Statistical modeling of time-dependent fMRI activation effects.

Functional magnetic resonance imaging (fMRI) activation detection within stimulus-based experimental paradigms is conventionally based on the assumption that activation effects remain constant over time. This assumption neglects the fact that the strength of activation may vary, for example, due to habituation processes or changing attention. Neither the functional form of time variation can be retrieved nor short-lasting effects can be detected by conventional methods. In this work, a new dynamic approach is proposed that allows to estimate time-varying effect profiles and hemodynamic response functions in event-related fMRI paradigms. To this end, we incorporate the time-varying coefficient methodology into the fMRI general regression framework. Inference is based on a voxelwise penalized least squares procedure. We assess the strength of activation and corresponding time variation on the basis of pointwise confidence intervals on a voxel level. Additionally, spatial clusters of effect curves are presented. Results of the analysis of an active oddball experiment show that activation effects deviating from a constant trend coexist with time-varying effects that exhibit different types of shapes, such as linear, (inversely) U-shaped or fluctuating forms. In a comparison to conventional approaches, like classical SPM, we observe that time-constant methods are rather insensitive to detect temporary effects, because these do not emerge when aggregated across the entire experiment. Hence, it is recommended to base activation detection analyses not merely on time-constant procedures but to include flexible time-varying effects that harbour valuable information on individual response patterns.

Geoadditive latent variable modeling of count data on multiple sexual partnering in Nigeria.

The 2005 National HIV/AIDS and Reproductive Health Survey (NARHS) in Nigeria provides evidence that multiple sexual partnering increases the risk of contracting HIV and other sexually transmitted diseases. Therefore, partner reduction is one of the prevention strategies to accomplish the Millenium Development Goal of halting and reversing the spread of HIV/AIDS. We consider the numbers of girlfriends, casual, and commercial partners of heterosexual men, reported in the NARHS study, as observed indicators of their latent attitude toward multiple partnering. To explore the influence of risk factors on this latent variable, we extend semiparametric methodology for latent variable models with continuous and categorical indicators to include count indicators. This allows us to simultaneously analyze linear and nonlinear effects of covariates, such as sociodemographic factors and knowledge about HIV/AIDS, on attitude toward multiple sexual partnering, which in turn influences the observable count indicators. The results provide insights for policy makers who are aiming to reduce the spread of HIV and AIDS among the Nigerian populace through partner reduction.

Alternative regression models to assess increase in childhood BMI.

BACKGROUND: Body mass index (BMI) data usually have skewed distributions, for which common statistical modeling approaches such as simple linear or logistic regression have limitations. METHODS: Different regression approaches to predict childhood BMI by goodness-of-fit measures and means of interpretation were compared including generalized linear models (GLMs), quantile regression and Generalized Additive Models for Location, Scale and Shape (GAMLSS). We analyzed data of 4967 children participating in the school entry health examination in Bavaria, Germany, from 2001 to 2002. TV watching, meal frequency, breastfeeding, smoking in pregnancy, maternal obesity, parental social class and weight gain in the first 2 years of life were considered as risk factors for obesity. RESULTS: GAMLSS showed a much better fit regarding the estimation of risk factors effects on transformed and untransformed BMI data than common GLMs with respect to the generalized Akaike information criterion. In comparison with GAMLSS, quantile regression allowed for additional interpretation of prespecified distribution quantiles, such as quantiles referring to overweight or obesity. The variables TV watching, maternal BMI and weight gain in the first 2 years were directly, and meal frequency was inversely significantly associated with body composition in any model type examined. In contrast, smoking in pregnancy was not directly, and breastfeeding and parental social class were not inversely significantly associated with body composition in GLM models, but in GAMLSS and partly in quantile regression models. Risk factor specific BMI percentile curves could be estimated from GAMLSS and quantile regression models. CONCLUSION: GAMLSS and quantile regression seem to be more appropriate than common GLMs for risk factor modeling of BMI data.

Inference of demographic history from genealogical trees using reversible jump Markov chain Monte Carlo.

BACKGROUND: Coalescent theory is a general framework to model genetic variation in a population. Specifically, it allows inference about population parameters from sampled DNA sequences. However, most currently employed variants of coalescent theory only consider very simple demographic scenarios of population size changes, such as exponential growth. RESULTS: Here we develop a coalescent approach that allows Bayesian non-parametric estimation of the demographic history using genealogies reconstructed from sampled DNA sequences. In this framework inference and model selection is done using reversible jump Markov chain Monte Carlo (MCMC). This method is computationally efficient and overcomes the limitations of related non-parametric approaches such as the skyline plot. We validate the approach using simulated data. Subsequently, we reanalyze HIV-1 sequence data from Central Africa and Hepatitis C virus (HCV) data from Egypt. CONCLUSIONS: The new method provides a Bayesian procedure for non-parametric estimation of the demographic history. By construction it additionally provides confidence limits and may be used jointly with other MCMC-based coalescent approaches.

Analyzing infant mortality with geoadditive categorical regression models: a case study for Nigeria.

In this paper, we analyze infant mortality in Nigeria based on the data set from the 1999 Nigeria Demographic and Health Survey (NDHS). We investigate spatial patterns at a highly disaggregated level of Nigerian states and consider non-linear effects of mother's age at birth. Time to the occurrence of a child's death can intuitively be considered to be categorical in nature and the determinants of a child's death may differ in different age groups. Thus, it may be desirable to investigate separately the death of a child in the first month and in the remaining 11 months of the first year of life. To avoid selection bias, the data set used for this case study is based on information on children who were born 12 months preceding the survey. Inference is Bayesian and is based on Markov chain Monte Carlo (MCMC) techniques. We find that spatial variation and the determinants of death indeed differ considerably for the two age groups considered.

