Association testing aims to discover the underlying relationship between genotypes (usually Single Nucleotide Polymorphisms, or SNPs) and phenotypes (attributes, or traits). The typically large data sets used in association testing often contain missing values. Standard statistical methods either impute the missing values using relatively simple assumptions, or delete them, or both, which can generate biased results. Here we describe the Bayesian hierarchical model BAMD (Bayesian Association with Missing Data). BAMD is a Gibbs sampler, in which missing values are multiply imputed based upon all of the available information in the data set. We estimate the parameters and prove that updating one SNP at each iteration preserves the ergodic property of the Markov chain, and at the same time improves computational speed. We also implement a model selection option in BAMD, which enables potential detection of SNP interactions. Simulations show that unbiased estimates of SNP effects are recovered with missing genotype data. Also, we validate associations between SNPs and a carbon isotope discrimination phenotype that were previously reported using a family based method, and discover an additional SNP associated with the trait. BAMD is available as an R-package from http://cran.r-project.org/package=BAMD.

Whole and targeted sequencing of human genomes is a promising, increasingly feasible tool for discovering genetic contributions to risk of complex diseases. A key step is calling an individual’s genotype from the multiple aligned short read sequences of his DNA, each of which is subject to nucleotide read error. Current methods are designed to call genotypes separately at each locus from the sequence data of unrelated individuals. Here we propose likelihood-based methods that improve calling accuracy by exploiting two features of sequence data. The first is the linkage disequilibrium (LD) between nearby SNPs. The second is the Mendelian pedigree information available when related individuals are sequenced. In both cases the likelihood involves the probabilities of read variant counts given genotypes, summed over the unobserved genotypes. Parameters governing the prior genotype distribution and the read error rates can be estimated either from the sequence data itself or from external reference data. We use simulations and synthetic read data based on the 1000 Genomes Project to evaluate the performance of the proposed methods. An R-program to apply the methods to small families is freely available at http://med.stanford.edu/epidemiology/PHGC/.

We propose a flexible change-point model for inhomogeneous Poisson Processes, which arise naturally from next-generation DNA sequencing, and derive score and generalized likelihood statistics for shifts in intensity functions. We construct a modified Bayesian information criterion (mBIC) to guide model selection, and point-wise approximate Bayesian confidence intervals for assessing the confidence in the segmentation. The model is applied to DNA Copy Number profiling with sequencing data and evaluated on simulated spike-in and real data sets.

Identifying differentially expressed (DE) genes associated with a sample characteristic is the primary objective of many microarray studies. As more and more studies are carried out with observational rather than well controlled experimental samples, it becomes important to evaluate and properly control the impact of sample heterogeneity on DE gene finding. Typical methods for identifying DE genes require ranking all the genes according to a preselected statistic based on a single model for two or more group comparisons, with or without adjustment for other covariates. Such single model approaches unavoidably result in model misspecification, which can lead to increased error due to bias for some genes and reduced efficiency for the others. We evaluated the impact of model misspecification from such approaches on detecting DE genes and identified parameters that affect the magnitude of impact. To properly control for sample heterogeneity and to provide a flexible and coherent framework for identifying simultaneously DE genes associated with a single or multiple sample characteristics and/or their interactions, we proposed a Bayesian model averaging approach which corrects the model misspecification by averaging over model space formed by all relevant covariates. An empirical approach is suggested for specifying prior model probabilities. We demonstrated through simulated microarray data that this approach resulted in improved performance in DE gene identification compared to the single model approaches. The flexibility of this approach is demonstrated through our analysis of data from two observational microarray studies.

