Addressing dispersion in mis-measured multivariate binomial outcomes: A novel statistical approach for detecting differentially methylated regions in bisulfite sequencing data.

Motivated by a DNA methylation application, this article addresses the problem of fitting and inferring a multivariate binomial regression model for outcomes that are contaminated by errors and exhibit extra-parametric variations, also known as dispersion. While dispersion in univariate binomial regression has been extensively studied, addressing dispersion in the context of multivariate outcomes remains a complex and relatively unexplored task. The complexity arises from a noteworthy data characteristic observed in our motivating dataset: non-constant yet correlated dispersion across outcomes. To address this challenge and account for possible measurement error, we propose a novel hierarchical quasi-binomial varying coefficient mixed model, which enables flexible dispersion patterns through a combination of additive and multiplicative dispersion components. To maximize the Laplace-approximated quasi-likelihood of our model, we further develop a specialized two-stage expectation-maximization (EM) algorithm, where a plug-in estimate for the multiplicative scale parameter enhances the speed and stability of the EM iterations. Simulations demonstrated that our approach yields accurate inference for smooth covariate effects and exhibits excellent power in detecting non-zero effects. Additionally, we applied our proposed method to investigate the association between DNA methylation, measured across the genome through targeted custom capture sequencing of whole blood, and levels of anti-citrullinated protein antibodies (ACPA), a preclinical marker for rheumatoid arthritis (RA) risk. Our analysis revealed 23 significant genes that potentially contribute to ACPA-related differential methylation, highlighting the relevance of cell signaling and collagen metabolism in RA. We implemented our method in the R Bioconductor package called "SOMNiBUS."

A novel rare variants association test for binary traits in family-based designs via copulas.

With the cost-effectiveness technology in whole-genome sequencing, more sophisticated statistical methods for testing genetic association with both rare and common variants are being investigated to identify the genetic variation between individuals. Several methods which group variants, also called gene-based approaches, are developed. For instance, advanced extensions of the sequence kernel association test, which is a widely used variant-set test, have been proposed for unrelated samples and extended for family data. Family data have been shown to be powerful when analyzing rare variants. However, most of such methods capture familial relatedness using a random effect component within the generalized linear mixed model framework. Therefore, there is a need to develop unified and flexible methods to study the association between a set of genetic variants and a trait, especially for a binary outcome. Copulas are multivariate distribution functions with uniform margins on the [0,1] interval and they provide suitable models to capture familial dependence structure. In this work, we propose a flexible family-based association test for both rare and common variants in the presence of binary traits. The method, termed novel rare variant association test (NRVAT), uses a marginal logistic model and a Gaussian Copula. The latter is employed to model the dependence between relatives. An analytic score-type test is derived. Through simulations, we show that our method can achieve greater power than existing approaches. The proposed model is applied to investigate the association between schizophrenia and bipolar disorder in a family-based cohort consisting of 17 extended families from Eastern Quebec.

A novel statistical method for modeling covariate effects in bisulfite sequencing derived measures of DNA methylation.

Identifying disease-associated changes in DNA methylation can help us gain a better understanding of disease etiology. Bisulfite sequencing allows the generation of high-throughput methylation profiles at single-base resolution of DNA. However, optimally modeling and analyzing these sparse and discrete sequencing data is still very challenging due to variable read depth, missing data patterns, long-range correlations, data errors, and confounding from cell type mixtures. We propose a regression-based hierarchical model that allows covariate effects to vary smoothly along genomic positions and we have built a specialized EM algorithm, which explicitly allows for experimental errors and cell type mixtures, to make inference about smooth covariate effects in the model. Simulations show that the proposed method provides accurate estimates of covariate effects and captures the major underlying methylation patterns with excellent power. We also apply our method to analyze data from rheumatoid arthritis patients and controls. The method has been implemented in R package SOMNiBUS.

Sequence kernel association test for survival outcomes in the presence of a non-susceptible fraction.

