A Permutation Approach for Selecting the Penalty Parameter in Penalized Model Selection

We describe a simple, efficient, permutation based procedure for selecting the penalty parameter in the LASSO. The procedure, which is intended for applications where variable selection is the primary focus, can be applied in a variety of structural settings, including generalized linear models. We briefly discuss connections between permutation selection and existing theory for the LASSO. In addition, we present a simulation study and an analysis of three real data sets in which permutation selection is compared with cross-validation (CV), the Bayesian information criterion (BIC), and a selection method based on recently developed testing procedures for the LASSO

Joint estimation of multiple dependent Gaussian graphical models with applications to mouse genomics

Gaussian graphical models are widely used to represent conditional dependence among random variables. In this paper, we propose a novel estimator for data arising from a group of Gaussian graphical models that are themselves dependent. A motivating example is that of modeling gene expression collected on multiple tissues from the same individual: here the multivariate outcome is affected by dependencies acting not only at the level of the specific tissues, but also at the level of the whole body; existing methods that assume independence among graphs are not applicable in this case. To estimate multiple dependent graphs, we decompose the problem into two graphical layers: the systemic layer, which affects all outcomes and thereby induces cross-graph dependence, and the category-specific layer, which represents graph-specific variation. We propose a graphical EM technique that estimates both layers jointly, establish estimation consistency and selection sparsistency of the proposed estimator, and confirm by simulation that the EM method is superior to a simple one-step method. We apply our technique to mouse genomics data and obtain biologically plausible results

Bayesian Modeling of Haplotype Effects in Multiparent Populations

A general Bayesian model, Diploffect, is described for estimating the effects of founder haplotypes at quantitative trait loci (QTL) detected in multiparental genetic populations; such populations include the Collaborative Cross (CC), Heterogeneous Socks (HS), and many others for which local genetic variation is well described by an underlying, usually probabilistically inferred, haplotype mosaic. Our aim is to provide a framework for coherent estimation of haplotype and diplotype (haplotype pair) effects that takes into account the following: uncertainty in haplotype composition for each individual; uncertainty arising from small sample sizes and infrequently observed haplotype combinations; possible effects of dominance (for noninbred subjects); genetic background; and that provides a means to incorporate data that may be incomplete or has a hierarchical structure. Using the results of a probabilistic haplotype reconstruction as prior information, we obtain posterior distributions at the QTL for both haplotype effects and haplotype composition. Two alternative computational approaches are supplied: a Markov chain Monte Carlo sampler and a procedure based on importance sampling of integrated nested Laplace approximations. Using simulations of QTL in the incipient CC (pre-CC) and Northport HS populations, we compare the accuracy of Diploffect, approximations to it, and more commonly used approaches based on Haley–Knott regression, describing trade-offs between these methods. We also estimate effects for three QTL previously identified in those populations, obtaining posterior intervals that describe how the phenotype might be affected by diplotype substitutions at the modeled locus

A Bayesian model selection approach to mediation analysis.

Genetic studies often seek to establish a causal chain of events originating from genetic variation through to molecular and clinical phenotypes. When multiple phenotypes share a common genetic association, one phenotype may act as an intermediate for the genetic effects on the other. Alternatively, the phenotypes may be causally unrelated but share genetic loci. Mediation analysis represents a class of causal inference approaches used to determine which of these scenarios is most plausible. We have developed a general approach to mediation analysis based on Bayesian model selection and have implemented it in an R package, bmediatR. Bayesian model selection provides a flexible framework that can be tailored to different analyses. Our approach can incorporate prior information about the likelihood of models and the strength of causal effects. It can also accommodate multiple genetic variants or multi-state haplotypes. Our approach reports posterior probabilities that can be useful in interpreting uncertainty among competing models. We compared bmediatR with other popular methods, including the Sobel test, Mendelian randomization, and Bayesian network analysis using simulated data. We found that bmediatR performed as well or better than these alternatives in most scenarios. We applied bmediatR to proteome data from Diversity Outbred (DO) mice, a multi-parent population, and demonstrate the power of mediation with multi-state haplotypes. We also applied bmediatR to data from human cell lines to identify transcripts that are mediated through or are expressed independently from local chromatin accessibility. We demonstrate that Bayesian model selection provides a powerful and versatile approach to identify causal relationships in genetic studies using model organism or human data

Mean-Variance QTL Mapping Identifies Novel QTL for Circadian Activity and Exploratory Behavior in Mice.

