Modeling Persistent Trends in Distributions

We present a nonparametric framework to model a short sequence of probability distributions that vary both due to underlying effects of sequential progression and confounding noise. To distinguish between these two types of variation and estimate the sequential-progression effects, our approach leverages an assumption that these effects follow a persistent trend. This work is motivated by the recent rise of single-cell RNA-sequencing experiments over a brief time course, which aim to identify genes relevant to the progression of a particular biological process across diverse cell populations. While classical statistical tools focus on scalar-response regression or order-agnostic differences between distributions, it is desirable in this setting to consider both the full distributions as well as the structure imposed by their ordering. We introduce a new regression model for ordinal covariates where responses are univariate distributions and the underlying relationship reflects consistent changes in the distributions over increasing levels of the covariate. This concept is formalized as a "trend" in distributions, which we define as an evolution that is linear under the Wasserstein metric. Implemented via a fast alternating projections algorithm, our method exhibits numerous strengths in simulations and analyses of single-cell gene expression data.Comment: To appear in: Journal of the American Statistical Associatio

Evaluation of statistical methods, modeling, and multiple testing in RNA-seq studies

Recent Next Generation Sequencing methods provide a count of RNA molecules in the form of short reads, yielding discrete, often highly non-normally distributed gene expression measurements. Due to this feature of RNA sequencing (RNA-seq) data, appropriate statistical inference methods are required. Although Negative Binomial (NB) regression has been generally accepted in the analysis of RNA-seq data, its appropriateness in the application to genetic studies has not been exhaustively evaluated. Additionally, adjusting for covariates that have an unknown relationship with expression of a gene has not been extensively evaluated in RNA-seq studies using the NB framework. Finally, the dependent structures in RNA-Seq data may violate the assumptions of some multiple testing correction methods. In this dissertation, we suggest an alternative regression method, evaluate the effect of covariates, and compare various multiple testing correction methods. We conduct simulation studies and apply these methods to a real data set. First, we suggest Firth’s logistic regression for detecting differentially expressed genes in RNA-seq data. We also recommend the data adaptive method that estimates a recalibrated distribution of test statistics. Firth’ logistic regression exhibits an appropriately controlled Type-I error rate using the data adaptive method and shows comparable power to NB regression in simulation studies. Next, we evaluate the effect of disease-associated covariates where the relationship between the covariate and gene expression is unknown. Although the power of NB and Firth’s logistic regression is decreased as disease-associated covariates are added in a model, Type-I error rates are well controlled in Firth’ logistic regression if the relationship between a covariate and disease is not strong. Finally, we compare multiple testing correction methods that control family-wise error rates and impose false discovery rates. The evaluation reveals that an understanding of study designs, RNA-seq data, and the consequences of applying specific regression and multiple testing correction methods are very important factors to control family-wise error rates or false discovery rates. We believe our statistical investigations will enrich gene expression studies and influence related statistical methods

Methods for Joint Normalization and Comparison of Hi-C data

The development of chromatin conformation capture technology has opened new avenues of study into the 3D structure and function of the genome. Chromatin structure is known to influence gene regulation, and differences in structure are now emerging as a mechanism of regulation between, e.g., cell differentiation and disease vs. normal states. Hi-C sequencing technology now provides a way to study the 3D interactions of the chromatin over the whole genome. However, like all sequencing technologies, Hi-C suffers from several forms of bias stemming from both the technology and the DNA sequence itself. Several normalization methods have been developed for normalizing individual Hi-C datasets, but little work has been done on developing joint normalization methods for comparing two or more Hi-C datasets. To make full use of Hi-C data, joint normalization and statistical comparison techniques are needed to carry out experiments to identify regions where chromatin structure differs between conditions. We develop methods for the joint normalization and comparison of two Hi-C datasets, which we then extended to more complex experimental designs. Our normalization method is novel in that it makes use of the distance-dependent nature of chromatin interactions. Our modification of the Minus vs. Average (MA) plot to the Minus vs. Distance (MD) plot allows for a nonparametric data-driven normalization technique using loess smoothing. Additionally, we present a simple statistical method using Z-scores for detecting differentially interacting regions between two datasets. Our initial method was published as the Bioconductor R package HiCcompare [http://bioconductor.org/packages/HiCcompare/](http://bioconductor.org/packages/HiCcompare/). We then further extended our normalization and comparison method for use in complex Hi-C experiments with more than two datasets and optional covariates. We extended the normalization method to jointly normalize any number of Hi-C datasets by using a cyclic loess procedure on the MD plot. The cyclic loess normalization technique can remove between dataset biases efficiently and effectively even when several datasets are analyzed at one time. Our comparison method implements a generalized linear model-based approach for comparing complex Hi-C experiments, which may have more than two groups and additional covariates. The extended methods are also available as a Bioconductor R package [http://bioconductor.org/packages/multiHiCcompare/](http://bioconductor.org/packages/multiHiCcompare/). Finally, we demonstrate the use of HiCcompare and multiHiCcompare in several test cases on real data in addition to comparing them to other similar methods (https://doi.org/10.1002/cpbi.76)