In this work, we propose a single nucleotide polymorphism set association test for survival phenotypes in the presence of a non-susceptible fraction. We consider a mixture model with a logistic regression for the susceptibility indicator and a proportional hazards regression to model survival in the susceptible group. We propose a joint test to assess the significance of the genetic variant in both logistic and survival regressions simultaneously. We adopt the spirit of SKAT and conduct a variance-component test treating the genetic effects of multiple variants as random. We derive score-type test statistics, and we investigate several approaches to compute their $p$-values. The finite-sample properties of the proposed tests are assessed and compared to existing approaches by simulations and their use is illustrated through an application to ovarian cancer data from the Consortium of Investigators of Modifiers of BRCA1 and BRCA2.

Testing the heritability and parent-of-origin hypotheses for ages at onset of psoriatic arthritis under biased sampling.

The heritability and parent-of-origin effect hypotheses for chronic diseases can be evaluated by estimating and conducting inference about the parameters that measure the within-family dependences in disease onset times. We model the within-family associations in these times using a Gaussian copula whose correlation matrix accommodates the different pairwise family relationships. We derive score-type statistics to test the heritability and parent-of-origin effect hypotheses when the families selection protocol induces a sampling bias. We illustrate the use of the developed methods through an application to a motivating family study in Psoriatic arthritis and provide strong evidence of excessive paternal transmission of risk.

Association measures for clustered competing risks.

We propose a semiparameteric model for multivariate clustered competing risks data when the cause-specific failure times and the occurrence of competing risk events among subjects within the same cluster are of interest. The cause-specific hazard functions are assumed to follow Cox proportional hazard models, and the associations between failure times given the same or different cause events and the associations between occurrences of competing risk events within the same cluster are investigated through copula models. A cross-odds ratio measure is explored under our proposed models. Two-stage estimation procedure is proposed in which the marginal models are estimated in the first stage, and the dependence parameters are estimated via an expectation-maximization algorithm in the second stage. The proposed estimators are shown to yield consistent and asymptotically normal under mild regularity conditions. Simulation studies are conducted to assess finite sample performance of the proposed method. The proposed technique is demonstrated through an application to a multicenter Bone Marrow transplantation dataset.

Risks of Colorectal Cancer and Cancer-Related Mortality in Familial Colorectal Cancer Type X and Lynch Syndrome Families.

BACKGROUND: The risk of cancers is well characterized in Lynch syndrome (LS) families but has been less studied in familial colorectal cancer type X (FCCTX) families. METHODS: In this article, we compare the risk estimates of first and second colorectal cancers (CRCs) in 168 FCTTX and 780 LS families recruited through the Colon Cancer Family Registry as well as the risk of cancer-related deaths and disease-free survival (DFS) after a first CRC. Our methodology is based on a survival analysis approach, developed specifically to model the occurrence of successive cancers (ie, first and second CRCs) in the presence of competing risk events (ie, death from any causes). RESULTS: We found an excess risk of first and second CRC in individuals with LS compared to FCCTX family members. However, for an average age at first CRC of 60 years in FCCTX families and 50 years in LS families, the DFS rates were comparable in men but lower in women from FCCTX vs LS families, eg , 75.1% (95% confidence interval [CI] = 69.0% to 80.9%) vs 78.9% (95% CI = 76.3% to 81.3%) for the 10-year DFS. The 10-year risk of cancer-related death was higher in FCCTX families vs LS families, eg, 15.4% in men (95% CI = 10.9% to 19.8%) and 19.3% in women (95% CI = 13.6% to 24.7%) vs 8.9% (95% CI = 7.5% to 11.4%) and 8.7% (95% CI = 7.1% to 10.8%), respectively. CONCLUSIONS: Individuals with CRCs arising in the context of FCCTX do not experience the same improved DFS and overall survival of those with LS, and that difference may be relevant in management decisions.

A smoothed EM-algorithm for DNA methylation profiles from sequencing-based methods in cell lines or for a single cell type.

