2,387 research outputs found
Biomarker Detection in Association Studies: Modeling SNPs Simultaneously via Logistic ANOVA
In genome-wide association studies, the primary task is to detect biomarkers in the form of Single Nucleotide Polymorphisms (SNPs) that have nontrivial associations with a disease phenotype and some other important clinical/environmental factors. However, the extremely large number of SNPs comparing to the sample size inhibits application of classical methods such as the multiple logistic regression. Currently the most commonly used approach is still to analyze one SNP at a time. In this pa- per, we propose to consider the genotypes of the SNPs simultaneously via a logistic analysis of variance (ANOVA) model, which expresses the logit transformed mean of SNP genotypes as the summation of the SNP effects, effects of the disease phenotype and/or other clinical variables, and the interaction effects. We use a reduced-rank representation of the interaction-effect matrix for dimensionality reduction, and employ the L1-penalty in a penalized likelihood framework to filter out the SNPs that have no associations. We develop a Majorization-Minimization algorithm for computational implementation. In addition, we propose a modified BIC criterion to select the penalty parameters and determine the rank number. The proposed method is applied to a Multiple Sclerosis data set and simulated data sets and shows promise in biomarker detection
Integrating Data Transformation in Principal Components Analysis
Principal component analysis (PCA) is a popular dimension-reduction method to reduce the complexity and obtain the informative aspects of high-dimensional datasets. When the data distribution is skewed, data transformation is commonly used prior to applying PCA. Such transformation is usually obtained from previous studies, prior knowledge, or trial-and-error. In this work, we develop a model-based method that integrates data transformation in PCA and finds an appropriate data transformation using the maximum profile likelihood. Extensions of the method to handle functional data and missing values are also developed. Several numerical algorithms are provided for efficient computation. The proposed method is illustrated using simulated and real-world data examples. Supplementary materials for this article are available online
Sparse logistic principal components analysis for binary data
We develop a new principal components analysis (PCA) type dimension reduction
method for binary data. Different from the standard PCA which is defined on the
observed data, the proposed PCA is defined on the logit transform of the
success probabilities of the binary observations. Sparsity is introduced to the
principal component (PC) loading vectors for enhanced interpretability and more
stable extraction of the principal components. Our sparse PCA is formulated as
solving an optimization problem with a criterion function motivated from a
penalized Bernoulli likelihood. A Majorization--Minimization algorithm is
developed to efficiently solve the optimization problem. The effectiveness of
the proposed sparse logistic PCA method is illustrated by application to a
single nucleotide polymorphism data set and a simulation study.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS327 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Analyzing Multiple-Probe Microarray: Estimation and Application of Gene Expression Indexes
Gene expression index estimation is an essential step in analyzing multiple probe microarray data. Various modeling methods have been proposed in this area. Amidst all, a popular method proposed in Li and Wong (2001) is based on a multiplicative model, which is similar to the additive model discussed in Irizarry et al. (2003a) at the logarithm scale. Along this line, Hu et al. (2006) proposed data transformation to improve expression index estimation based on an ad hoc entropy criteria and naive grid search approach. In this work, we re-examined this problem using a new profile likelihood-based transformation estimation approach that is more statistically elegant and computationally efficient. We demonstrate the applicability of the proposed method using a benchmark Affymetrix U95A spiked-in experiment. Moreover, We introduced a new multivariate expression index and used the empirical study to shows its promise in terms of improving model fitting and power of detecting differential expression over the commonly used univariate expression index. As the other important content of the work, we discussed two generally encountered practical issues in application of gene expression index: normalization and summary statistic used for detecting differential expression. Our empirical study shows somewhat different findings from the MAQC project (MAQC, 2006)
Asymptotic optimality and efficient computation of the leave-subject-out cross-validation
Although the leave-subject-out cross-validation (CV) has been widely used in
practice for tuning parameter selection for various nonparametric and
semiparametric models of longitudinal data, its theoretical property is unknown
and solving the associated optimization problem is computationally expensive,
especially when there are multiple tuning parameters. In this paper, by
focusing on the penalized spline method, we show that the leave-subject-out CV
is optimal in the sense that it is asymptotically equivalent to the empirical
squared error loss function minimization. An efficient Newton-type algorithm is
developed to compute the penalty parameters that optimize the CV criterion.
Simulated and real data are used to demonstrate the effectiveness of the
leave-subject-out CV in selecting both the penalty parameters and the working
correlation matrix.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1063 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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