Many models for the study of point-referenced data explicitly introduce spatial random effects to capture residual spatial association. These spatial effects are customarily modelled as a zero-mean stationary Gaussian process. The spatial Dirichlet process introduced by Gelfand et al. (2005) produces a random spatial process which is neither Gaussian nor stationary. Rather, it varies about a process that is assumed to be stationary and Gaussian. The spatial Dirichlet process arises as a probability-weighted collection of random surfaces. This can be limiting for modelling and inferential purposes since it insists that a process realization must be one of these surfaces. We introduce a random distribution for the spatial effects that allows different surface selection at different sites. Moreover, we can specify the model so that the marginal distribution of the effect at each site still comes from a Dirichlet process. The development is offered constructively, providing a multivariate extension of the stick-breaking representation of the weights. We then introduce mixing using this generalized spatial Dirichlet process. We illustrate with a simulated dataset of independent replications and note that we can embed the generalized process within a dynamic model specification to eliminate the independence assumption.
12 June 2009 in Journal of the Royal Statistical Society Series B: Statistical Methodology
Understanding longitudinal variability of the microbiome in ill patients is critical to moving microbiome-based measurements and therapeutics into clinical practice. However, the vast majority of data regarding microbiome stability are derived from healthy subjects. Herein, we sought to determine intra-patient temporal microbiota variability, the factors driving such variability, and its clinical impact in an extensive longitudinal cohort of hospitalized cancer patients during chemotherapy. The stool (n = 365) and oral (n = 483) samples of 59 patients with acute myeloid leukemia (AML) undergoing induction chemotherapy (IC) were sampled from initiation of chemotherapy until neutrophil recovery. Microbiome characterization was performed via analysis of 16S rRNA gene sequencing. Temporal variability was determined using coefficients of variation (CV) of the Shannon diversity index (SDI) and unweighted and weighted UniFrac distances per patient, per site. Measurements of intra-patient temporal variability and patient stability categories were analyzed for their correlations with genera abundances. Groups of patients were analyzed to determine if patients with adverse outcomes had significantly different levels of microbiome temporal variability. Potential clinical drivers of microbiome temporal instability were determined using multivariable regression analyses. Our cohort evidenced a high degree of intra-patient temporal instability of stool and oral microbial diversity based on SDI CV. We identified statistically significant differences in the relative abundance of multiple taxa amongst individuals with different levels of microbiota temporal stability. Increased intra-patient temporal variability of the oral SDI was correlated with increased risk of infection during IC (P = 0.02), and higher stool SDI CVs were correlated with increased risk of infection 90 days post-IC (P = 0.04). Total days on antibiotics was significantly associated with increased temporal variability of both oral microbial diversity (P = 0.03) and community structure (P = 0.002). These data quantify the longitudinal variability of the oral and gut microbiota in AML patients, show that increased variability was correlated with adverse clinical outcomes, and offer the possibility of using stabilizing taxa as a method of focused microbiome repletion. Furthermore, these results support the importance of longitudinal microbiome sampling and analyses, rather than one time measurements, in research and future clinical practice.
The Human Microbiome has been variously associated with the immune-regulatory mechanisms involved in the prevention or development of many non-infectious human diseases such as autoimmunity, allergy and cancer. Integrative approaches which aim at associating the composition of the human microbiome with other available information, such as clinical covariates and environmental predictors, are paramount to develop a more complete understanding of the role of microbiome in disease development. In this manuscript, we propose a Bayesian Dirichlet-Multinomial regression model which uses spike-and-slab priors for the selection of significant associations between a set of available covariates and taxa from a microbiome abundance table. The approach allows straightforward incorporation of the covariates through a log-linear regression parametrization of the parameters of the Dirichlet-Multinomial likelihood. Inference is conducted through a Markov Chain Monte Carlo algorithm, and selection of the significant covariates is based upon the assessment of posterior probabilities of inclusions and the thresholding of the Bayesian false discovery rate. We design a simulation study to evaluate the performance of the proposed method, and then apply our model on a publicly available dataset obtained from the Human Microbiome Project which associates taxa abundances with KEGG orthology pathways. The method is implemented in specifically developed R code, which has been made publicly available. Our method compares favorably in simulations to several recently proposed approaches for similarly structured data, in terms of increased accuracy and reduced false positive as well as false negative rates. In the application to the data from the Human Microbiome Project, a close evaluation of the biological significance of our findings confirms existing associations in the literature.