Kathryn Roeder

A SAS Procedure Based on Mixture Models for Estimating Developmental Trajectories

This article introduces a new SAS procedure written by the authors that analyzes longitudinal data (developmental trajectories) by fitting a mixture model. The TRAJ procedure fits semiparametric (discrete) mixtures of censored normal, Poisson, zero-inflated Poisson, and Bernoulli distributions to longitudinal data. Applications to psychometric scale data, offense counts, and a dichotomous prevalence measure in violence research are illustrated. In addition, the use of the Bayesian information criterion to address the problem of model selection, including the estimation of the number of components in the mixture, is demonstrated.

De novo mutations revealed by whole-exome sequencing are strongly associated with autism

Multiple studies have confirmed the contribution of rare de novo copy number variations to the risk for autism spectrum disorders. But whereas de novo single nucleotide variants have been identified in affected individuals, their contribution to risk has yet to be clarified. Specifically, the frequency and distribution of these mutations have not been well characterized in matched unaffected controls, and such data are vital to the interpretation of de novo coding mutations observed in probands. Here we show, using whole-exome sequencing of 928 individuals, including 200 phenotypically discordant sibling pairs, that highly disruptive (nonsense and splice-site) de novo mutations in brain-expressed genes are associated with autism spectrum disorders and carry large effects. On the basis of mutation rates in unaffected individuals, we demonstrate that multiple independent de novo single nucleotide variants in the same gene among unrelated probands reliably identifies risk alleles, providing a clear path forward for gene discovery. Among a total of 279 identified de novo coding mutations, there is a single instance in probands, and none in siblings, in which two independent nonsense variants disrupt the same gene, SCN2A (sodium channel, voltage-gated, type II, α subunit), a result that is highly unlikely by chance.

Patterns and rates of exonic de novo mutations in autism spectrum disorders

Autism spectrum disorders (ASD) are believed to have genetic and environmental origins, yet in only a modest fraction of individuals can specific causes be identified. To identify further genetic risk factors, here we assess the role of de novo mutations in ASD by sequencing the exomes of ASD cases and their parents (n = 175 trios). Fewer than half of the cases (46.3%) carry a missense or nonsense de novo variant, and the overall rate of mutation is only modestly higher than the expected rate. In contrast, the proteins encoded by genes that harboured de novo missense or nonsense mutations showed a higher degree of connectivity among themselves and to previous ASD genes as indexed by protein-protein interaction screens. The small increase in the rate of de novo events, when taken together with the protein interaction results, are consistent with an important but limited role for de novo point mutations in ASD, similar to that documented for de novo copy number variants. Genetic models incorporating these data indicate that most of the observed de novo events are unconnected to ASD; those that do confer risk are distributed across many genes and are incompletely penetrant (that is, not necessarily sufficient for disease). Our results support polygenic models in which spontaneous coding mutations in any of a large number of genes increases risk by 5- to 20-fold. Despite the challenge posed by such models, results from de novo events and a large parallel case–control study provide strong evidence in favour of CHD8 and KATNAL2 as genuine autism risk factors.

Multiple Recurrent De Novo CNVs, Including Duplications of the 7q11.23 Williams Syndrome Region, Are Strongly Associated with Autism

We have undertaken a genome-wide analysis of rare copy-number variation (CNV) in 1124 autism spectrum disorder (ASD) families, each comprised of a single proband, unaffected parents, and, in most kindreds, an unaffected sibling. We find significant association of ASD with de novo duplications of 7q11.23, where the reciprocal deletion causes Williams-Beuren syndrome, characterized by a highly social personality. We identify rare recurrent de novo CNVs at five additional regions, including 16p13.2 (encompassing genes USP7 and C16orf72) and Cadherin 13, and implement a rigorous approach to evaluating the statistical significance of these observations. Overall, large de novo CNVs, particularly those encompassing multiple genes, confer substantial risks (OR = 5.6; CI = 2.6-12.0, p = 2.4 × 10(-7)). We estimate there are 130-234 ASD-related CNV regions in the human genome and present compelling evidence, based on cumulative data, for association of rare de novo events at 7q11.23, 15q11.2-13.1, 16p11.2, and Neurexin 1.

Testing for an Unusual Distribution of Rare Variants

Technological advances make it possible to use high-throughput sequencing as a primary discovery tool of medical genetics, specifically for assaying rare variation. Still this approach faces the analytic challenge that the influence of very rare variants can only be evaluated effectively as a group. A further complication is that any given rare variant could have no effect, could increase risk, or could be protective. We propose here the C-alpha test statistic as a novel approach for testing for the presence of this mixture of effects across a set of rare variants. Unlike existing burden tests, C-alpha, by testing the variance rather than the mean, maintains consistent power when the target set contains both risk and protective variants. Through simulations and analysis of case/control data, we demonstrate good power relative to existing methods that assess the burden of rare variants in individuals.

