Generalized functional linear model with a point process predictor.

Point process data have become increasingly popular these days. For example, many of the data captured in electronic health records (EHR) are in the format of point process data. It is of great interest to study the association between a point process predictor and a scalar response using generalized functional linear regression models. Various generalized functional linear regression models have been developed under different settings in the past decades. However, existing methods can only deal with functional or longitudinal predictors, not point process predictors. In this article, we propose a novel generalized functional linear regression model for a point process predictor. Our proposed model is based on the joint modeling framework, where we adopt a log-Gaussian Cox process model for the point process predictor and a generalized linear regression model for the outcome. We also develop a new algorithm for fast model estimation based on the Gaussian variational approximation method. We conduct extensive simulation studies to evaluate the performance of our proposed method and compare it to competing methods. The performance of our proposed method is further demonstrated on an EHR dataset of patients admitted into the intensive care units of the Beth Israel Deaconess Medical Center between 2001 and 2008.

Conditional Functional Graphical Models.

Graphical modeling of multivariate functional data is becoming increasingly important in a wide variety of applications. The changes of graph structure can often be attributed to external variables, such as the diagnosis status or time, the latter of which gives rise to the problem of dynamic graphical modeling. Most existing methods focus on estimating the graph by aggregating samples, but largely ignore the subject-level heterogeneity due to the external variables. In this article, we introduce a conditional graphical model for multivariate random functions, where we treat the external variables as conditioning set, and allow the graph structure to vary with the external variables. Our method is built on two new linear operators, the conditional precision operator and the conditional partial correlation operator, which extend the precision matrix and the partial correlation matrix to both the conditional and functional settings. We show that their nonzero elements can be used to characterize the conditional graphs, and develop the corresponding estimators. We establish the uniform convergence of the proposed estimators and the consistency of the estimated graph, while allowing the graph size to grow with the sample size, and accommodating both completely and partially observed data. We demonstrate the efficacy of the method through both simulations and a study of brain functional connectivity network.

Functional Structural Equation Model.

In this article, we introduce a functional structural equation model for estimating directional relations from multivariate functional data. We decouple the estimation into two major steps: directional order determination and selection through sparse functional regression. We first propose a score function at the linear operator level, and show that its minimization can recover the true directional order when the relation between each function and its parental functions is nonlinear. We then develop a sparse functional additive regression, where both the response and the multivariate predictors are functions and the regression relation is additive and nonlinear. We also propose strategies to speed up the computation and scale up our method. In theory, we establish the consistencies of order determination, sparse functional additive regression, and directed acyclic graph estimation, while allowing both the dimension of the Karhunen-Loéve expansion coefficients and the number of random functions to diverge with the sample size. We illustrate the efficacy of our method through simulations, and an application to brain effective connectivity analysis.

FUNCTIONAL SUFFICIENT DIMENSION REDUCTION THROUGH AVERAGE FRÉCHET DERIVATIVES.

Sufficient dimension reduction (SDR) embodies a family of methods that aim for reduction of dimensionality without loss of information in a regression setting. In this article, we propose a new method for nonparametric function-on-function SDR, where both the response and the predictor are a function. We first develop the notions of functional central mean subspace and functional central subspace, which form the population targets of our functional SDR. We then introduce an average Fréchet derivative estimator, which extends the gradient of the regression function to the operator level and enables us to develop estimators for our functional dimension reduction spaces. We show the resulting functional SDR estimators are unbiased and exhaustive, and more importantly, without imposing any distributional assumptions such as the linearity or the constant variance conditions that are commonly imposed by all existing functional SDR methods. We establish the uniform convergence of the estimators for the functional dimension reduction spaces, while allowing both the number of Karhunen-Loève expansions and the intrinsic dimension to diverge with the sample size. We demonstrate the efficacy of the proposed methods through both simulations and two real data examples.

AUDIT-C and ICD codes as phenotypes for harmful alcohol use: association with ADH1B polymorphisms in two US populations.

BACKGROUND AND AIMS: Longitudinal electronic health record (EHR) data offer a large-scale, untapped source of phenotypical information on harmful alcohol use. Using established, alcohol-associated variants in the gene that encodes the enzyme alcohol dehydrogenase 1B (ADH1B) as criterion standards, we compared the individual and combined validity of three longitudinal EHR-based phenotypes of harmful alcohol use: Alcohol Use Disorders Identification Test-Consumption (AUDIT-C) trajectories; mean age-adjusted AUDIT-C; and diagnoses of alcohol use disorder (AUD). DESIGN: With longitudinal EHR data from the Million Veteran Program (MVP) linked to genetic data, we used two population-specific polymorphisms in ADH1B that are associated strongly with AUD in African Americans (AAs) and European Americans (EAs): rs2066702 (Arg369Cys, AAs) and rs1229984 (Arg48His, EAs) as criterion measures. SETTING: United States Department of Veterans Affairs Healthcare System. PARTICIPANTS: A total of 167 721 veterans (57 677 AAs and 110 044 EAs; 92% male, mean age = 63 years) took part in this study. Data were collected from 1  October 2007 to 1 May 2017. MEASUREMENTS: Using all AUDIT-C scores and AUD diagnostic codes recorded in the EHR, we calculated age-adjusted mean AUDIT-C values, longitudinal statistical trajectories of AUDIT-C scores and ICD-9/10 diagnostic groupings for AUD. FINDINGS: A total of 19 793 AAs (34.3%) had one or two minor alleles at rs2066702 [minor allele frequency (MAF) = 0.190] and 6933 EAs (6.3%) had one or two minor alleles at rs1229984 (MAF = 0.032). In both populations, trajectories and age-adjusted mean AUDIT-C were correlated (r = 0.90) but, when considered separately, highest score (8+ versus 0) of age-adjusted mean AUDIT-C demonstrated a stronger association with the ADH1B variants [adjusted odds ratio (aOR) 0.54 in AAs and 0.37 in AAs] than did the highest trajectory (aOR 0.71 in AAs and 0.53 in EAs); combining AUDIT-C metrics did not improve discrimination. When age-adjusted mean AUDIT-C score and AUD diagnoses were considered together, age-adjusted mean AUDIT-C (8+ versus 0) was associated with lower odds of having the ADH1B minor allele than were AUD diagnostic codes: aOR = 0.59 versus 0.86 in AAs and 0.48 versus 0.68 in EAs. These independent associations combine to yield an even lower aOR of 0.51 for AAs and 0.33 for EAs. CONCLUSIONS: The age-adjusted mean AUDIT-C score is associated more strongly with genetic polymorphisms of known risk for alcohol use disorder than are longitudinal trajectories of AUDIT-C or AUD diagnostic codes. AUD diagnostic codes modestly enhance this association.