Public data repositories have enabled researchers to compare results across multiple genomic studies in order to replicate findings. A common approach is to first rank genes according to an hypothesis of interest within each study. Then, lists of the top-ranked genes within each study are compared across studies. Genes recaptured as highly ranked (usually above some threshold) in multiple studies are considered to be significant. However, this comparison strategy often remains informal, in that type I error and false discovery rate (FDR) are usually uncontrolled. In this paper, we formalize an inferential strategy for this kind of list-intersection discovery test. We show how to compute a $p$-value associated with a “recaptured” set of genes, using a closed-form Poisson approximation to the distribution of the size of the recaptured set. We investigate operating characteristics of the test as a function of the total number of studies considered, the rank threshold within each study, and the number of studies within which a gene must be recaptured to be declared significant. We investigate the trade off between FDR control and expected sensitivity (the expected proportion of true-positive genes identified as significant). We give practical guidance on how to design a bioinformatic list-intersection study with maximal expected sensitivity and prespecified control of type I error (at the set level) and false discovery rate (at the gene level). We show how optimal choice of parameters may depend on particular alternative hypothesis which might hold. We illustrate our methods using prostate cancer gene-expression datasets from the curated Oncomine database, and discuss the effects of dependence between genes on the test.

In this paper we propose a Bayesian approach for inference about dependence of high throughput gene expression. Our goals are to use prior knowledge about pathways to anchor inference about dependence among genes; to account for this dependence while making inferences about differences in mean expression across phenotypes; and to explore differences in the dependence itself across phenotypes. Useful features of the proposed approach are a model-based parsimonious representation of expression as an ordinal outcome, a novel and flexible representation of prior information on the nature of dependencies, and the use of a coherent probability model over both the structure and strength of the dependencies of interest. We evaluate our approach through simulations and in the analysis of data on expression of genes in the Complement and Coagulation Cascade pathway in ovarian cancer.

We consider multivariate two-sample tests of means, where the location shift between the two populations is expected to be related to a known graph structure. An important application of such tests is the detection of differentially expressed genes between two patient populations, as shifts in expression levels are expected to be coherent with the structure of graphs reflecting gene properties such as biological process, molecular function, regulation or metabolism. For a fixed graph of interest, we demonstrate that accounting for graph structure can yield more powerful tests under the assumption of smooth distribution shift on the graph. We also investigate the identification of nonhomogeneous subgraphs of a given large graph, which poses both computational and multiple hypothesis testing problems. The relevance and benefits of the proposed approach are illustrated on synthetic data and on breast and bladder cancer gene expression data analyzed in the context of KEGG and NCI pathways.

We present a new approach to factor rotation for functional data. This is achieved by rotating the functional principal components toward a predefined space of periodic functions designed to decompose the total variation into components that are nearly-periodic and nearly-aperiodic with a predefined period. We show that the factor rotation can be obtained by calculation of canonical correlations between appropriate spaces which make the methodology computationally efficient. Moreover, we demonstrate that our proposed rotations provide stable and interpretable results in the presence of highly complex covariance. This work is motivated by the goal of finding interpretable sources of variability in gridded time series of vegetation index measurements obtained from remote sensing, and we demonstrate our methodology through an application of factor rotation of this data.

Global marketing managers are interested in understanding the speed of the new product diffusion process and how the speed has changed in our ever more technologically advanced and global marketplace. Understanding the process allows firms to forecast the expected rate of return on their new products and develop effective marketing strategies. The most recent major study on this topic [Marketing Science 21 (2002) 97–114] investigated new product diffusions in the United States. We expand upon that study in three important ways. (1) Van den Bulte notes that a similar study is needed in the international context, especially in developing countries. Our study covers four new product diffusions across 31 developed and developing nations from 1980–2004. Our sample accounts for about 80% of the global economic output and 60% of the global population, allowing us to examine more general phenomena. (2) His model contains the implicit assumption that the diffusion speed parameter is constant throughout the diffusion life cycle of a product. Recognizing the likely effects on the speed parameter of recent changes in the marketplace, we model the parameter as a semiparametric function, allowing it the flexibility to change over time. (3) We perform a variable selection to determine that the number of internet users and the consumer price index are strongly associated with the speed of diffusion.

We propose a statistical modeling technique, called the Hierarchical Association Rule Model (HARM), that predicts a patient’s possible future medical conditions given the patient’s current and past history of reported conditions. The core of our technique is a Bayesian hierarchical model for selecting predictive association rules (such as “condition 1 and condition 2 → condition 3”) from a large set of candidate rules. Because this method “borrows strength” using the conditions of many similar patients, it is able to provide predictions specialized to any given patient, even when little information about the patient’s history of conditions is available.