The false discovery rate: a variable selection perspective

In many scientific and medical settings, large-scale experiments are generating large quantities of data that lead to inferential problems involving multiple hypotheses. This has led to recent tremendous interest in statistical methods regarding the false discovery rate (FDR). Several authors have studied the properties involving FDR in a univariate mixture model setting. In this article, we turn the problem on its side; in this manuscript, we show that FDR is a by-product of Bayesian analysis of variable selection problem for a hierarchical linear regression model. This equivalence gives many Bayesian insights as to why FDR is a natural quantity to consider. In addition, we relate the risk properties of FDR-controlling procedures to those from variable selection procedures from a decision theoretic framework different from that considered by other authors

An Extended General Location Model for Causal Inference from Data Subject to Noncompliance and Missing Values

Noncompliance is a common problem in experiments involving randomized assignment of treatments, and standard analyses based on intention-to treat or treatment received have limitations. An attractive alternative is to estimate the Complier-Average Causal Effect (CACE), which is the average treatment effect for the subpopulation of subjects who would comply under either treatment (Angrist, Imbens and Rubin, 1996, henceforth AIR). We propose an Extended General Location Model to estimate the CACE from data with non-compliance and missing data in the outcome and in baseline covariates. Models for both continuous and categorical outcomes and ignorable and latent ignorable (Frangakis and Rubin, 1999) missing data mechanisms are developed. Inferences for the models are based on the EM algorithm and Bayesian MCMC methods. We present results from simulations that investigate sensitivity to model assumptions and the influence of missing-data mechanism. We also apply the method to the data from a job search intervention for the unemployed workers

A Bayesian method for finding interactions in genomic studies

An important step in building a multiple regression model is the selection of predictors. In genomic and epidemiologic studies, datasets with a small sample size and a large number of predictors are common. In such settings, most standard methods for identifying a good subset of predictors are unstable. Furthermore, there is an increasing emphasis towards identification of interactions, which has not been studied much in the statistical literature. We propose a method, called BSI (Bayesian Selection of Interactions), for selecting predictors in a regression setting when the number of predictors is considerably larger than the sample size with a focus towards selecting interactions. Latent variables are used to infer subset choices based on the posterior distribution. Inference about interactions is implemented by a constraint on the latent variables. The posterior distribution is computed using the Gibbs Sampling methods. The finite-sample properties of the proposed method are assessed by simulation studies. We illustrate the BSI method by analyzing data from a hypertension study involving Single Nucleotide Polymorphisms (SNPs)

Combining Information from Two Surveys to Estimate County-Level Prevalence Rates of Cancer Risk Factors and Screening

Cancer surveillance requires estimates of the prevalence of cancer risk factors and screening for small areas such as counties. Two popular data sources are the Behavioral Risk Factor Surveillance System (BRFSS), a telephone survey conducted by state agencies, and the National Health Interview Survey (NHIS), an area probability sample survey conducted through face-to-face interviews. Both data sources have advantages and disadvantages. The BRFSS is a larger survey, and almost every county is included in the survey; but it has lower response rates as is typical with telephone surveys, and it does not include subjects who live in households with no telephones. On the other hand, the NHIS is a smaller survey, with the majority of counties not included; but it includes both telephone and non-telephone households and has higher response rates. A preliminary analysis shows that the distributions of cancer screening and risk factors are different for telephone and non-telephone households. Thus, information from the two surveys may be combined to address both nonresponse and noncoverage errors. A hierarchical Bayesian approach that combines information from both surveys is used to construct county-level estimates. The proposed model incorporates potential noncoverage and nonresponse biases in the BRFSS as well as complex sample design features of both surveys. A Markov Chain Monte Carlo method is used to simulate draws from the joint posterior distribution of unknown quantities in the model based on the design-based direct estimates and county-level covariates. Yearly prevalence estimates at the county level for 49 states, as well as for the entire state of Alaska and the District of Columbia, are developed for six outcomes using BRFSS and NHIS data from the years 1997-2000. The outcomes include smoking and use of common cancer screening procedures. The NHIS/BRFSS combined county-level estimates are substantially different from those based on BRFSS alone