We consider the assessment of DNA methylation profiles for sequencing-derived data from a single cell type or from cell lines. We derive a kernel smoothed EM-algorithm, capable of analyzing an entire chromosome at once, and to simultaneously correct for experimental errors arising from either the pre-treatment steps or from the sequencing stage and to take into account spatial correlations between DNA methylation profiles at neighbouring CpG sites. The outcomes of our algorithm are then used to (i) call the true methylation status at each CpG site, (ii) provide accurate smoothed estimates of DNA methylation levels, and (iii) detect differentially methylated regions. Simulations show that the proposed methodology outperforms existing analysis methods that either ignore the correlation between DNA methylation profiles at neighbouring CpG sites or do not correct for errors. The use of the proposed inference procedure is illustrated through the analysis of a publicly available data set from a cell line of induced pluripotent H9 human embryonic stem cells and also a data set where methylation measures were obtained for a small genomic region in three different immune cell types separated from whole blood.

Modeling of successive cancer risks in Lynch syndrome families in the presence of competing risks using copulas.

In this article, we propose an association model to estimate the penetrance (risk) of successive cancers in the presence of competing risks. The association between the successive events is modeled via a copula and a proportional hazards model is specified for each competing event. This work is motivated by the analysis of successive cancers for people with Lynch Syndrome in the presence of competing risks. The proposed inference procedure is adapted to handle missing genetic covariates and selection bias, induced by the data collection protocol of the data at hand. The performance of the proposed estimation procedure is evaluated by simulations and its use is illustrated with data from the Colon Cancer Family Registry (Colon CFR).

Association measures for bivariate failure times in the presence of a cure fraction.

This paper proposes a new joint model for pairs of failure times in the presence of a cure fraction. The proposed model relaxes some of the assumptions required by the existing approaches. This allows us to add some flexibility to the dependence structure and to widen the range of association measures that can be defined. A numerically stable iterative algorithm based on estimating equations is proposed to estimate the parameters. The estimators are shown to be consistent and asymptotically normal. Simulations show that they have good finite-sample properties. The added flexibility of the proposal is illustrated with an application to data from a diabetes retinopathy study.

Software Application Profile: RVPedigree: a suite of family-based rare variant association tests for normally and non-normally distributed quantitative traits.

MOTIVATION: RVPedigree (Rare Variant association tests in Pedigrees) implements a suite of programs facilitating genome-wide analysis of association between a quantitative trait and autosomal region-based genetic variation. The main features here are the ability to appropriately test for association of rare variants with non-normally distributed quantitative traits, and also to appropriately adjust for related individuals, either from families or from population structure and cryptic relatedness. IMPLEMENTATION: RVPedigree is available as an R package. GENERAL FEATURES: The package includes calculation of kinship matrices, various options for coping with non-normality, three different ways of estimating statistical significance incorporating triaging to enable efficient use of the most computationally-intensive calculations, and a parallelization option for genome-wide analysis. AVAILABILITY: The software is available from the Comprehensive R Archive Network [CRAN.R-project.org] under the name 'RVPedigree' and at [https://github.com/GreenwoodLab]. It has been published under General Public License (GPL) version 3 or newer.

A rare variant association test in family-based designs and non-normal quantitative traits.

Rare variant studies are now being used to characterize the genetic diversity between individuals and may help to identify substantial amounts of the genetic variation of complex diseases and quantitative phenotypes. Family data have been shown to be powerful to interrogate rare variants. Consequently, several rare variants association tests have been recently developed for family-based designs, but typically, these assume the normality of the quantitative phenotypes. In this paper, we present a family-based test for rare-variants association in the presence of non-normal quantitative phenotypes. The proposed model relaxes the normality assumption and does not specify any parametric distribution for the marginal distribution of the phenotype. The dependence between relatives is modeled via a Gaussian copula. A score-type test is derived, and several strategies to approximate its distribution under the null hypothesis are derived and investigated. The performance of the proposed test is assessed and compared with existing methods by simulations. The methodology is illustrated with an association study involving the adiponectin trait from the UK10K project.

