Multicomponent variance estimation for binary traits in family-based studies

Future Preventive Gene Therapy of Polygenic Diseases from a Population Genetics Perspective

With the accumulation of scientific knowledge of the genetic causes of common diseases and continuous advancement of gene-editing technologies, gene therapies to prevent polygenic diseases may soon become possible. This study endeavored to assess population genetics consequences of such therapies. Computer simulations were used to evaluate the heterogeneity in causal alleles for polygenic diseases that could exist among geographically distinct populations. The results show that although heterogeneity would not be easily detectable by epidemiological studies following population admixture, even significant heterogeneity would not impede the outcomes of preventive gene therapies. Preventive gene therapies designed to correct causal alleles to a naturally-occurring neutral state of nucleotides would lower the prevalence of polygenic early- to middle-age-onset diseases in proportion to the decreased population relative risk attributable to the edited alleles. The outcome would manifest differently for late-onset diseases, for which the therapies would result in a delayed disease onset and decreased lifetime risk; however, the lifetime risk would increase again with prolonging population life expectancy, which is a likely consequence of such therapies. If the preventive heritable gene therapies were to be applied on a large scale, the decreasing frequency of risk alleles in populations would reduce the disease risk or delay the age of onset, even with a fraction of the population receiving such therapies. With ongoing population admixture, all groups would benefit over generations.

Association of Genetic and Environmental Factors With Autism in a 5-Country Cohort

IMPORTANCE

The origins and development of autism spectrum disorder (ASD) remain unresolved. No individual-level study has provided estimates of additive genetic, maternal, and environmental effects in ASD across several countries.

OBJECTIVE

To estimate the additive genetic, maternal, and environmental effects in ASD.

DESIGN, SETTING, AND PARTICIPANTS

Population-based, multinational cohort study including full birth cohorts of children from Denmark, Finland, Sweden, Israel, and Western Australia born between January 1, 1998, and December 31, 2011, and followed up to age 16 years. Data were analyzed from September 23, 2016 through February 4, 2018.

MAIN OUTCOMES AND MEASURES

Across 5 countries, models were fitted to estimate variance components describing the total variance in risk for ASD occurrence owing to additive genetics, maternal, and shared and nonshared environmental effects.

RESULTS

The analytic sample included 2 001 631 individuals, of whom 1 027 546 (51.3%) were male. Among the entire sample, 22 156 were diagnosed with ASD. The median (95% CI) ASD heritability was 80.8% (73.2%-85.5%) for country-specific point estimates, ranging from 50.9% (25.1%-75.6%) (Finland) to 86.8% (69.8%-100.0%) (Israel). For the Nordic countries combined, heritability estimates ranged from 81.2% (73.9%-85.3%) to 82.7% (79.1%-86.0%). Maternal effect was estimated to range from 0.4% to 1.6%. Estimates of genetic, maternal, and environmental effects for autistic disorder were similar with ASD.

CONCLUSIONS AND RELEVANCE

Based on population data from 5 countries, the heritability of ASD was estimated to be approximately 80%, indicating that the variation in ASD occurrence in the population is mostly owing to inherited genetic influences, with no support for contribution from maternal effects. The results suggest possible modest differences in the sources of ASD risk between countries.

Evaluating the Potential of Younger Cases and Older Controls Cohorts to Improve Discovery Power in Genome-Wide Association Studies of Late-Onset Diseases

For more than a decade, genome-wide association studies have been making steady progress in discovering the causal gene variants that contribute to late-onset human diseases. Polygenic late-onset diseases in an aging population display a risk allele frequency decrease at older ages, caused by individuals with higher polygenic risk scores becoming ill proportionately earlier and bringing about a change in the distribution of risk alleles between new cases and the as-yet-unaffected population. This phenomenon is most prominent for diseases characterized by high cumulative incidence and high heritability, examples of which include Alzheimer’s disease, coronary artery disease, cerebral stroke, and type 2 diabetes, while for late-onset diseases with relatively lower prevalence and heritability, exemplified by cancers, the effect is significantly lower. In this research, computer simulations have demonstrated that genome-wide association studies of late-onset polygenic diseases showing high cumulative incidence together with high initial heritability will benefit from using the youngest possible age-matched cohorts. Moreover, rather than using age-matched cohorts, study cohorts combining the youngest possible cases with the oldest possible controls may significantly improve the discovery power of genome-wide association studies.