Boosting structured additive quantile regression for longitudinal childhood obesity data.

Childhood obesity and the investigation of its risk factors has become an important public health issue. Our work is based on and motivated by a German longitudinal study including 2,226 children with up to ten measurements on their body mass index (BMI) and risk factors from birth to the age of 10 years. We introduce boosting of structured additive quantile regression as a novel distribution-free approach for longitudinal quantile regression. The quantile-specific predictors of our model include conventional linear population effects, smooth nonlinear functional effects, varying-coefficient terms, and individual-specific effects, such as intercepts and slopes. Estimation is based on boosting, a computer intensive inference method for highly complex models. We propose a component-wise functional gradient descent boosting algorithm that allows for penalized estimation of the large variety of different effects, particularly leading to individual-specific effects shrunken toward zero. This concept allows us to flexibly estimate the nonlinear age curves of upper quantiles of the BMI distribution, both on population and on individual-specific level, adjusted for further risk factors and to detect age-varying effects of categorical risk factors. Our model approach can be regarded as the quantile regression analog of Gaussian additive mixed models (or structured additive mean regression models), and we compare both model classes with respect to our obesity data.

Analysis of childhood morbidity with geoadditive probit and latent variable model: a case study for Egypt.

This work applies geoadditive latent variable models to analyze the impact of risk factors and the spatial effects on the latent, unobservable variable "health status" or "frailty" of a child less than 5 years of age using the 2003 Demographic and Health survey (DHS) data from Egypt. Childhood diseases are a major cause of death of children in the developing world. In developing countries a quarter of infant and childhood mortality is related to childhood disease, particularly to diarrhea. Our case study is based on the 2003 Demographic and Health Survey for Egypt (EDHS). It provided data on the prevalence and treatment of common childhood disease such as diarrhea, cough, and fever, which are seen as symptoms or indicators of children's health status, causing increased morbidity and mortality. These causes are often associated with a number of risk factors, including inadequate antenatal care, lack of or inadequate vaccination, and environmental factors that affected the health of the child in early years, various bio-demographic and socioeconomic variables. In this work, we investigate the impact of such factors on childhood disease with flexible geoadditive models. These models allow us to analyze usual linear effects of covariates, nonlinear effects of continuous covariates, and small-area regional effects within a unified, semi-parametric Bayesian framework for modeling and inference. As a first step, we use separate geoadditive probit models the binary target variables for diarrhea, cough, and fever using covariate information from the EDHS. Based on these results, we then apply recently developed geoadditive latent variable models where the three observable disease variables are taken as indicators for the latent individual variable "health status" or "frailty" of a child. This modeling approach allows us to study the common influence of risk factors on individual frailties of children, thereby automatically accounting for association between diseases as indicators for health status.

Structured additive regression for categorical space-time data: a mixed model approach.

Motivated by a space-time study on forest health with damage state of trees as the response, we propose a general class of structured additive regression models for categorical responses, allowing for a flexible semiparametric predictor. Nonlinear effects of continuous covariates, time trends, and interactions between continuous covariates are modeled by penalized splines. Spatial effects can be estimated based on Markov random fields, Gaussian random fields, or two-dimensional penalized splines. We present our approach from a Bayesian perspective, with inference based on a categorical linear mixed model representation. The resulting empirical Bayes method is closely related to penalized likelihood estimation in a frequentist setting. Variance components, corresponding to inverse smoothing parameters, are estimated using (approximate) restricted maximum likelihood. In simulation studies we investigate the performance of different choices for the spatial effect, compare the empirical Bayes approach to competing methodology, and study the bias of mixed model estimates. As an application we analyze data from the forest health survey.

Analysing child mortality in Nigeria with geoadditive discrete-time survival models.

Child mortality reflects a country's level of socio-economic development and quality of life. In developing countries, mortality rates are not only influenced by socio-economic, demographic and health variables but they also vary considerably across regions and districts. In this paper, we analysed child mortality in Nigeria with flexible geoadditive discrete-time survival models. This class of models allows us to measure small-area district-specific spatial effects simultaneously with possibly non-linear or time-varying effects of other factors. Inference is fully Bayesian and uses computationally efficient Markov chain Monte Carlo (MCMC) simulation techniques. The application is based on the 1999 Nigeria Demographic and Health Survey. Our method assesses effects at a high level of temporal and spatial resolution not available with traditional parametric models, and the results provide some evidence on how to reduce child mortality by improving socio-economic and public health conditions.

Assessing brain activity through spatial Bayesian variable selection.

Statistical parametric mapping (SPM), relying on the general linear model and classical hypothesis testing, is a benchmark tool for assessing human brain activity using data from fMRI experiments. Friston et al. discuss some limitations of this frequentist approach and point out promising Bayesian perspectives. In particular, a Bayesian formulation allows explicit modeling and estimation of activation probabilities. In this study, we directly address this issue and develop a new regression based approach using spatial Bayesian variable selection. Our method has several advantages. First, spatial correlation is directly modeled for activation probabilities and indirectly for activation amplitudes. As a consequence, there is no need for spatial adjustment in a postprocessing step. Second, anatomical prior information, such as the distribution of grey matter or expert knowledge, can be included as part of the model. Third, the method has superior edge-preservation properties as well as being fast to compute. When applied to data from a simple visual experiment, the results demonstrate improved sensitivity for detecting activated cortical areas and for better preserving details of activated structures.