Volume 12, Issue 6

In this paper, we introduce a new family of power transformations, which has the generalized logarithm as one of its members, in the same manner as the usual logarithm belongs to the family of Box-Cox power transformations. Although the new family has been developed for analyzing gene expression data, it allows a wider scope of mean-variance related data to be reached. We study the analytical properties of the new family of transformations, as well as the mean-variance relationships that are stabilized by using its members. We propose a methodology based on this new family, which includes a simple strategy for selecting the family member adequate for a data set. We evaluate the finite sample behavior of different classical and robust estimators based on this strategy by Monte Carlo simulations. We analyze real genomic data by using the proposed transformation to empirically show how the new methodology allows the variance of these data to be stabilized.

Approximate Bayesian computation (ABC) is a likelihood-free approach for Bayesian inferences based on a rejection algorithm method that applies a tolerance of dissimilarity between summary statistics from observed and simulated data. Although several improvements to the algorithm have been proposed, none of these improvements avoid the following two sources of approximation: 1) lack of sufficient statistics: sampling is not from the true posterior density given data but from an approximate posterior density given summary statistics; and 2) non-zero tolerance: sampling from the posterior density given summary statistics is achieved only in the limit of zero tolerance. The first source of approximation can be improved by adding a summary statistic, but an increase in the number of summary statistics could introduce additional variance caused by the low acceptance rate. Consequently, many researchers have attempted to develop techniques to choose informative summary statistics. The present study evaluated the utility of a kernel-based ABC method [Fukumizu, K., L. Song and A. Gretton (2010): “Kernel Bayes’ rule: Bayesian inference with positive definite kernels,” arXiv, 1009.5736 and Fukumizu, K., L. Song and A. Gretton (2011): “Kernel Bayes’ rule. Advances in Neural Information Processing Systems 24.” In: J. Shawe-Taylor and R. S. Zemel and P. Bartlett and F. Pereira and K. Q. Weinberger, (Eds.), pp. 1549–1557., NIPS 24: 1549–1557] for complex problems that demand many summary statistics. Specifically, kernel ABC was applied to population genetic inference. We demonstrate that, in contrast to conventional ABCs, kernel ABC can incorporate a large number of summary statistics while maintaining high performance of the inference.

There is a need for a reliable statistical test which is appropriate for assessing cospeciation of more than two phylogenies. We have developed an algorithm using a permutation method that can be used to test for and infer tri-trophic evolutionary relationships of organisms given both their phylogenies and pairwise interactions. An overall statistic has been developed based on the dominant eigenvalue of a covariance matrix, and compared to values of the statistic computed when tree labels are permuted. The resulting overall p -value is used to test for the presence or absence of cospeciation in a tri-trophic system. If cospeciation is detected, we propose new test statistics based on partial correlations to uncover more details about the relationships between multiple phylogenies. One of the strengths of our method is that it allows more parasites than hosts or more hosts than parasites, with multiple associations and more than one parasite attached to a host (or one parasite attached to multiple hosts). The new method does not require any parametric assumptions of the distribution of the data, and unlike the old methods, which utilize several pairwise steps, the overall statistic used is obtained in one step. We have applied our method to two published datasets where we obtained detailed information about the strength of associations among species with calculated partial p -values and one overall p -value from the dominant eigenvalue test statistic. Our permutation method produces reliable results with a clear procedure and statistics applied in an intuitive manner. Our algorithm is useful in testing evidence for three-way cospeciation in multiple phylogenies with tri-trophic associations and determining which phylogenies are involved in cospeciation.

Mass spectrometry is an important high-throughput technique for profiling small molecular compounds in biological samples and is widely used to identify potential diagnostic and prognostic compounds associated with disease. Commonly, this data generated by mass spectrometry has many missing values resulting when a compound is absent from a sample or is present but at a concentration below the detection limit. Several strategies are available for statistically analyzing data with missing values. The accelerated failure time (AFT) model assumes all missing values result from censoring below a detection limit. Under a mixture model, missing values can result from a combination of censoring and the absence of a compound. We compare power and estimation of a mixture model to an AFT model. Based on simulated data, we found the AFT model to have greater power to detect differences in means and point mass proportions between groups. However, the AFT model yielded biased estimates with the bias increasing as the proportion of observations in the point mass increased while estimates were unbiased with the mixture model except if all missing observations came from censoring. These findings suggest using the AFT model for hypothesis testing and mixture model for estimation. We demonstrated this approach through application to glycomics data of serum samples from women with ovarian cancer and matched controls.

The ENCODE project has funded the generation of a diverse collection of methylation profiles using reduced representation bisulfite sequencing (RRBS) technology, enabling the analysis of epigenetic variation on a genomic scale at single-site resolution. A standard application of RRBS experiments is in the location of differentially methylated regions (DMRs) between two sets of samples. Despite numerous publications reporting DMRs identified from RRBS datasets, there have been no formal analyses of the effects of experimental and biological factors on the performance of existing or newly developed analytical methods. These factors include variable read coverage, differing group sample sizes across genomic regions, uneven spacing between CpG dinucleotide sites, and correlation in methylation levels among sites in close proximity. To better understand the interplay among technical and biological variables in the analysis of RRBS methylation profiles, we have developed an algorithm for the generation of experimentally realistic RRBS datasets. Applying insights derived from our simulation studies, we present a novel procedure that can identify DMRs spanning as few as three CpG sites with both high sensitivity and specificity. Using RRBS data from muscle vs. non-muscle cell cultures as an example, we demonstrate that our method reveals many more DMRs that are likely to be of biological significance than previous methods.

MicroRNAs (miRNAs) are short non-coding RNAs that play critical roles in numerous cellular processes through post-transcriptional functions. The aberrant role of miRNAs has been reported in a number of diseases. A robust computational method is vital to discover novel miRNAs where level of noise varies dramatically across the different miRNAs. In this paper, we propose a flexible rank-based procedure for estimating a weighted log partial area under the receiver operating characteristic (ROC) curve statistic for selecting differentially expressed miRNAs. The statistic combines results taking partial area under the curve (pAUC) and their corresponding variance. The proposed method does not involve complicated formulas and does not require advanced programming skills. Two real datasets are analyzed to illustrate the method and a simulation study is carried out to assess the performance of different miRNA ranking statistics. We conclude that the proposed method offers robust results with large samples for miRNA expression data, and the method can be used as an alternative analytical tool for identifying a list of target miRNAs for further biological and clinical investigation.

We propose a non-parametric regression methodology, Random Forests on Distance Matrices (RFDM), for detecting genetic variants associated to quantitative phenotypes, obtained using neuroimaging techniques, representing the human brain’s structure or function. RFDM, which is an extension of decision forests, requires a distance matrix as the response that encodes all pair-wise phenotypic distances in the random sample. We discuss ways to learn such distances directly from the data using manifold learning techniques, and how to define such distances when the phenotypes are non-vectorial objects such as brain connectivity networks. We also describe an extension of RFDM to detect espistatic effects while keeping the computational complexity low. Extensive simulation results and an application to an imaging genetics study of Alzheimer’s Disease are presented and discussed.