Ordinal Probit Functional Regression Models with Application to Computer-Use Behavior in Rhesus Monkeys

Research in functional regression has made great strides in expanding to non-Gaussian functional outcomes, however the exploration of ordinal functional outcomes remains limited. Motivated by a study of computer-use behavior in rhesus macaques (\emph{Macaca mulatta}), we introduce the Ordinal Probit Functional Regression Model or OPFRM to perform ordinal function-on-scalar regression. The OPFRM is flexibly formulated to allow for the choice of different basis functions including penalized B-splines, wavelets, and O'Sullivan splines. We demonstrate the operating characteristics of the model in simulation using a variety of underlying covariance patterns showing the model performs reasonably well in estimation under multiple basis functions. We also present and compare two approaches for conducting posterior inference showing that joint credible intervals tend to out perform point-wise credible. Finally, in application, we determine demographic factors associated with the monkeys' computer use over the course of a year and provide a brief analysis of the findings

Joint analysis of SNP and gene expression data in genetic association studies of complex diseases

Genetic association studies have been a popular approach for assessing the association between common Single Nucleotide Polymorphisms (SNPs) and complex diseases. However, other genomic data involved in the mechanism from SNPs to disease, for example, gene expressions, are usually neglected in these association studies. In this paper, we propose to exploit gene expression information to more powerfully test the association between SNPs and diseases by jointly modeling the relations among SNPs, gene expressions and diseases. We propose a variance component test for the total effect of SNPs and a gene expression on disease risk. We cast the test within the causal mediation analysis framework with the gene expression as a potential mediator. For eQTL SNPs, the use of gene expression information can enhance power to test for the total effect of a SNP-set, which is the combined direct and indirect effects of the SNPs mediated through the gene expression, on disease risk. We show that the test statistic under the null hypothesis follows a mixture of $\chi^2$ distributions, which can be evaluated analytically or empirically using the resampling-based perturbation method. We construct tests for each of three disease models that are determined by SNPs only, SNPs and gene expression, or include also their interactions. As the true disease model is unknown in practice, we further propose an omnibus test to accommodate different underlying disease models. We evaluate the finite sample performance of the proposed methods using simulation studies, and show that our proposed test performs well and the omnibus test can almost reach the optimal power where the disease model is known and correctly specified. We apply our method to reanalyze the overall effect of the SNP-set and expression of the ORMDL3 gene on the risk of asthma.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS690 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

The relative efficiency of time-to-progression and continuous measures of cognition in presymptomatic Alzheimer's disease.

IntroductionClinical trials on preclinical Alzheimer's disease are challenging because of the slow rate of disease progression. We use a simulation study to demonstrate that models of repeated cognitive assessments detect treatment effects more efficiently than models of time to progression.MethodsMultivariate continuous data are simulated from a Bayesian joint mixed-effects model fit to data from the Alzheimer's Disease Neuroimaging Initiative. Simulated progression events are algorithmically derived from the continuous assessments using a random forest model fit to the same data.ResultsWe find that power is approximately doubled with models of repeated continuous outcomes compared with the time-to-progression analysis. The simulations also demonstrate that a plausible informative missing data pattern can induce a bias that inflates treatment effects, yet 5% type I error is maintained.DiscussionGiven the relative inefficiency of time to progression, it should be avoided as a primary analysis approach in clinical trials of preclinical Alzheimer's disease

Machine Learning and Integrative Analysis of Biomedical Big Data.

Recent developments in high-throughput technologies have accelerated the accumulation of massive amounts of omics data from multiple sources: genome, epigenome, transcriptome, proteome, metabolome, etc. Traditionally, data from each source (e.g., genome) is analyzed in isolation using statistical and machine learning (ML) methods. Integrative analysis of multi-omics and clinical data is key to new biomedical discoveries and advancements in precision medicine. However, data integration poses new computational challenges as well as exacerbates the ones associated with single-omics studies. Specialized computational approaches are required to effectively and efficiently perform integrative analysis of biomedical data acquired from diverse modalities. In this review, we discuss state-of-the-art ML-based approaches for tackling five specific computational challenges associated with integrative analysis: curse of dimensionality, data heterogeneity, missing data, class imbalance and scalability issues

Functional Regression

Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the development of this field, which has accelerated in the past 10 years to become one of the fastest growing areas of statistics, fueled by the growing number of applications yielding this type of data. One unique characteristic of FDA is the need to combine information both across and within functions, which Ramsay and Silverman called replication and regularization, respectively. This article will focus on functional regression, the area of FDA that has received the most attention in applications and methodological development. First will be an introduction to basis functions, key building blocks for regularization in functional regression methods, followed by an overview of functional regression methods, split into three types: [1] functional predictor regression (scalar-on-function), [2] functional response regression (function-on-scalar) and [3] function-on-function regression. For each, the role of replication and regularization will be discussed and the methodological development described in a roughly chronological manner, at times deviating from the historical timeline to group together similar methods. The primary focus is on modeling and methodology, highlighting the modeling structures that have been developed and the various regularization approaches employed. At the end is a brief discussion describing potential areas of future development in this field

Graphical Markov models: overview

We describe how graphical Markov models started to emerge in the last 40 years, based on three essential concepts that had been developed independently more than a century ago. Sequences of joint or single regressions and their regression graphs are singled out as being best suited for analyzing longitudinal data and for tracing developmental pathways. Interpretations are illustrated using two sets of data and some of the more recent, important results for sequences of regressions are summarized.Comment: 22 pages, 9 figure