Quantifying the Potential for Future Gene Therapy to Lower Lifetime Risk of Polygenic Late-Onset Diseases

Gene therapy techniques and genetic knowledge may sufficiently advance, within the next few decades, to support prophylactic gene therapy for the prevention of polygenic late-onset diseases. The risk of these diseases may, hypothetically, be lowered by correcting the effects of a subset of common low effect gene variants. In this paper, simulations show that if such gene therapy were to become technically possible; and if the incidences of the treated diseases follow the proportional hazards model with a multiplicative genetic architecture composed of a sufficient number of common small effect gene variants, then: (a) late-onset diseases with the highest familial heritability will have the largest number of variants available for editing; (b) diseases that currently have the highest lifetime risk, particularly those with the highest incidence rate continuing into older ages, will prove the most challenging cases in lowering lifetime risk and delaying the age of onset at a population-wide level; (c) diseases that are characterized by the lowest lifetime risk will show the strongest and longest-lasting response to such therapies; and (d) longer life expectancy is associated with a higher lifetime risk of these diseases, and this tendency, while delayed, will continue after therapy.

Quantifying the Potential for Future Gene Therapy to Lower Lifetime Risk of Polygenic Late-Onset Diseases

Gene therapy techniques and genetic knowledge may sufficiently advance, within the next few decades, to support prophylactic gene therapy for the prevention of polygenic late-onset diseases. The risk of these diseases may, hypothetically, be lowered by correcting the effects of a subset of common low effect gene variants. In this paper, simulations show that if such gene therapy were to become technically possible; and if the incidences of the treated diseases follow the proportional hazards model with a multiplicative genetic architecture composed of a sufficient number of common small effect gene variants, then: (a) late-onset diseases with the highest familial heritability will have the largest number of variants available for editing; (b) diseases that currently have the highest lifetime risk, particularly those with the highest incidence rate continuing into older ages, will prove the most challenging cases in lowering lifetime risk and delaying the age of onset at a population-wide level; (c) diseases that are characterized by the lowest lifetime risk will show the strongest and longest-lasting response to such therapies; and (d) longer life expectancy is associated with a higher lifetime risk of these diseases, and this tendency, while delayed, will continue after therapy.

Age-related late-onset disease heritability patterns and implications for genome-wide association studies

Genome-wide association studies (GWASs) and other computational biology techniques are gradually discovering the causal gene variants that contribute to late-onset human diseases. After more than a decade of genome-wide association study efforts, these can account for only a fraction of the heritability implied by familial studies, the so-called "missing heritability" problem. Computer simulations of polygenic late-onset diseases (LODs) in an aging population have quantified the risk allele frequency decrease at older ages caused by individuals with higher polygenic risk scores (PRSs) becoming ill proportionately earlier. This effect is most prominent for diseases characterized by high cumulative incidence and high heritability, examples of which include Alzheimer's disease, coronary artery disease, cerebral stroke, and type 2 diabetes. The incidence rate for LODs grows exponentially for decades after early onset ages, guaranteeing that the cohorts used for GWASs overrepresent older individuals with lower PRSs, whose disease cases are disproportionately due to environmental causes such as old age itself. This mechanism explains the decline in clinical predictive power with age and the lower discovery power of familial studies of heritability and GWASs. It also explains the relatively constant-with-age heritability found for LODs of lower prevalence, exemplified by cancers.

