arXiv subjects

Andrea Riebler

Publications and source records attributed to Andrea Riebler.

24 records · Page 2Linked to original sources

arXiv2016

An intuitive Bayesian spatial model for disease mapping that accounts for scaling

In recent years, disease mapping studies have become a routine application within geographical epidemiology and are typically analysed within a Bayesian hierarchical model formulation. A variety of model formulations for the latent level have been proposed but all come with inherent issues. In the classical BYM model, the spatially structured component cannot be seen independently from the unstructured component. This makes prior definitions for the hyperparameters of the two random effects challenging. There are alternative model formulations that address this confounding, however, the issue on how to choose interpretable hyperpriors is still unsolved. Here, we discuss a recently proposed parameterisation of the BYM model that leads to improved parameter control as the hyperparameters can be seen independently from each other. Furthermore, the need for a scaled spatial component is addressed, which facilitates assignment of interpretable hyperpriors and make these transferable between spatial applications with different graph structures. We provide implementation details for the new model formulation which preserve sparsity properties, and we investigate systematically the model performance and compare it to existing parameterisations. Through a simulation study, we show that the new model performs well, both showing good learning abilities and good shrinkage behaviour. In terms of model choice criteria, the proposed model performs at least equally well as existing parameterisations, but only the new formulation offers parameters that are interpretable and hyperpriors that have a clear meaning.

stat.ME↗

arXiv2015

Bayesian bivariate meta-analysis of diagnostic test studies with interpretable priors

In a bivariate meta-analysis the number of diagnostic studies involved is often very low so that frequentist methods may result in problems. Bayesian inference is attractive as informative priors that add small amount of information can stabilise the analysis without overwhelming the data. However, Bayesian analysis is often computationally demanding and the selection of the prior for the covariance matrix of the bivariate structure is crucial with little data. The integrated nested Laplace approximations (INLA) method provides an efficient solution to the computational issues by avoiding any sampling, but the important question of priors remain. We explore the penalised complexity (PC) prior framework for specifying informative priors for the variance parameters and the correlation parameter. PC priors facilitate model interpretation and hyperparameter specification as expert knowledge can be incorporated intuitively. We conduct a simulation study to compare the properties and behaviour of differently defined PC priors to currently used priors in the field. The simulation study shows that the use of PC priors results in more precise estimates when specified in a sensible neighbourhood around the truth. To investigate the usage of PC priors in practice we reanalyse a meta-analysis using the telomerase marker for the diagnosis of bladder cancer.

stat.ME↗

arXiv2015

Penalising model component complexity: A principled, practical approach to constructing priors

In this paper, we introduce a new concept for constructing prior distributions. We exploit the natural nested structure inherent to many model components, which defines the model component to be a flexible extension of a base model. Proper priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user-defined scaling parameter for that model component, both in the univariate and the multivariate case. These priors are invariant to reparameterisations, have a natural connection to Jeffreys' priors, are designed to support Occam's razor and seem to have excellent robustness properties, all which are highly desirable and allow us to use this approach to define default prior distributions. Through examples and theoretical results, we demonstrate the appropriateness of this approach and how it can be applied in various situations.

stat.ME↗

arXiv2013

BayMeth: Improved DNA methylation quantification for affinity capture sequencing data using a flexible Bayesian approach

DNA methylation (DNAme) is a critical component of the epigenetic regulatory machinery and aberrations in DNAme patterns occur in many diseases, such as cancer. Mapping and understanding DNAme profiles offers considerable promise for reversing the aberrant states. There are several approaches to analyze DNAme, which vary widely in cost, resolution and coverage. Affinity capture and high-throughput sequencing of methylated DNA strike a good balance between the high cost of whole genome bisulphite sequencing (WGBS) and the low coverage of methylation arrays. However, existing methods cannot adequately differentiate between hypomethylation patterns and low capture efficiency, and do not offer flexibility to integrate copy number variation (CNV). Furthermore, no uncertainty estimates are provided, which may prove useful for combining data from multiple protocols or propagating into downstream analysis. We propose an empirical Bayes framework that uses a fully methylated (i.e. SssI treated) control sample to transform observed read densities into regional methylation estimates. In our model, inefficient capture can be distinguished from low methylation levels by means of larger posterior variances. Furthermore, we can integrate CNV by introducing a multiplicative offset into our Poisson model framework. Notably, our model offers analytic expressions for the mean and variance of the methylation level and thus is fast to compute. Our algorithm outperforms existing approaches in terms of bias, mean-squared error and coverage probabilities as illustrated on multiple reference datasets. Although our method provides advantages even without the SssI-control, considerable improvement is achieved by its incorporation. Our method can be applied to methylated DNA affinity enrichment assays (e.g MBD-seq, MeDIP-seq) and a software implementation is available in the Bioconductor Repitools package.

q-bio.GN↗

arXiv2013

Bayesian analysis of measurement error models using INLA

To account for measurement error (ME) in explanatory variables, Bayesian approaches provide a flexible framework, as expert knowledge about unobserved covariates can be incorporated in the prior distributions. However, given the analytic intractability of the posterior distribution, model inference so far has to be performed via time-consuming and complex Markov chain Monte Carlo implementations. In this paper we extend the Integrated nested Laplace approximations (INLA) approach to formulate Gaussian ME models in generalized linear mixed models. We present three applications, and show how parameter estimates are obtained for common ME models, such as the classical and Berkson error model including heteroscedastic variances. To illustrate the practical feasibility, R-code is provided.

stat.ME↗

arXiv2012

Estimation and extrapolation of time trends in registry data---Borrowing strength from related populations

To analyze and project age-specific mortality or morbidity rates age-period-cohort (APC) models are very popular. Bayesian approaches facilitate estimation and improve predictions by assigning smoothing priors to age, period and cohort effects. Adjustments for overdispersion are straightforward using additional random effects. When rates are further stratified, for example, by countries, multivariate APC models can be used, where differences of stratum-specific effects are interpretable as log relative risks. Here, we incorporate correlated stratum-specific smoothing priors and correlated overdispersion parameters into the multivariate APC model, and use Markov chain Monte Carlo and integrated nested Laplace approximations for inference. Compared to a model without correlation, the new approach may lead to more precise relative risk estimates, as shown in an application to chronic obstructive pulmonary disease mortality in three regions of England and Wales. Furthermore, the imputation of missing data for one particular stratum may be improved, since the new approach takes advantage of the remaining strata if the corresponding observations are available there. This is shown in an application to female mortality in Denmark, Sweden and Norway from the 20th century, where we treat for each country in turn either the first or second half of the observations as missing and then impute the omitted data. The projections are compared to those obtained from a univariate APC model and an extended Lee--Carter demographic forecasting approach using the proper Dawid--Sebastiani scoring rule.

stat.AP↗