Statistical inference for familial disease clusters

In many epidemiologic studies, the first indication of an environmental or genetic contribution to the disease is the way in which the diseased cases cluster within the same family units. The concept of clustering is contrasted with incidence. We assume that all individuals are exchangeable except for their disease status. This assumption is used to provide an exact test of the initial hypothesis of no familial link with the disease, conditional on the number of diseased cases and the distribution of the sizes of the various family units. New parametric generalizations of binomial sampling models are described to provide measures of the effect size of the disease clustering. We consider models and an example that takes covariates into account. Ascertainment bias is described and the appropriate sampling distribution is demonstrated. Four numerical examples with real data illustrate these methods.     

Marginalized transition models and likelihood inference for longitudinal categorical data

Marginal generalized linear models are now frequently used for the analysis of longitudinal data. Semiparametric inference for marginal models was introduced by Liang and Zeger (1986, Biometrics 73, 13-22). This article develops a general parametric class of serial dependence models that permits likelihood-based marginal regression analysis of binary response data. The methods naturally extend the first-order Markov models of Azzalini (1994, Biometrika 81, 767-775) and prove computationally feasible for long series.     

Dynamic occupancy models for analyzing species' range dynamics across large geographic scales

Large‐scale biodiversity data are needed to predict species' responses to global change and to address basic questions in macroecology. While such data are increasingly becoming available, their analysis is challenging because of the typically large heterogeneity in spatial sampling intensity and the need to account for observation processes. Two further challenges are accounting for spatial effects that are not explained by covariates, and drawing inference on dynamics at these large spatial scales. We developed dynamic occupancy models to analyze large‐scale atlas data. In addition to occupancy, these models estimate local colonization and persistence probabilities. We accounted for spatial autocorrelation using conditional autoregressive models and autologistic models. We fitted the models to detection/nondetection data collected on a quarter‐degree grid across southern Africa during two atlas projects, using the hadeda ibis (Bostrychia hagedash) as an example. The model accurately reproduced the range expansion between the first (SABAP1: 1987–1992) and second (SABAP2: 2007–2012) Southern African Bird Atlas Project into the drier parts of interior South Africa. Grid cells occupied during SABAP1 generally remained occupied, but colonization of unoccupied grid cells was strongly dependent on the number of occupied grid cells in the neighborhood. The detection probability strongly varied across space due to variation in effort, observer identity, seasonality, and unexplained spatial effects. We present a flexible hierarchical approach for analyzing grid‐based atlas data using dynamical occupancy models. Our model is similar to a species' distribution model obtained using generalized additive models but has a number of advantages. Our model accounts for the heterogeneous sampling process, spatial correlation, and perhaps most importantly, allows us to examine dynamic aspects of species ranges.     

Spatial multistate transitional models for longitudinal event data

Summary .   Follow-up medical studies often collect longitudinal data on patients. Multistate transitional models are useful for analysis in such studies where at any point in time, individuals may be said to occupy one of a discrete set of states and interest centers on the transition process between states. For example, states may refer to the number of recurrences of an event, or the stage of a disease. We develop a hierarchical modeling framework for the analysis of such longitudinal data when the processes corresponding to different subjects may be correlated spatially over a region. Continuous-time Markov chains incorporating spatially correlated random effects are introduced. Here, joint modeling of both spatial dependence as well as dependence between different transition rates is required and a multivariate spatial approach is employed. A proportional intensities frailty model is developed where baseline intensity functions are modeled using parametric Weibull forms, piecewise-exponential formulations, and flexible representations based on cubic B-splines. The methodology is developed within the context of a study examining invasive cardiac procedures in Quebec. We consider patients admitted for acute coronary syndrome throughout the 139 local health units of the province and examine readmission and mortality rates over a 4-year period.     

A general model of G protein-coupled receptor sequences and its application to detect remote homologs

G protein-coupled receptors (GPCRs) constitute a large superfamily involved in various types of signal transduction pathways triggered by hormones, odorants, peptides, proteins, and other types of ligands. The superfamily is so diverse that many members lack sequence similarity, although they all span the cell membrane seven times with an extracellular N and a cytosolic C terminus. We analyzed a divergent set of GPCRs and found distinct loop length patterns and differences in amino acid composition between cytosolic loops, extracellular loops, and membrane regions. We configured GPCRHMM, a hidden Markov model, to fit those features and trained it on a large dataset representing the entire superfamily. GPCRHMM was benchmarked to profile HMMs and generic transmembrane detectors on sets of known GPCRs and non-GPCRs. In a cross-validation procedure, profile HMMs produced an error rate nearly twice as high as GPCRHMM. In a sensitivity-selectivity test, GPCRHMM's sensitivity was about 15% higher than that of the best transmembrane predictors, at comparable false positive rates. We used GPCRHMM to search for novel members of the GPCR superfamily in five proteomes. All in all we detected 120 sequences that lacked annotation and are potentially novel GPCRs. Out of those 102 were found in Caenorhabditis elegans, four in human, and seven in mouse. Many predictions (65) belonged to Pfam domains of unknown function. GPCRHMM strongly rejected a family of arthropod-specific odorant receptors believed to be GPCRs. A detailed analysis showed that these sequences are indeed very different from other GPCRs. GPCRHMM is available at http://gpcrhmm.cgb.ki.se.     