Variance Components Models for Analysis of Big Family Data of Health Outcomes in the Lifelines Cohort Study

Large multigenerational cohort studies offer powerful ways to study the hereditary effects on various health outcomes. However, accounting for complex kinship relations in big data structures can be methodologically challenging. The traditional kinship model is computationally infeasible when considering thousands of individuals. In this article, we propose a computationally efficient alternative that employs fractional relatedness of family members through a series of founding members. The primary goal of this study is to investigate whether the effect of determinants on health outcome variables differs with and without accounting for family structure. We compare a fixed-effects model without familial effects with several variance components models that account for heritability and shared environment structure. Our secondary goal is to apply the fractional relatedness model in a realistic setting. Lifelines is a three-generation cohort study investigating the biological, behavioral, and environmental determinants of healthy aging. We analyzed a sample of 89,353 participants from 32,452 reconstructed families. Our primary conclusion is that the effect of determinants on health outcome variables does not differ with and without accounting for family structure. However, accounting for family structure through fractional relatedness allows for estimating heritability in a computationally efficient way, showing some interesting differences between physical and mental quality of life heritability. We have shown through simulations that the proposed fractional relatedness model performs better than the standard kinship model, not only in terms of computational time and convenience of fitting using standard functions in R, but also in terms of bias of heritability estimates and coverage.

Heritable Variation, With Little or No Maternal Effect, Accounts for Recurrence Risk to Autism Spectrum Disorder in Sweden

BACKGROUND

Autism spectrum disorder (ASD) has both genetic and environmental origins, including potentially maternal effects. Maternal effects describe the association of one or more maternal phenotypes with liability to ASD in progeny that are independent of maternally transmitted risk alleles. While maternal effects could play an important role, consistent with association to maternal traits such as immune status, no study has estimated maternal, additive genetic, and environmental effects in ASD.

METHODS

Using a population-based sample consisting of all children born in Sweden from 1998 to 2007 and their relatives, we fitted statistical models to family data to estimate the variance in ASD liability originating from maternal, additive genetic, and shared environmental effects. We calculated sibling and cousin family recurrence risk ratio as a direct measure of familial, genetic, and environmental risk factors and repeated the calculations on diagnostic subgroups, specifically autistic disorder (AD) and spectrum disorder (SD), which included Asperger's syndrome and/or pervasive developmental disorder not otherwise specified.

RESULTS

The sample consisted of 776,212 children of whom 11,231 had a diagnosis of ASD: 4554 with AD, 6677 with SD. We found support for large additive genetic contribution to liability; heritability (95% confidence interval [CI]) was estimated to 84.8% (95% CI: 73.1-87.3) for ASD, 79.6% (95% CI: 61.2-85.1) for AD, and 76.4% (95% CI: 63.0-82.5) for SD.

CONCLUSIONS

There was modest, if any, contribution of maternal effects to liability for ASD, including subtypes AD and SD, and there was no support for shared environmental effects. These results show liability to ASD arises largely from additive genetic variation.

Biometrical modelling in genetics: are complex traits too complex?

The field of traditional biometrical genetics uses mixed-effects models to quantify the influence of genetic and environmental factors on a biological trait, based essentially on estimating within-family trait correlations. Such analyses provide a useful preview of what may be discovered with the emerging full-scale genotyping strategies. However, biometrical analyses require unrealistically large sample sizes to obtain a reasonable precision, particularly for dichotomous traits. In addition, it may be very difficult to separate genetic and environmental effects because environmental correlations are poorly understood. We illustrate these and other difficulties using population-based cousins and nuclear family data for birth weight, collected from the Medical Birth Registry of Norway.

Genetic variance components estimation for binary traits using multiple related individuals

Understanding and modeling genetic or nongenetic factors that influence susceptibility to complex traits has been the focus of many genetic studies. Large pedigrees with known complex structure may be advantageous in epidemiological studies since they can significantly increase the number of factors whose influence on the trait can be estimated. We propose a likelihood approach, developed in the context of generalized linear mixed models, for modeling dichotomous traits based on data from hundreds of individuals all of whom are potentially correlated through either a known pedigree or an estimated covariance matrix. Our approach is based on a hierarchical model where we first assess the probability of each individual having the trait and then formulate a likelihood assuming conditional independence of individuals. The advantage of our formulation is that it easily incorporates information from pertinent covariates as fixed effects and at the same time takes into account the correlation between individuals that share genetic background or other random effects. The high dimensionality of the integration involved in the likelihood prohibits exact computations. Instead, an automated Monte Carlo expectation maximization algorithm is employed for obtaining the maximum likelihood estimates of the model parameters. Through a simulation study we demonstrate that our method can provide reliable estimates of the model parameters when the sample size is close to 500. Implementation of our method to data from a pedigree of 491 Hutterites evaluated for Type 2 diabetes (T2D) reveal evidence of a strong genetic component to T2D risk, particularly for younger and leaner cases.

