment, the j-Cypher registry was associated with a significantly lower risk of all-cause mortality (HR 0.56, 95% CI: 0.49-0.64) as well as definite stent thrombosis (HR 0.46, 95% CI: 0.35-0.61). Conclusions: The baseline characteristics of the two large registries were different. After statistical adjustment, JC was associated with lower mortality and ST.

Thyroid antibody status, subclinical hypothyroidism, and the risk of coronary heart disease: an individual participant data analysis.

CONTEXT Subclinical hypothyroidism has been associated with increased risk of coronary heart disease (CHD), particularly with thyrotropin levels of 10.0 mIU/L or greater. The measurement of thyroid antibodies helps predict the progression to overt hypothyroidism, but it is unclear whether thyroid autoimmunity independently affects CHD risk. OBJECTIVE The objective of the study was to compare the CHD risk of subclinical hypothyroidism with and without thyroid peroxidase antibodies (TPOAbs). DATA SOURCES AND STUDY SELECTION A MEDLINE and EMBASE search from 1950 to 2011 was conducted for prospective cohorts, reporting baseline thyroid function, antibodies, and CHD outcomes. DATA EXTRACTION Individual data of 38 274 participants from six cohorts for CHD mortality followed up for 460 333 person-years and 33 394 participants from four cohorts for CHD events. DATA SYNTHESIS Among 38 274 adults (median age 55 y, 63% women), 1691 (4.4%) had subclinical hypothyroidism, of whom 775 (45.8%) had positive TPOAbs. During follow-up, 1436 participants died of CHD and 3285 had CHD events. Compared with euthyroid individuals, age- and gender-adjusted risks of CHD mortality in subclinical hypothyroidism were similar among individuals with and without TPOAbs [hazard ratio (HR) 1.15, 95% confidence interval (CI) 0.87-1.53 vs HR 1.26, CI 1.01-1.58, P for interaction = .62], as were risks of CHD events (HR 1.16, CI 0.87-1.56 vs HR 1.26, CI 1.02-1.56, P for interaction = .65). Risks of CHD mortality and events increased with higher thyrotropin, but within each stratum, risks did not differ by TPOAb status. CONCLUSIONS CHD risk associated with subclinical hypothyroidism did not differ by TPOAb status, suggesting that biomarkers of thyroid autoimmunity do not add independent prognostic information for CHD outcomes.

Introduction to Bayesian Data Analysis

A workshop providing an introduction to Bayesian data analysis and hypothesis testing using R, Jags and the BayesFactor package.

Functional error modeling for uncertainty quantification in hydrogeology

Approximate models (proxies) can be employed to reduce the computational costs of estimating uncertainty. The price to pay is that the approximations introduced by the proxy model can lead to a biased estimation. To avoid this problem and ensure a reliable uncertainty quantification, we propose to combine functional data analysis and machine learning to build error models that allow us to obtain an accurate prediction of the exact response without solving the exact model for all realizations. We build the relationship between proxy and exact model on a learning set of geostatistical realizations for which both exact and approximate solvers are run. Functional principal components analysis (FPCA) is used to investigate the variability in the two sets of curves and reduce the dimensionality of the problem while maximizing the retained information. Once obtained, the error model can be used to predict the exact response of any realization on the basis of the sole proxy response. This methodology is purpose-oriented as the error model is constructed directly for the quantity of interest, rather than for the state of the system. Also, the dimensionality reduction performed by FPCA allows a diagnostic of the quality of the error model to assess the informativeness of the learning set and the fidelity of the proxy to the exact model. The possibility of obtaining a prediction of the exact response for any newly generated realization suggests that the methodology can be effectively used beyond the context of uncertainty quantification, in particular for Bayesian inference and optimization.