Reporting and Interpretation in Genome-Wide Association Studies

In the context of genome-wide association studies we critique a number of methods that have been suggested for flagging associations for further investigation. The p-value is by far the most commonly used measure, but requires careful calibration when the a priori probability of an association is small, and discards information by not considering the power associated with each test. The q-value is a frequentist method by which the false discovery rate (FDR) may be controlled. We advocate the use of the Bayes factor as a summary of the information in the data with respect to the comparison of the null and alternative hypotheses, and describe a recently-proposed approach to the calculation of the Bayes factor that is easily implemented. The combination of data across studies is straightforward using the Bayes factor approach, as are power calculations. The Bayes factor and the q-value provide complementary information and when used in addition to the p-value may be used to reduce the number of reported findings that are subsequently not reproduced

Restricted Covariance Priors with Applications in Spatial Statistics

We present a Bayesian model for area-level count data that uses Gaussian random effects with a novel type of G-Wishart prior on the inverse variance--covariance matrix. Specifically, we introduce a new distribution called the truncated G-Wishart distribution that has support over precision matrices that lead to positive associations between the random effects of neighboring regions while preserving conditional independence of non-neighboring regions. We describe Markov chain Monte Carlo sampling algorithms for the truncated G-Wishart prior in a disease mapping context and compare our results to Bayesian hierarchical models based on intrinsic autoregression priors. A simulation study illustrates that using the truncated G-Wishart prior improves over the intrinsic autoregressive priors when there are discontinuities in the disease risk surface. The new model is applied to an analysis of cancer incidence data in Washington State.Comment: Published at http://dx.doi.org/10.1214/14-BA927 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/

A linear noise approximation for stochastic epidemic models fit to partially observed incidence counts

Stochastic epidemic models (SEMs) fit to incidence data are critical to elucidating outbreak dynamics, shaping response strategies, and preparing for future epidemics. SEMs typically represent counts of individuals in discrete infection states using Markov jump processes (MJPs), but are computationally challenging as imperfect surveillance, lack of subject-level information, and temporal coarseness of the data obscure the true epidemic. Analytic integration over the latent epidemic process is impossible, and integration via Markov chain Monte Carlo (MCMC) is cumbersome due to the dimensionality and discreteness of the latent state space. Simulation-based computational approaches can address the intractability of the MJP likelihood, but are numerically fragile and prohibitively expensive for complex models. A linear noise approximation (LNA) that approximates the MJP transition density with a Gaussian density has been explored for analyzing prevalence data in large-population settings, but requires modification for analyzing incidence counts without assuming that the data are normally distributed. We demonstrate how to reparameterize SEMs to appropriately analyze incidence data, and fold the LNA into a data augmentation MCMC framework that outperforms deterministic methods, statistically, and simulation-based methods, computationally. Our framework is computationally robust when the model dynamics are complex and applies to a broad class of SEMs. We evaluate our method in simulations that reflect Ebola, influenza, and SARS-CoV-2 dynamics, and apply our method to national surveillance counts from the 2013--2015 West Africa Ebola outbreak

Efficient data augmentation for fitting stochastic epidemic models to prevalence data

Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time evolution of an epidemic gives rise to a complicated latent variable problem in which the state space size of the epidemic grows large as the population size increases. This makes analytically integrating over the missing data infeasible for populations of even moderate size. We present a data augmentation Markov chain Monte Carlo (MCMC) framework for Bayesian estimation of stochastic epidemic model parameters, in which measurements are augmented with subject-level disease histories. In our MCMC algorithm, we propose each new subject-level path, conditional on the data, using a time-inhomogeneous continuous-time Markov process with rates determined by the infection histories of other individuals. The method is general, and may be applied, with minimal modifications, to a broad class of stochastic epidemic models. We present our algorithm in the context of multiple stochastic epidemic models in which the data are binomially sampled prevalence counts, and apply our method to data from an outbreak of influenza in a British boarding school