Extended Bayesian model averaging in generalized linear mixed models applied to schizophrenia family data

The study of disease etiology and the search for susceptible genes of schizophrenia have attracted scientists' attention for decades. Many findings however are inconsistent, possibly due to the higher order interactions involving multi-dimensional genetic and environmental factors or due to the commingling of different ethnic groups. Several studies applied generalized linear mixed models (GLMMs) with family data to identify the genetic contribution to, and environmental influence on, schizophrenia, and to clarify the existence and sources of familial aggregation. Based on an extended Bayesian model averaging (EBMA) procedure, here we estimate the gene-gene (GG) and gene-environment (GE) interactions, and heritability of schizophrenia via variance components of random-effects in GLMMs. Our proposal takes into account the uncertainty in covariates and in genetic model structures, where each competing model includes environmental and genetic covariates, and GE and GG interactions. Simulation studies are conducted to compare the performance of the EBMA approach, permutation test procedure and GEE method. We also illustrate this approach with data from singleton and multiplex schizophrenia families. The results indicate that EBMA is a flexible and stable tool in exploring true candidate genes, and GE and GG interactions, after adjusting for explanatory variables and correlation structures within family members.

Fitting ACE structural equation models to case-control family data

Investigators interested in whether a disease aggregates in families often collect case-control family data, which consist of disease status and covariate information for members of families selected via case or control probands. Here, we focus on the use of case-control family data to investigate the relative contributions to the disease of additive genetic effects (A), shared family environment (C), and unique environment (E). We describe an ACE model for binary family data; this structural equation model, which has been described previously, combines a general-family extension of the classic ACE twin model with a (possibly covariate-specific) liability-threshold model for binary outcomes. We then introduce our contribution, a likelihood-based approach to fitting the model to singly ascertained case-control family data. The approach, which involves conditioning on the proband's disease status and also setting prevalence equal to a prespecified value that can be estimated from the data, makes it possible to obtain valid estimates of the A, C, and E variance components from case-control (rather than only from population-based) family data. In fact, simulation experiments suggest that our approach to fitting yields approximately unbiased estimates of the A, C, and E variance components, provided that certain commonly made assumptions hold. Further, when our approach is used to fit the ACE model to Austrian case-control family data on depression, the resulting estimate of heritability is very similar to those from previous analyses of twin data.

Matched ascertainment of informative families for complex genetic modelling

Family data are used extensively in quantitative genetic studies to disentangle the genetic and environmental contributions to various diseases. Many family studies based their analysis on population-based registers containing a large number of individuals composed of small family units. For binary trait analyses, exact marginal likelihood is a common approach, but, due to the computational demand of the enormous data sets, it allows only a limited number of effects in the model. This makes it particularly difficult to perform joint estimation of variance components for a binary trait and the potential confounders. We have developed a data-reduction method of ascertaining informative families from population-based family registers. We propose a scheme where the ascertained families match the full cohort with respect to some relevant statistics, such as the risk to relatives of an affected individual. The ascertainment-adjusted analysis, which we implement using a pseudo-likelihood approach, is shown to be efficient relative to the analysis of the whole cohort and robust to mis-specification of the random effect distribution.

Genetic heterogeneity of residual variance - estimation of variance components using double hierarchical generalized linear models

Background

The sensitivity to microenvironmental changes varies among animals and may be under genetic control. It is essential to take this element into account when aiming at breeding robust farm animals. Here, linear mixed models with genetic effects in the residual variance part of the model can be used. Such models have previously been fitted using EM and MCMC algorithms.