ZINBA integrates local covariates with DNA-seq data to identify broad and narrow regions of enrichment, even within amplified genomic regions

ZINBA (Zero-Inflated Negative Binomial Algorithm) identifies genomic regions enriched in a variety of ChIP-seq and related next-generation sequencing experiments (DNA-seq), calling both broad and narrow modes of enrichment across a range of signal-to-noise ratios. ZINBA models and accounts for factors that co-vary with background or experimental signal, such as G/C content, and identifies enrichment in genomes with complex local copy number variations. ZINBA provides a single unified framework for analyzing DNA-seq experiments in challenging genomic contexts

IsoDOT Detects Differential RNA-isoform Expression/Usage with respect to a Categorical or Continuous Covariate with High Sensitivity and Specificity

We have developed a statistical method named IsoDOT to assess differential isoform expression (DIE) and differential isoform usage (DIU) using RNA-seq data. Here isoform usage refers to relative isoform expression given the total expression of the corresponding gene. IsoDOT performs two tasks that cannot be accomplished by existing methods: to test DIE/DIU with respect to a continuous covariate, and to test DIE/DIU for one case versus one control. The latter task is not an uncommon situation in practice, e.g., comparing paternal and maternal allele of one individual or comparing tumor and normal sample of one cancer patient. Simulation studies demonstrate the high sensitivity and specificity of IsoDOT. We apply IsoDOT to study the effects of haloperidol treatment on mouse transcriptome and identify a group of genes whose isoform usages respond to haloperidol treatment

Study of the distribution and behaviour of the "0" values in large omic data arrays

Existen evidencias de que muchas enfermedades no están determinadas sólo por alteraciones genéticas. Un claro ejemplo es el cáncer que engloba muchas enfermedades producidas por la interacción de factores genéticos y no genéticos durante toda la vida. Entre los factores no-genéticos se encuentran la forma en que los seres humanos viven e interactúan con el medio ambiente y el microbioma; ambas exposiciones pueden ser caracterizadas con datos ómicos. Las tecnologías ómicas representan una reciente área de estudio que engloba diversas disciplinas biológicas. Las tecnologías aplicadas a las ómicas permiten estudiar, a nivel molecular los diferentes elementos que componen los sistemas biológicos. Hoy en día, el foco se encuentra en una nueva área: la microbioma, puesto que se han encontrado diversas asociaciones entre ciertos microorganismos y enfermedades. El reto principal en el análisis de datos de microbioma es el escaso número en los datos de conteo de microbioma, los cuales son de gran dimensión y contienen una gran proporción de ceros. En este proyecto se pretende mostrar diferentes alternativas para el análisis de datos de conteo que se caracterizan por una clara sobre dispersión y exceso de ceros. Aplicando modelos de regresión como los modelos de inflación de cero o los modelos Hurdle pude establecer qué tipo de ceros se encuentran en la base de datos. Estos modelos y sus correspondientes distribuciones están sometidos a diferentes criterios de selección con el objetivo de establecer cuál es el modelo que mejor se ajuste a los datos en función del porcentaje de ceros que presente. Ello me ha permitido definir relaciones entre diferentes microorganismos y expresiones genéticas, estadios tumorales, subtipos inmunes, género, IMC, ..