Using informative Multinomial-Dirichlet prior in a t-mixture with reversible jump estimation of nucleosome positions for genome-wide profiling.

Genome-wide mapping of nucleosomes has revealed a great deal about the relationships between chromatin structure and control of gene expression. Recent next generation CHIP-chip and CHIP-Seq technologies have accelerated our understanding of basic principles of chromatin organization. These technologies have taught us that nucleosomes play a crucial role in gene regulation by allowing physical access to transcription factors. Recent methods and experimental advancements allow the determination of nucleosome positions for a given genome area. However, most of these methods estimate the number of nucleosomes either by an EM algorithm using a BIC criterion or an effective heuristic strategy. Here, we introduce a Bayesian method for identifying nucleosome positions. The proposed model is based on a Multinomial-Dirichlet classification and a hierarchical mixture distributions. The number and the positions of nucleosomes are estimated using a reversible jump Markov chain Monte Carlo simulation technique. We compare the performance of our method on simulated data and MNase-Seq data from Saccharomyces cerevisiae against PING and NOrMAL methods.

SNP Set Association Testing for Survival Outcomes in the Presence of Intrafamilial Correlation.

In this work, we propose a single nucleotide polymorphism (SNP) set association test for censored phenotypes in the presence of a family-based design. The proposed test is valid for both common and rare variants. A proportional hazards Cox model is specified for the marginal distribution of the trait and the familial dependence is modeled via a Gaussian copula. Censored values are treated as partially missing data and a multiple imputation procedure is proposed in order to compute the test statistics. The P-value is then deduced analytically. The finite-sample empirical properties of the proposed method are evaluated and compared to existing competitors by simulations and its use is illustrated using a breast cancer data set from the Consortium of Investigators of Modifiers of BRCA1 and BRCA2.

On the association between variables with lower detection limits.

In this paper, we define a modified version τ(b) of Kendall's tau to measure the association in a pair (X,Y) of random variables subject to fixed left censoring due to known lower detection limits. We provide a nonparametric estimator of τ(b) and investigate its asymptotic properties. We then assume an Archimedean copula for (X,Y) and express τ(b) in terms of the copula parameter α and the censoring fractions. We deduce estimators for α and for the global Kendall's tau. We develop a goodness-of-fit test for the assumed copula. We evaluate the finite-sample performance of the proposed methods by simulations and illustrate their use with a real data set on plasma and saliva viral loads.

Outdoor temperature, age, sex, body mass index, and diabetic status determine the prevalence, mass, and glucose-uptake activity of 18F-FDG-detected BAT in humans.

CONTEXT: In humans, the prevalence, mass, and glucose-uptake activity of (18)F-fluorodeoxyglucose ((18)F-FDG)-detected brown adipose tissue (BAT), which are expectedly enhanced by a cold stimulus, also appear modulated by other factors that still have to be disentangled. OBJECTIVE: The objective of the study was to investigate the factors determining the prevalence, mass, and glucose-uptake activity of (18)F-FDG-detected BAT in humans. RESEARCH DESIGN AND METHODS: We retrospectively analyzed all (18)F-FDG positron emission tomography/computed tomography examinations performed between January 2007 and December 2008 at our institution for (18)F-FDG uptake within the cervical/supraclavicular, mediastinal, paravertebral, and perirenal fat areas. The influence of outdoor temperature, sex, age, body mass index (BMI), plasma glucose level, diabetes diagnosis, day length, and cancer status on the prevalence, mass, and glucose-uptake activity of (18)F-FDG-detected BAT depots was investigated. RESULTS: Three hundred twenty-eight of the 4842 patients (6.8%) had (18)F-FDG-detected BAT. The prevalence of (18)F-FDG BAT was negatively associated with outdoor temperature (P < 0.0001), age (P < 0.0001), BMI (P < 0.0001), and diabetes status (P = 0.0003). Moreover, there was a significant age × sex interaction for the prevalence of (18)F-FDG BAT (the younger the subjects, the greater the sex difference). The mass and glucose-uptake activity of (18)F-FDG-detected BAT also decreased with increasing outdoor temperature (P < 0.0001), age (P < 0.0001), and BMI (P < 0.0001). They were lower in men than in women (P < 0.001) and lower in diabetic than in nondiabetic patients (P = 0.0002). CONCLUSIONS: The present study identifies outdoor temperature, age, sex, BMI, and diabetes status as determinants of the prevalence, mass, and glucose-uptake activity of (18)F-FDG-detected BAT.