Results

We propose the use of double hierarchical generalized linear models (DHGLM), where the squared residuals are assumed to be gamma distributed and the residual variance is fitted using a generalized linear model. The algorithm iterates between two sets of mixed model equations, one on the level of observations and one on the level of variances. The method was validated using simulations and also by re-analyzing a data set on pig litter size that was previously analyzed using a Bayesian approach. The pig litter size data contained 10,060 records from 4,149 sows. The DHGLM was implemented using the ASReml software and the algorithm converged within three minutes on a Linux server. The estimates were similar to those previously obtained using Bayesian methodology, especially the variance components in the residual variance part of the model.

Conclusions

We have shown that variance components in the residual variance part of a linear mixed model can be estimated using a DHGLM approach. The method enables analyses of animal models with large numbers of observations. An important future development of the DHGLM methodology is to include the genetic correlation between the random effects in the mean and residual variance parts of the model as a parameter of the DHGLM.

How many genetic variants remain to be discovered?

A great majority of genetic markers discovered in recent genome-wide association studies have small effect sizes, and they explain only a small fraction of the genetic contribution to the diseases. How many more variants can we expect to discover and what study sizes are needed? We derive the connection between the cumulative risk of the SNP variants to the latent genetic risk model and heritability of the disease. We determine the sample size required for case-control studies in order to achieve a certain expected number of discoveries in a collection of most significant SNPs. Assuming similar allele frequencies and effect sizes of the currently validated SNPs, complex phenotypes such as type-2 diabetes would need approximately 800 variants to explain its 40% heritability. Much smaller numbers of variants are needed if we assume rare-variants but higher penetrance models. We estimate that up to 50,000 cases and an equal number of controls are needed to discover 800 common low-penetrant variants among the top 5000 SNPs. Under common and rare low-penetrance models, the very large studies required to discover the numerous variants are probably at the limit of practical feasibility. Under rare-variant with medium- to high-penetrance models (odds-ratios between 1.6 and 4.0), studies comparable in size to many existing studies are adequate provided the genotyping technology can interrogate more and rarer variants.

Approaches for unraveling the joint genetic determinants of schizophrenia and bipolar disorder

Since Emil Kraepelin proposed in 1919 that dementia praecox (schizophrenia) be differentiated from manic depression (bipolar disorder), the concept of nosological dichotomy has greatly influenced the diagnosis, treatment, and research of pathogenesis of these 2 disorders. However, this concept has recently been challenged by increasing evidence showing biological overlap between schizophrenia and bipolar disorder. This article reviews some of the previous evidence for phenomenological and molecular overlaps between these 2 disorders. We then discuss approaches for examining shared etiological mechanisms with a concentration on genetic factors. We have put a particular emphasis on incorporating the concept of endophenotypes in research of shared genetic liability for these 2 disorders.

Covariance component models for multivariate binary traits in family data analysis

For family studies, there is now an established analytical framework for binary-trait outcomes within the generalized linear mixed models (GLMMs). However, the corresponding analysis of multivariate binary-trait (MBT) outcomes is still limited. Certain diseases, such as schizophrenia and bipolar disorder, have similarities in epidemiological features, risk factor patterns and intermediate phenotypes. To have a better etiological understanding, it is important to investigate the common genetic and environmental factors driving the comorbidity of the diseases. In this paper, we develop a suitable GLMM for MBT outcomes from extended families, such as nuclear, paternal- and maternal-halfsib families. We motivate our problem with real questions from psychiatric epidemiology and demonstrate how different substantive issues of comorbidity between two diseases can be put into the analytical framework.

Score Test for Linkage in Generalized Linear Models

We derive a test for linkage in a Generalized Linear Mixed Model (GLMM) framework which provides a natural adjustment for marginal covariate effects. The method boils down to the score test of a quasi-likelihood derived from the GLMM, it is computationally inexpensive and can be applied to arbitrary pedigrees. In particular, for binary traits, relative pairs of different nature (affected and discordant) and individuals with different covariate values can be naturally combined in a single test. The model introduced could explain a number of situations usually described as gene by covariate interaction phenomena, and offers substantial gains in efficiency compared to methods classically used in those instances.