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1.  Controlling the local false discovery rate in the adaptive Lasso 
Biostatistics (Oxford, England)  2013;14(4):653-666.
The Lasso shrinkage procedure achieved its popularity, in part, by its tendency to shrink estimated coefficients to zero, and its ability to serve as a variable selection procedure. Using data-adaptive weights, the adaptive Lasso modified the original procedure to increase the penalty terms for those variables estimated to be less important by ordinary least squares. Although this modified procedure attained the oracle properties, the resulting models tend to include a large number of “false positives” in practice. Here, we adapt the concept of local false discovery rates (lFDRs) so that it applies to the sequence, λn, of smoothing parameters for the adaptive Lasso. We define the lFDR for a given λn to be the probability that the variable added to the model by decreasing λn to λn−δ is not associated with the outcome, where δ is a small value. We derive the relationship between the lFDR and λn, show lFDR=1 for traditional smoothing parameters, and show how to select λn so as to achieve a desired lFDR. We compare the smoothing parameters chosen to achieve a specified lFDR and those chosen to achieve the oracle properties, as well as their resulting estimates for model coefficients, with both simulation and an example from a genetic study of prostate specific antigen.
PMCID: PMC3769997  PMID: 23575212
Adaptive Lasso; Local false discovery rate; Smoothing parameter; Variable selection
2.  Structured variable selection with q-values 
Biostatistics (Oxford, England)  2013;14(4):695-707.
When some of the regressors can act on both the response and other explanatory variables, the already challenging problem of selecting variables when the number of covariates exceeds the sample size becomes more difficult. A motivating example is a metabolic study in mice that has diet groups and gut microbial percentages that may affect changes in multiple phenotypes related to body weight regulation. The data have more variables than observations and diet is known to act directly on the phenotypes as well as on some or potentially all of the microbial percentages. Interest lies in determining which gut microflora influence the phenotypes while accounting for the direct relationship between diet and the other variables A new methodology for variable selection in this context is presented that links the concept of q-values from multiple hypothesis testing to the recently developed weighted Lasso.
PMCID: PMC3841382  PMID: 23580317
False discovery rate; Microbial data; q-Values; Variable selection; Weighted Lasso
3.  Identifying genetic marker sets associated with phenotypes via an efficient adaptive score test 
Biostatistics (Oxford, England)  2012;13(4):776-790.
In recent years, genome-wide association studies (GWAS) and gene-expression profiling have generated a large number of valuable datasets for assessing how genetic variations are related to disease outcomes. With such datasets, it is often of interest to assess the overall effect of a set of genetic markers, assembled based on biological knowledge. Genetic marker-set analyses have been advocated as more reliable and powerful approaches compared with the traditional marginal approaches (Curtis and others, 2005. Pathways to the analysis of microarray data. TRENDS in Biotechnology 23, 429–435; Efroni and others, 2007. Identification of key processes underlying cancer phenotypes using biologic pathway analysis. PLoS One 2, 425). Procedures for testing the overall effect of a marker-set have been actively studied in recent years. For example, score tests derived under an Empirical Bayes (EB) framework (Liu and others, 2007. Semiparametric regression of multidimensional genetic pathway data: least-squares kernel machines and linear mixed models. Biometrics 63, 1079–1088; Liu and others, 2008. Estimation and testing for the effect of a genetic pathway on a disease outcome using logistic kernel machine regression via logistic mixed models. BMC bioinformatics 9, 292–2; Wu and others, 2010. Powerful SNP-set analysis for case-control genome-wide association studies. American Journal of Human Genetics 86, 929) have been proposed as powerful alternatives to the standard Rao score test (Rao, 1948. Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. Mathematical Proceedings of the Cambridge Philosophical Society, 44, 50–57). The advantages of these EB-based tests are most apparent when the markers are correlated, due to the reduction in the degrees of freedom. In this paper, we propose an adaptive score test which up- or down-weights the contributions from each member of the marker-set based on the Z-scores of their effects. Such an adaptive procedure gains power over the existing procedures when the signal is sparse and the correlation among the markers is weak. By combining evidence from both the EB-based score test and the adaptive test, we further construct an omnibus test that attains good power in most settings. The null distributions of the proposed test statistics can be approximated well either via simple perturbation procedures or via distributional approximations. Through extensive simulation studies, we demonstrate that the proposed procedures perform well in finite samples. We apply the tests to a breast cancer genetic study to assess the overall effect of the FGFR2 gene on breast cancer risk.
PMCID: PMC3440238  PMID: 22734045
Adaptive procedures; Empirical Bayes; GWAS; Pathway analysis; Score test; SNP sets
4.  Fast methods for spatially correlated multilevel functional data 
Biostatistics (Oxford, England)  2010;11(2):177-194.
We propose a new methodological framework for the analysis of hierarchical functional data when the functions at the lowest level of the hierarchy are correlated. For small data sets, our methodology leads to a computational algorithm that is orders of magnitude more efficient than its closest competitor (seconds versus hours). For large data sets, our algorithm remains fast and has no current competitors. Thus, in contrast to published methods, we can now conduct routine simulations, leave-one-out analyses, and nonparametric bootstrap sampling. Our methods are inspired by and applied to data obtained from a state-of-the-art colon carcinogenesis scientific experiment. However, our models are general and will be relevant to many new data sets where the object of inference are functions or images that remain dependent even after conditioning on the subject on which they are measured. Supplementary materials are available at Biostatistics online.
PMCID: PMC2830578  PMID: 20089508
Colon carcinogenesis; Covariogram estimation; Functional data analysis; Hierarchical modeling; Mixed models; Spatial modeling
5.  Combining assays for estimating prevalence of human herpesvirus 8 infection using multivariate mixture models 
Biostatistics (Oxford, England)  2007;9(1):137-151.
For many diseases, it is difficult or impossible to establish a definitive diagnosis because a perfect “gold standard” may not exist or may be too costly to obtain. In this paper, we propose a method to use continuous test results to estimate prevalence of disease in a given population and to estimate the effects of factors that may influence prevalence. Motivated by a study of human herpesvirus 8 among children with sickle-cell anemia in Uganda, where 2 enzyme immunoassays were used to assess infection status, we fit 2-component multivariate mixture models. We model the component densities using parametric densities that include data transformation as well as flexible transformed models. In addition, we model the mixing proportion, the probability of a latent variable corresponding to the true unknown infection status, via a logistic regression to incorporate covariates. This model includes mixtures of multivariate normal densities as a special case and is able to accommodate unusual shapes and skewness in the data. We assess model performance in simulations and present results from applying various parameterizations of the model to the Ugandan study.
PMCID: PMC2710882  PMID: 17566074
Diagnostic tests; Mixture models; Semi-nonparametric densities; Semiparametrics; Sensitivity; Specificity; Transformations

Results 1-5 (5)