Most genetic risk for autism resides with common variation

A key component of genetic architecture is the allelic spectrum influencing trait variability. For autism spectrum disorder (herein termed autism), the nature of the allelic spectrum is uncertain. Individual risk-associated genes have been identified from rare variation, especially de novo mutations. From this evidence, one might conclude that rare variation dominates the allelic spectrum in autism, yet recent studies show that common variation, individually of small effect, has substantial impact en masse. At issue is how much of an impact relative to rare variation this common variation has. Using a unique epidemiological sample from Sweden, new methods that distinguish total narrow-sense heritability from that due to common variation and synthesis of results from other studies, we reach several conclusions about autisms genetic architecture: its narrow-sense heritability is ∼52.4%, with most due to common variation, and rare de novo mutations contribute substantially to individual liability, yet their contribution to variance in liability, 2.6%, is modest compared to that for heritable variation.

Practical Bayesian Density Estimation Using Mixtures of Normals

Abstract Mixtures of normals provide a flexible model for estimating densities in a Bayesian framework. There are some difficulties with this model, however. First, standard reference priors yield improper posteriors. Second, the posterior for the number of components in the mixture is not well defined (if the reference prior is used). Third, posterior simulation does not provide a direct estimate of the posterior for the number of components. We present some practical methods for coping with these problems. Finally, we give some results on the consistency of the method when the maximum number of components is allowed to grow with the sample size.

A framework for the interpretation of de novo mutation in human disease

Spontaneously arising (de novo) mutations have an important role in medical genetics. For diseases with extensive locus heterogeneity, such as autism spectrum disorders (ASDs), the signal from de novo mutations is distributed across many genes, making it difficult to distinguish disease-relevant mutations from background variation. Here we provide a statistical framework for the analysis of excesses in de novo mutation per gene and gene set by calibrating a model of de novo mutation. We applied this framework to de novo mutations collected from 1,078 ASD family trios, and, whereas we affirmed a significant role for loss-of-function mutations, we found no excess of de novo loss-of-function mutations in cases with IQ above 100, suggesting that the role of de novo mutations in ASDs might reside in fundamental neurodevelopmental processes. We also used our model to identify ∼1,000 genes that are significantly lacking in functional coding variation in non-ASD samples and are enriched for de novo loss-of-function mutations identified in ASD cases.

The heritability of IQ

IQ heritability, the portion of a populations IQ variability attributable to the effects of genes, has been investigated for nearly a century, yet it remains controversial. Covariance between relatives may be due not only to genes, but also to shared environments, and most previous models have assumed different degrees of similarity induced by environments specific to twins, to non-twin siblings (henceforth siblings), and to parents and offspring. We now evaluate an alternative model that replaces these three environments by two maternal womb environments, one for twins and another for siblings, along with a common home environment. Meta-analysis of 212 previous studies shows that our ‘maternal-effects’ model fits the data better than the ‘family-environments’ model. Maternal effects, often assumed to be negligible, account for 20% of covariance between twins and 5% between siblings, and the effects of genes are correspondingly reduced, with two measures of heritability being less than 50%. The shared maternal environment may explain the striking correlation between the IQs of twins, especially those of adult twins that were reared apart. IQ heritability increases during early childhood, but whether it stabilizes thereafter remains unclear. A recent study of octogenarians, for instance, suggests that IQ heritability either remains constant through adolescence and adulthood, or continues to increase with age. Although the latter hypothesis has recently been endorsed, it gathers only modest statistical support in our analysis when compared to the maternal-effects hypothesis. Our analysis suggests that it will be important to understand the basis for these maternal effects if ways in which IQ might be increased are to be identified.

Modeling Uncertainty in Latent Class Membership: A Case Study in Criminology

Abstract Social scientists are commonly interested in relating a latent trait (e.g., criminal tendency) to measurable individual covariates (e.g., poor parenting) to understand what defines or perhaps causes the latent trait. In this article we develop an efficient and convenient method for answering such questions. The basic model presumes that two types of variables have been measured: Response variables (possibly longitudinal) that partially determine the latent class membership, and covariates or risk factors that we wish to relate to these latent class variables. The model assumes that these observable variables are conditionally independent, given the latent class variable. We use a mixture model for the joint distribution of the observables. We apply this model to a longitudinal dataset assembled as part of the Cambridge Study of Delinquent Development to test a fundamental theory of criminal development. This theory holds that crime is committed by two distinct groups within the population: Adoles...