We illustrate, through two case studies, that mean-variance QTL mapping -QTL mapping that models effects on the mean and the variance simultaneously-can discover QTL that traditional interval mapping cannot. Mean-variance QTL mapping is based on the double generalized linear model, which extends the standard linear model used in interval mapping by incorporating not only a set of genetic and covariate effects for mean but also set of such effects for the residual variance. Its potential for use in QTL mapping has been described previously, but it remains underutilized, with certain key advantages undemonstrated until now. In the first case study, a reduced complexity intercross of C57BL/6J and C57BL/6N mice examining circadian behavior, our reanalysis detected a mean-controlling QTL for circadian wheel running activity that interval mapping did not; mean-variance QTL mapping was more powerful than interval mapping at the QTL because it accounted for the fact that mice homozygous for the C57BL/6N allele had less residual variance than other mice. In the second case study, an intercross between C57BL/6J and C58/J mice examining anxiety-like behaviors, our reanalysis detected a variance-controlling QTL for rearing behavior; interval mapping did not identify this QTL because it does not target variance QTL. We believe that the results of these reanalyses, which in other respects largely replicated the original findings, support the use of mean-variance QTL mapping as standard practice

Fine-Mapping Additive and Dominant SNP Effects Using Group-LASSO and Fractional Resample Model Averaging

Genomewide association studies sometimes identify loci at which both the number and identities of the underlying causal variants are ambiguous. In such cases, statistical methods that model effects of multiple SNPs simultaneously can help disentangle the observed patterns of association and provide information about how those SNPs could be prioritized for follow-up studies. Current multi-SNP methods, however, tend to assume that SNP effects are well captured by additive genetics; yet when genetic dominance is present, this assumption translates to reduced power and faulty prioritizations. We describe a statistical procedure for prioritizing SNPs at GWAS loci that efficiently models both additive and dominance effects. Our method, LLARRMA-dawg, combines a group LASSO procedure for sparse modeling of multiple SNP effects with a resampling procedure based on fractional observation weights; it estimates for each SNP the robustness of association with the phenotype both to sampling variation and to competing explanations from other SNPs. In producing a SNP prioritization that best identifies underlying true signals, we show that: our method easily outperforms a single marker analysis; when additive-only signals are present, our joint model for additive and dominance is equivalent to or only slightly less powerful than modeling additive-only effects; and, when dominance signals are present, even in combination with substantial additive effects, our joint model is unequivocally more powerful than a model assuming additivity. We also describe how performance can be improved through calibrated randomized penalization, and discuss how dominance in ungenotyped SNPs can be incorporated through either heterozygote dosage or multiple imputation

A General Bayesian Approach to Analyzing Diallel Crosses of Inbred Strains

The classic diallel takes a set of parents and produces offspring from all possible mating pairs. Phenotype values among the offspring can then be related back to their respective parentage. When the parents are diploid, sexed, and inbred, the diallel can characterize aggregate effects of genetic background on a phenotype, revealing effects of strain dosage, heterosis, parent of origin, epistasis, and sex-specific versions thereof. However, its analysis is traditionally intricate, unforgiving of unplanned missing information, and highly sensitive to imbalance, making the diallel unapproachable to many geneticists. Nonetheless, imbalanced and incomplete diallels arise frequently, albeit unintentionally, as by-products of larger-scale experiments that collect F1 data, for example, pilot studies or multiparent breeding efforts such as the Collaborative Cross or the Arabidopsis MAGIC lines. We present a general Bayesian model for analyzing diallel data on dioecious diploid inbred strains that cleanly decomposes the observed patterns of variation into biologically intuitive components, simultaneously models and accommodates outliers, and provides shrinkage estimates of effects that automatically incorporate uncertainty due to imbalance, missing data, and small sample size. We further present a model selection procedure for weighing evidence for or against the inclusion of those components in a predictive model. We evaluate our method through simulation and apply it to incomplete diallel data on the founders and F1's of the Collaborative Cross, robustly characterizing the genetic architecture of 48 phenotypes

Detecting Major Genetic Loci Controlling Phenotypic Variability in Experimental Crosses

Traditional methods for detecting genes that affect complex diseases in humans or animal models, milk production in livestock, or other traits of interest, have asked whether variation in genotype produces a change in that trait’s average value. But focusing on differences in the mean ignores differences in variability about that mean. The robustness, or uniformity, of an individual’s character is not only of great practical importance in medical genetics and food production but is also of scientific and evolutionary interest (e.g., blood pressure in animal models of heart disease, litter size in pigs, flowering time in plants). We describe a method for detecting major genes controlling the phenotypic variance, referring to these as vQTL. Our method uses a double generalized linear model with linear predictors based on probabilities of line origin. We evaluate our method on simulated F2 and collaborative cross data, and on a real F2 intercross, demonstrating its accuracy and robustness to the presence of ordinary mean-controlling QTL. We also illustrate the connection between vQTL and QTL involved in epistasis, explaining how these concepts overlap. Our method can be applied to a wide range of commonly used experimental crosses and may be extended to genetic association more generally