Sylvia Richardson

On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)

New methodology for fully Bayesian mixture analysis is developed, making use of reversible jump Markov chain Monte Carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture. A sample from the full joint distribution of all unknown variables is thereby generated, and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution. The methodology is applied here to the analysis of univariate normal mixtures, using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context.

Modifying the t test for assessing the correlation between two spatial processes

Clifford, Richardson, and Hm they require the estimation of an effective sample size that takes into account the spatial structure of both processes. Clifford et al. developed their method on the basis of an approximation of the variance of the sample correlation coefficient and assessed it by Monte Carlo simulations for lattice and non-lattice networks of moderate to large size. In the present paper, the variance of the sample covariance is computed for a finite number of locations, under the multinormality assumption, and the mathematical derivation of the definition of effective sample size is given. The theoretically expected number of degrees of freedom for the modified t test with renewed modifications is compared with that computed on the basis of equation (2.9) of Clifford et al. (1989). The largest differences are observed for small numbers of locations and high autocorrelation, in particular when the latter is present with opposite sign in the two processes. Basic references that were missing in Clifford et al. (1989) are given and inherent ambiguities are discussed.

Assessing the significance of the correlation between two spatial processes.

Modified tests of association based on the correlation coefficient or the covariance between two spatially autocorrelated processes are presented. These tests can be used both for lattice and nonlattice data. They are based on the evaluation of an effective sample size that takes into account the spatial structure. For positively autocorrelated processes, the effective sample size is reduced. A method for evaluating this reduction via an approximation of the variance of the correlation coefficient is developed. The performance of the tests is assessed by Monte Carlo simulations. The method is illustrated by examples from geographical epidemiology.

A comparison of Bayesian spatial models for disease mapping

With the advent of routine health data indexed at a fine geographical resolution, small area disease mapping studies have become an established technique in geographical epidemiology. The specific issues posed by the sparseness of the data and possibility for local spatial dependence belong to a generic class of statistical problems involving an underlying (latent) spatial process of interest corrupted by observational noise. These are naturally formulated within the framework of hierarchical models, and over the past decade, a variety of spatial models have been proposed for the latent level(s) of the hierarchy. In this article, we provide a comprehensive review of the main classes of such models that have been used for disease mapping within a Bayesian estimation paradigm, and report a performance comparison between representative models in these classes, using a set of simulated data to help illustrate their respective properties. We also consider recent extensions to model the joint spatial distribution of multiple disease or health indicators. The aim is to help the reader choose an appropriate structural prior for the second level of the hierarchical model and to discuss issues of sensitivity to this choice.

Interpreting Posterior Relative Risk Estimates in Disease-Mapping Studies

There is currently much interest in conducting spatial analyses of health outcomes at the small-area scale. This requires sophisticated statistical techniques, usually involving Bayesian models, to smooth the underlying risk estimates because the data are typically sparse. However, questions have been raised about the performance of these models for recovering the “true” risk surface, about the influence of the prior structure specified, and about the amount of smoothing of the risks that is actually performed. We describe a comprehensive simulation study designed to address these questions. Our results show that Bayesian disease-mapping models are essentially conservative, with high specificity even in situations with very sparse data but low sensitivity if the raised-risk areas have only a moderate (< 2-fold) excess or are not based on substantial expected counts (> 50 per area). Semiparametric spatial mixture models typically produce less smoothing than their conditional autoregressive counterpart when there is sufficient information in the data (moderate-size expected count and/or high true excess risk). Sensitivity may be improved by exploiting the whole posterior distribution to try to detect true raised-risk areas rather than just reporting and mapping the mean posterior relative risk. For the widely used conditional autoregressive model, we show that a decision rule based on computing the probability that the relative risk is above 1 with a cutoff between 70 and 80% gives a specific rule with reasonable sensitivity for a range of scenarios having moderate expected counts (~ 20) and excess risks (~1.5- to 2-fold). Larger (3-fold) excess risks are detected almost certainly using this rule, even when based on small expected counts, although the mean of the posterior distribution is typically smoothed to about half the true value.

