Statistical modeling and inference for complex-structured count data with applications in genomics and social science
Date
2020
Authors
Cao, Meng, author
Zhou, Wen, advisor
Breidt, F. Jay, advisor
Estep, Don, committee member
Meyer, Mary C., committee member
Peers, Graham, committee member
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Abstract
This dissertation describes models, estimation methods, and testing procedures for count data that build upon classic generalized linear models, including Gaussian, Poisson, and negative binomial regression. The methodological extensions proposed in this dissertation are motivated by complex structures for count data arising in three important classes of scientific problems, from both genomics and sociological contexts. Complexities include large scale, temporal dependence, zero-inflation and other mixture features, and group structure. The first class of problems involves count data that are collected from longitudinal RNA sequencing (RNA-seq) experiments, where the data consist of tens of thousands of short time series of counts, with replicate time series under treatment and under control. In order to determine if the time course differs between treatment and control, we consider two questions: 1) whether the treatment affects the geometric attributes of the temporal profiles and 2) whether any treatment effect varies over time. To answer the first question, we determine whether there has been a fundamental change in shape by modeling the transformed count data for genes at each time point using a Gaussian distribution, with the mean temporal profile generated by spline models, and introduce a measurement that quantifies the average minimum squared distance between the locations of peaks (or valleys) of each gene's temporal profile across experimental conditions. We then develop a testing framework based on a permutation procedure. Via simulation studies, we show that the proposed test achieves good power while controlling the false discovery rate. We also apply the test to data collected from a light physiology experiment on maize. To answer the second question, we model the time series of counts for each gene by a Gaussian-Negative Binomial model and introduce a new testing procedure that enjoys the optimality property of maximum average power. The test allows not only identification of traditional differentially expressed genes but also testing of a variety of composite hypotheses of biological interest. We establish the identifiability of the proposed model, implement the proposed method via efficient algorithms, and expose its good performance via simulation studies. The procedure reveals interesting biological insights when applied to data from an experiment that examines the effect of varying light environments on the fundamental physiology of a marine diatom. The second class of problems involves analyzing group-structured sRNA data that consist of independent replicates of counts for each sRNA across experimental conditions. Most existing methods—for both normalization and differential expression—are designed for non-group structured data. These methods may fail to provide correct normalization factors or fail to control FDR. They may lack power and may not be able to make inference on group effects. To address these challenges simultaneously, we introduce an inferential procedure using a group-based negative binomial model and a bootstrap testing method. This procedure not only provides a group-based normalization factor, but also enables group-based differential expression analysis. Our method shows good performance in both simulation studies and analysis of experimental data on roundworm. The last class of problems is motivated by the study of sensitive behaviors. These problems involve mixture-distributed count data that are collected by a quantitative randomized response technique (QRRT) which guarantees respondent anonymity. We propose a Poisson regression method based on maximum likelihood estimation computed via the EM algorithm. This method allows assessment of the importance of potential drivers of different quantities of non-compliant behavior. The method is illustrated with a case study examining potential drivers of non-compliance with hunting regulations in Sierra Leone.
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Subject
generalized linear model
randomized response technique
small RNA
longitudinal
count data
RNA-seq