Gauss-Seidel Estimation of Generalized Linear Mixed Models with Application to Poisson Modeling of Spatially Varying Disease Rates

Generalized linear mixed models (GLMMs) provide an elegant framework for the analysis of correlated data. Due to the non-closed form of the likelihood, GLMMs are often fit by computational procedures like penalized quasi-likelihood (PQL). Special cases of these models are generalized linear models (GLMs), which are often fit using algorithms like iterative weighted least squares (IWLS). High computational costs and memory space constraints often make it difficult to apply these iterative procedures to data sets with very large number of cases. This paper proposes a computationally efficient strategy based on the Gauss-Seidel algorithm that iteratively fits sub-models of the GLMM to subsetted versions of the data. Additional gains in efficiency are achieved for Poisson models, commonly used in disease mapping problems, because of their special collapsibility property which allows data reduction through summaries. Convergence of the proposed iterative procedure is guaranteed for canonical link functions. The strategy is applied to investigate the relationship between ischemic heart disease, socioeconomic status and age/gender category in New South Wales, Australia, based on outcome data consisting of approximately 33 million records. A simulation study demonstrates the algorithm's reliability in analyzing a data set with 12 million records for a (non-collapsible) logistic regression model.

Semiparametric Normal Transformation Models for Spatially Correlated Survival Data

There is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiological studies. In this paper, we propose a new class of semiparametric normal transformation models for right censored spatially correlated survival data. This class of models assumes that survival outcomes marginally follow a Cox proportional hazard model with unspecified baseline hazard, and their joint distribution is obtained by transforming survival outcomes to normal random variables, whose joint distribution is assumed to be multivariate normal with a spatial correlation structure. A key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields. We study the relationship of the spatial correlation structure of the transformed normal variables and the dependence measures of the original survival times. Direct nonparametric maximum likelihood estimation in such models is practically prohibited due to the high dimensional intractable integration of the likelihood function and the infinite dimensional nuisance baseline hazard parameter. We hence develop a class of spatial semiparametric estimating equations, which conveniently estimate the population-level regression coefficients and the dependence parameters simultaneously. We study the asymptotic properties of the proposed estimators, and show that they are consistent and asymptotically normal. The proposed method is illustrated with an analysis of data from the East Boston Ashma Study and its performance is evaluated using simulations.

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.

Colonization history of the Swiss Rhine basin by the bullhead (Cottus gobio): inference under a Bayesian spatially explicit framework

The present distribution of freshwater fish in the Alpine region has been strongly affected by colonization events occurring after the last glacial maximum (LGM), some 20,000 years ago. We use here a spatially explicit simulation framework to model and better understand their colonization dynamics in the Swiss Rhine basin. This approach is applied to the European bullhead (Cottus gobio), which is an ideal model organism to study fish past demographic processes since it has not been managed by humans. The molecular diversity of eight sampled populations is simulated and compared to observed data at six microsatellite loci under an approximate Bayesian computation framework to estimate the parameters of the colonization process. Our demographic estimates fit well with current knowledge about the biology of this species, but they suggest that the Swiss Rhine basin was colonized very recently, after the Younger Dryas some 6600 years ago. We discuss the implication of this result, as well as the strengths and limits of the spatially explicit approach coupled to the approximate Bayesian computation framework.

Enterococcus faecalis PcfC, a spatially localized substrate receptor for type IV secretion of the pCF10 transfer intermediate.

Upon sensing of peptide pheromone, Enterococcus faecalis efficiently transfers plasmid pCF10 through a type IV secretion (T4S) system to recipient cells. The PcfF accessory factor and PcfG relaxase initiate transfer by catalyzing strand-specific nicking at the pCF10 origin of transfer sequence (oriT). Here, we present evidence that PcfF and PcfG spatially coordinate docking of the pCF10 transfer intermediate with PcfC, a membrane-bound putative ATPase related to the coupling proteins of gram-negative T4S machines. PcfC and PcfG fractionated with the membrane and PcfF with the cytoplasm, yet all three proteins formed several punctate foci at the peripheries of pheromone-induced cells as monitored by immunofluorescence microscopy. A PcfC Walker A nucleoside triphosphate (NTP) binding site mutant (K156T) fractionated with the E. faecalis membrane and also formed foci, whereas PcfC deleted of its N-terminal putative transmembrane domain (PcfCDelta N103) distributed uniformly throughout the cytoplasm. Native PcfC and mutant proteins PcfCK156T and PcfCDelta N103 bound pCF10 but not pcfG or Delta oriT mutant plasmids as shown by transfer DNA immunoprecipitation, indicating that PcfC binds only the processed form of pCF10 in vivo. Finally, purified PcfCDelta N103 bound DNA substrates and interacted with purified PcfF and PcfG in vitro. Our findings support a model in which (i) PcfF recruits PcfG to oriT to catalyze T-strand nicking, (ii) PcfF and PcfG spatially position the relaxosome at the cell membrane to stimulate substrate docking with PcfC, and (iii) PcfC initiates substrate transfer through the pCF10 T4S channel by an NTP-dependent mechanism.

Agrobacterium ParA/MinD-like VirC1 spatially coordinates early conjugative DNA transfer reactions.

Agrobacterium tumefaciens translocates T-DNA through a polar VirB/D4 type IV secretion (T4S) system. VirC1, a factor required for efficient T-DNA transfer, bears a deviant Walker A and other sequence motifs characteristic of ParA and MinD ATPases. Here, we show that VirC1 promotes conjugative T-DNA transfer by stimulating generation of multiple copies per cell of the T-DNA substrate (T-complex) through pairwise interactions with the processing factors VirD2 relaxase, VirC2, and VirD1. VirC1 also associates with the polar membrane and recruits T-complexes to cell poles, the site of VirB/D4 T4S machine assembly. VirC1 Walker A mutations abrogate T-complex generation and polar recruitment, whereas the native protein recruits T-complexes to cell poles independently of other polar processing factors (VirC2, VirD1) or T4S components (VirD4 substrate receptor, VirB channel subunits). We propose that A. tumefaciens has appropriated a progenitor ParA/MinD-like ATPase to promote conjugative DNA transfer by: (i) nucleating relaxosome assembly at oriT-like T-DNA border sequences and (ii) spatially positioning the transfer intermediate at the cell pole to coordinate substrate-T4S channel docking.