Bayesian Modeling of ChIP‐chip Data Through a High‐Order Ising Model

Summary ChIP‐chip experiments are procedures that combine chromatin immunoprecipitation (ChIP) and DNA microarray (chip) technology to study a variety of biological problems, including protein–DNA interaction, histone modification, and DNA methylation. The most important feature of ChIP‐chip data is that the intensity measurements of probes are spatially correlated because the DNA fragments are hybridized to neighboring probes in the experiments. We propose a simple, but powerful Bayesian hierarchical approach to ChIP‐chip data through an Ising model with high‐order interactions. The proposed method naturally takes into account the intrinsic spatial structure of the data and can be used to analyze data from multiple platforms with different genomic resolutions. The model parameters are estimated using the Gibbs sampler. The proposed method is illustrated using two publicly available data sets from Affymetrix and Agilent platforms, and compared with three alternative Bayesian methods, namely, Bayesian hierarchical model, hierarchical gamma mixture model, and Tilemap hidden Markov model. The numerical results indicate that the proposed method performs as well as the other three methods for the data from Affymetrix tiling arrays, but significantly outperforms the other three methods for the data from Agilent promoter arrays. In addition, we find that the proposed method has better operating characteristics in terms of sensitivities and false discovery rates under various scenarios.     

Monte carlo inference for state-space models of wild animal populations

Summary .  We compare two Monte Carlo (MC) procedures, sequential importance sampling (SIS) and Markov chain Monte Carlo (MCMC), for making Bayesian inferences about the unknown states and parameters of state–space models for animal populations. The procedures were applied to both simulated and real pup count data for the British grey seal metapopulation, as well as to simulated data for a Chinook salmon population. The MCMC implementation was based on tailor-made proposal distributions combined with analytical integration of some of the states and parameters. SIS was implemented in a more generic fashion. For the same computing time MCMC tended to yield posterior distributions with less MC variation across different runs of the algorithm than the SIS implementation with the exception in the seal model of some states and one of the parameters that mixed quite slowly. The efficiency of the SIS sampler greatly increased by analytically integrating out unknown parameters in the observation model. We consider that a careful implementation of MCMC for cases where data are informative relative to the priors sets the gold standard, but that SIS samplers are a viable alternative that can be programmed more quickly. Our SIS implementation is particularly competitive in situations where the data are relatively uninformative; in other cases, SIS may require substantially more computer power than an efficient implementation of MCMC to achieve the same level of MC error.     

Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models

Inference for Dirichlet process hierarchical models is typicallyperformed using Markov chain Monte Carlo methods, which canbe roughly categorized into marginal and conditional methods.The former integrate out analytically the infinite-dimensionalcomponent of the hierarchical model and sample from the marginaldistribution of the remaining variables using the Gibbs sampler.Conditional methods impute the Dirichlet process and updateit as a component of the Gibbs sampler. Since this requiresimputation of an infinite-dimensional process, implementationof the conditional method has relied on finite approximations.In this paper, we show how to avoid such approximations by designingtwo novel Markov chain Monte Carlo algorithms which sample fromthe exact posterior distribution of quantities of interest.The approximations are avoided by the new technique of retrospectivesampling. We also show how the algorithms can obtain samplesfrom functionals of the Dirichlet process. The marginal andthe conditional methods are compared and a careful simulationstudy is included, which involves a non-conjugate model, differentdatasets and prior specifications.     

Model selection and parameter estimation for ion channel recordings with an application to the K + outward-rectifier in barley leaf

We present a statistical method, and its accompanying algorithms, for the selection of a mathematical model of the gating mechanism of an ion channel and for the estimation of the parameters of this model. The method assumes a hidden Markov model that incorporates filtering, colored noise and state-dependent white excess noise for the recorded data. The model selection and parameter estimation are performed via a Bayesian approach using Markov chain Monte Carlo. The method is illustrated by its application to single-channel recordings of the K⁺ outward-rectifier in barley leaf.Acknowledgement The authors thank Sake Vogelzang, Bert van Duijn and Bert de Boer for their helpful advice and useful comments and suggestions.     

Discovering structure in multiple outcomes models for tests of childhood neurodevelopment

Bayesian model–based clustering provides a powerful and flexible tool that can be incorporated into regression models to better understand the grouping of observations. Using data from the Seychelles Child Development Study, we explore the effect of prenatal methylmercury exposure on 20 neurodevelopmental outcomes measured in 9-year-old children. Rather than cluster individual subjects, we cluster the outcomes within a multiple outcomes model. By using information in the data to nest the outcomes into groups called domains, the model more accurately reflects the shared characteristics of neurodevelopmental domains and improves estimation of the overall and outcome-specific exposure effects by shrinking effects within and between domains selected by the data. The Bayesian paradigm allows for sampling from the posterior distribution of the grouping parameters; thus, inference can be made about group membership and their defining characteristics. We avoid the often difficult and highly subjective requirement of a priori identification of the total number of groups by incorporating a Dirichlet process prior to form a fully Bayesian multiple outcomes model.