Uncovering Genomic Regions Associated with Trypanosoma Infections in Wild Populations of the Tsetse Fly Glossina fuscipes.

Vector-borne diseases are responsible for > 1 million deaths every year but genomic resources for most species responsible for their transmission are limited. This is true for neglected diseases such as sleeping sickness (Human African Trypanosomiasis), a disease caused by Trypanosoma parasites vectored by several species of tseste flies within the genus Glossina We describe an integrative approach that identifies statistical associations between trypanosome infection status of Glossina fuscipes fuscipes (Gff) flies from Uganda, for which functional studies are complicated because the species cannot be easily maintained in laboratory colonies, and ∼73,000 polymorphic sites distributed across the genome. Then, we identify candidate genes involved in Gff trypanosome susceptibility by taking advantage of genomic resources from a closely related species, G. morsitans morsitans (Gmm). We compiled a comprehensive transcript library from 72 published and unpublished RNAseq experiments of trypanosome-infected and uninfected Gmm flies, and improved the current Gmm transcriptome assembly. This new assembly was then used to enhance the functional annotations on the Gff genome. As a consequence, we identified 56 candidate genes in the vicinity of the 18 regions associated with Trypanosoma infection status in Gff Twenty-nine of these genes were differentially expressed (DE) among parasite-infected and uninfected Gmm, suggesting that their orthologs in Gff may correlate with disease transmission. These genes were involved in DNA regulation, neurophysiological functions, and immune responses. We highlight the power of integrating population and functional genomics from related species to enhance our understanding of the genetic basis of physiological traits, particularly in nonmodel organisms.

Genomic analyses of African Trypanozoon strains to assess evolutionary relationships and identify markers for strain identification.

African trypanosomes of the sub-genus Trypanozoon) are eukaryotic parasitesthat cause disease in either humans or livestock. The development of genomic resources can be of great use to those interested in studying and controlling the spread of these trypanosomes. Here we present a large comparative analysis of Trypanozoon whole genomes, 83 in total, including human and animal infective African trypanosomes: 21 T. brucei brucei, 22 T. b. gambiense, 35 T. b. rhodesiense and 4 T. evansi strains, of which 21 were from Uganda. We constructed a maximum likelihood phylogeny based on 162,210 single nucleotide polymorphisms (SNPs.) The three Trypanosoma brucei sub-species and Trypanosoma evansi are not monophyletic, confirming earlier studies that indicated high similarity among Trypanosoma "sub-species". We also used discriminant analysis of principal components (DAPC) on the same set of SNPs, identifying seven genetic clusters. These clusters do not correspond well with existing taxonomic classifications, in agreement with the phylogenetic analysis. Geographic origin is reflected in both the phylogeny and clustering analysis. Finally, we used sparse linear discriminant analysis to rank SNPs by their informativeness in differentiating the strains in our data set. As few as 84 SNPs can completely distinguish the strains used in our study, and discriminant analysis was still able to detect genetic structure using as few as 10 SNPs. Our results reinforce earlier results of high genetic similarity between the African Trypanozoon. Despite this, a small subset of SNPs can be used to identify genetic markers that can be used for strain identification or other epidemiological investigations.

On an additive partial correlation operator and nonparametric estimation of graphical models.

We introduce an additive partial correlation operator as an extension of partial correlation to the nonlinear setting, and use it to develop a new estimator for nonparametric graphical models. Our graphical models are based on additive conditional independence, a statistical relation that captures the spirit of conditional independence without having to resort to high-dimensional kernels for its estimation. The additive partial correlation operator completely characterizes additive conditional independence, and has the additional advantage of putting marginal variation on appropriate scales when evaluating interdependence, which leads to more accurate statistical inference. We establish the consistency of the proposed estimator. Through simulation experiments and analysis of the DREAM4 Challenge dataset, we demonstrate that our method performs better than existing methods in cases where the Gaussian or copula Gaussian assumption does not hold, and that a more appropriate scaling for our method further enhances its performance.