Hidden Markov Models and Disease Mapping

We present new methodology to extend hidden Markov models to the spatial domain, and use this class of models to analyze spatial heterogeneity of count data on a rare phenomenon. This situation occurs commonly in many domains of application, particularly in disease mapping. We assume that the counts follow a Poisson model at the lowest level of the hierarchy, and introduce a finite-mixture model for the Poisson rates at the next level. The novelty lies in the model for allocation to the mixture components, which follows a spatially correlated process, the Potts model, and in treating the number of components of the spatial mixture as unknown. Inference is performed in a Bayesian framework using reversible jump Markov chain Monte Carlo. The model introduced can be viewed as a Bayesian semiparametric approach to specifying flexible spatial distribution in hierarchical models. Performance of the model and comparison with an alternative well-known Markov random field specification for the Poisson rates are demonstrated on synthetic datasets. We show that our allocation model avoids the problem of oversmoothing in cases where the underlying rates exhibit discontinuities, while giving equally good results in cases of smooth gradient-like or highly autocorrelated rates. The methodology is illustrated on an epidemiologic application to data on a rare cancer in France.

Risk of adverse birth outcomes in populations living near landfill sites

Abstract Objective: To investigate the risk of adverse birth outcomes associated with residence near landfill sites in Great Britain. Design: Geographical study of risks of adverse birth outcomes in populations living within 2 km of 9565 landfill sites operational at some time between 1982 and 1997 (from a total of 19 196 sites) compared with those living further away. Setting: Great Britain. Subjects: Over 8.2 million live births, 43 471 stillbirths, and 124 597 congenital anomalies (including terminations). Main outcome measures: All congenital anomalies combined, some specific anomalies, and prevalence of low and very low birth weight (<2500 g and <1500 g). Results: For all anomalies combined, relative risk of residence near landfill sites (all waste types) was 0.92 (99% confidence interval 0.907 to 0.923) unadjusted, and 1.01 (1.005 to 1.023) adjusted for confounders. Adjusted risks were 1.05 (1.01 to 1.10) for neural tube defects, 0.96 (0.93 to 0.99) for cardiovascular defects, 1.07 (1.04 to 1.10) for hypospadias and epispadias (with no excess of surgical correction), 1.08 (1.01 to 1.15) for abdominal wall defects, 1.19 (1.05 to 1.34) for surgical correction of gastroschisis and exomphalos, and 1.05 (1.047 to 1.055) and 1.04 (1.03 to 1.05) for low and very low birth weight respectively. There was no excess risk of stillbirth. Findings for special (hazardous) waste sites did not differ systematically from those for non-special sites. For some specific anomalies, higher risks were found in the period before opening compared with after opening of a landfill site, especially hospital admissions for abdominal wall defects. Conclusions: We found small excess risks of congenital anomalies and low and very low birth weight in populations living near landfill sites. No causal mechanisms are available to explain these findings, and alternative explanations include data artefacts and residual confounding. Further studies are needed to help differentiate between the various possibilities. What is already known on this topic Various studies have found excess risks of certain congenital anomalies and low birth weight near landfill sites Risks up to two to three times higher have been reported These studies have been difficult to interpret because of problems of exposure classification, small sample size, confounding, and reporting bias What this study adds Some 80% of the British population lives within 2 km of known landfill sites in Great Britain By including all landfill sites in the country, we avoided the problem of selective reporting, and maximised statistical power Although we found excess risks of congenital anomalies and low birth weight near landfill sites in Great Britain, they were smaller than in some other studies Further work is needed to differentiate potential data artefacts and confounding effects from possible causal associations with landfill

Modelling Heterogeneity With and Without the Dirichlet Process

We investigate the relationships between Dirichlet process (DP) based models and allocation models for a variable number of components, based on exchangeable distributions. It is shown that the DP partition distribution is a limiting case of a Dirichlet–multinomial allocation model. Comparisons of posterior performance of DP and allocation models are made in the Bayesian paradigm and illustrated in the context of univariate mixture models. It is shown in particular that the unbalancedness of the allocation distribution, present in the prior DP model, persists a posteriori. Exploiting the model connections, a new MCMC sampler for general DP based models is introduced, which uses split/merge moves in a reversible jump framework. Performance of this new sampler relative to that of some traditional samplers for DP processes is then explored.

Haplotype and isoform specific expression estimation using multi-mapping RNA-seq reads

We present a novel pipeline and methodology for simultaneously estimating isoform expression and allelic imbalance in diploid organisms using RNA-seq data. We achieve this by modeling the expression of haplotype-specific isoforms. If unknown, the two parental isoform sequences can be individually reconstructed. A new statistical method, MMSEQ, deconvolves the mapping of reads to multiple transcripts (isoforms or haplotype-specific isoforms). Our software can take into account non-uniform read generation and works with paired-end reads.