A human ALDH1A2 gene variant is associated with increased newborn kidney size and serum retinoic acid.

Nephron number varies widely between 0.3 and 1.3 million per kidney in humans. During fetal life, the rate of nephrogenesis is influenced by local retinoic acid (RA) level such that even moderate maternal vitamin A deficiency limits the final nephron number in rodents. Inactivation of genes in the RA pathway causes renal agenesis in mice; however, the impact of retinoids on human kidney development is unknown. To resolve this, we tested for associations between variants of genes involved in RA metabolism (ALDH1A2, CYP26A1, and CYP26B1) and kidney size among normal newborns. Homozygosity for a common (1 in 5) variant, rs7169289(G), within an Sp1 transcription factor motif of the ALDH1A2 gene, showed a significant 22% increase in newborn kidney volume when adjusted for body surface area. Infants bearing this allele had higher umbilical cord blood RA levels compared to those with homozygous wild-type ALDH1A2 rs7169289(A) alleles. Furthermore, the effect of the rs7169289(G) variant was evident in subgroups with or without a previously reported hypomorphic RET 1476(A) proto-oncogene allele that is critical in determining final nephron number. As maternal vitamin A deficiency is widespread in developing countries and may compromise availability of retinol for fetal RA synthesis, our study suggests that the ALDH1A2 rs7169289(G) variant might be protective for such individuals.

Newborn serum retinoic acid level is associated with variants of genes in the retinol metabolism pathway.

Retinoic acid (RA) is a critical regulator of gene expression during embryonic development. In rodents, moderate maternal vitamin A deficiency leads to subtle morphogenetic defects and inactivation of RA pathway genes causes major disturbances of embryogenesis. In this study, we quantified RA in umbilical cord blood of 145 healthy full-term Caucasian infants from Montreal. Sixty seven percent of values were <10 nmol/L (84 were <0.07 nmol/L) and 33% had moderate or high levels. Variation in RA could not be explained by parallel variation in its precursor, retinol (ROL). However, we found that the (A) allele of the rs12591551 single nucleotide polymorphism (SNP) in the ALDH1A2 gene (ALDH1A2rs12591551(A)), occurring in 19% of newborns, was associated with 2.5-fold higher serum RA levels. ALDH1A2 encodes retinaldehyde dehydrogenase (RALDH) 2, which synthesizes RA in fetal tissues. We also found that homozygosity for the (A) allele of the rs12724719 SNP in the CRABP2 gene (CRABP2rs12724719(A/A)) was associated with 4.4-fold increase in umbilical cord serum RA. CRABP2 facilitates RA binding to its cognate receptor complex and transfer to the nucleus. We hypothesize that individual variation in RA pathway genes may account for subtle variations in RA-dependent human embryogenesis.

Inverse probability of censoring weighted estimates of Kendall's τ for gap time analyses.

In life history studies, interest often lies in the analysis of the interevent, or gap times and the association between event times. Gap time analyses are challenging however, even when the length of follow-up is determined independently of the event process, because associations between gap times induce dependent censoring for second and subsequent gap times. This article discusses nonparametric estimation of the association between consecutive gap times based on Kendall's τ in the presence of this type of dependent censoring. A nonparametric estimator that uses inverse probability of censoring weights is provided. Estimates of conditional gap time distributions can be obtained following specification of a particular copula function. Simulation studies show the estimator performs well and compares favorably with an alternative estimator. Generalizations to a piecewise constant Clayton copula are given. Several simulation studies and illustrations with real data sets are also provided.