Transcriptional diversity during lineage commitment of human blood progenitors

Introduction Blood production in humans culminates in the daily release of around 1011 cells into the circulation, mainly platelets and red blood cells. All blood cells originate from a minute population of hematopoietic stem cells (HSCs) that expands and differentiates into progenitor cells with increasingly restricted lineage choice. Characterizing alternative splicing events involved in hematopoiesis is critical for interpreting the effects of mutations leading to inherited disorders and blood cancers and for the rational design of strategies to advance transplantation and regenerative medicine. Overview of methodology. RNA-sequencing reads from human blood progenitors [opaque cells in (A)] were mapped to the transcriptome to quantify gene and transcript expression. Reads were also mapped to the genome to identify novel splice junctions and characterize alternative splicing events (B). Rationale To address this, we explored the transcriptional diversity of human blood progenitors by sequencing RNA from six progenitor and two precursor populations representing the classical myeloid commitment stages of hematopoiesis and the main lymphoid stage. Data were aligned to the human reference transcriptome and genome to quantify known transcript isoforms and to identify novel splicing events, respectively. We used Bayesian polytomous model selection to classify transcripts into distinct expression patterns across the three cell types that comprise each differentiation step. Results We identified extensive transcriptional changes involving 6711 genes and 10,724 transcripts and validated a number of these. Many of the changes at the transcript isoform level did not result in significant changes at the gene expression level. Moreover, we identified transcripts unique to each of the progenitor populations, observing enrichment in non–protein-coding elements at the early stages of differentiation. We discovered 7881 novel splice junctions and 2301 differentially used alternative splicing events, enriched in genes involved in regulatory processes and often resulting in the gain or loss of functional domains. Of the alternative splice sites displaying differential usage, 73% resulted in exon-skipping events involving at least one protein domain (38.5%) or introducing a premature stop codon (26%). Enrichment analysis of RNA-binding motifs provided insights into the regulation of cell type–specific splicing events. To demonstrate the importance of specific isoforms in driving lineage fating events, we investigated the role of a transcription factor highlighted by our analyses. Our data show that nuclear factor I/B (NFIB) is highly expressed in megakaryocytes and that it is transcribed from an unannotated transcription start site preceding a novel exon. The novel NFIB isoform lacks the DNA binding/dimerization domain and therefore is unable to interact with its binding partner, NFIC. We further show that NFIB and NFIC are important in megakaryocyte differentiation. Conclusion We produced a quantitative catalog of transcriptional changes and splicing events representing the early progenitors of human blood. Our analyses unveil a previously undetected layer of regulation affecting cell fating, which involves transcriptional isoforms switching without noticeable changes at the gene level and resulting in the gain or loss of protein functions. A BLUEPRINT of immune cell development To determine the epigenetic mechanisms that direct blood cells to develop into the many components of our immune system, the BLUEPRINT consortium examined the regulation of DNA and RNA transcription to dissect the molecular traits that govern blood cell differentiation. By inducing immune responses, Saeed et al. document the epigenetic changes in the genome that underlie immune cell differentiation. Cheng et al. demonstrate that trained monocytes are highly dependent on the breakdown of sugars in the presence of oxygen, which allows cells to produce the energy needed to mount an immune response. Chen et al. examine RNA transcripts and find that specific cell lineages use RNA transcripts of different length and composition (isoforms) to form proteins. Together, the studies reveal how epigenetic effects can drive the development of blood cells involved in the immune system. Science, this issue 10.1126/science.1251086, 10.1126/science.1250684, 10.1126/science.1251033 RNA sequencing identifies how different cell fate decisions are made during blood cell differentiation. Blood cells derive from hematopoietic stem cells through stepwise fating events. To characterize gene expression programs driving lineage choice, we sequenced RNA from eight primary human hematopoietic progenitor populations representing the major myeloid commitment stages and the main lymphoid stage. We identified extensive cell type–specific expression changes: 6711 genes and 10,724 transcripts, enriched in non–protein-coding elements at early stages of differentiation. In addition, we found 7881 novel splice junctions and 2301 differentially used alternative splicing events, enriched in genes involved in regulatory processes. We demonstrated experimentally cell-specific isoform usage, identifying nuclear factor I/B (NFIB) as a regulator of megakaryocyte maturation—the platelet precursor. Our data highlight the complexity of fating events in closely related progenitor populations, the understanding of which is essential for the advancement of transplantation and regenerative medicine.