Biometrical modelling in genetics: are complex traits too complex?

Disentangling Multiple Sclerosis heterogeneity in the French territory among genetic and environmental factors via Bayesian heritability analysis

BACKGROUND

This study aimed to investigate the factors contributing to the variability of Multiple Sclerosis (MS) among individuals born and residing in France. Geographical variation in MS prevalence was observed in France, but the role of genetic and environmental factors in explaining this heterogeneity has not been yet elucidated.

METHODS

We employed a heritability analysis on a cohort of 403 trios with an MS-affected proband in the French population. This sample was retrieved from REFGENSEP register of MS cases collected in 23 French hospital centers from 1992 to 2017. Our objective was to quantify the proportion of MS liability variability explained by genetic variability, sex, shared environment effects, region of birth and year of birth. We further considered gene x environment (GxE) interaction effects between genetic variability and region of birth. We have implemented a Bayesian liability threshold model to obtain posterior distributions for the parameters of interest adjusting for ascertainment bias.

RESULTS

Our analysis revealed that GxE interaction effects between genetic variability and region of birth represent the primary significant explanatory factor for MS liability variability in French individuals (29 % [95 %CI: 5 %; 53 %]), suggesting that additive genetic effects are modified by environmental factors associated to the region of birth. The individual contributions of genetic variability and region of birth explained, respectively, ≈15 % and ≈16 % of MS variability, highlighting a significantly higher MS liability in individuals born in the Northern regions compared to the Southern region. Overall, the joint contribution of genetic variability, region of birth, and their interaction was then estimated to explain 65 % [95 %CI: 35 %; 92 %] of MS liability variability. The remaining proportion of MS variability is attributed to environmental exposures associated with the year of birth, shared within the same household, and specific to individuals.

CONCLUSION

Overall, our analysis highlighted the interaction between genetic variability and environmental exposures linked to the region of birth as the main factor explaining MS variability within individuals born and residing in France. Among the environmental exposures prevalent in the Northern regions, and potentially interacting with genetic variability, lower vitamin D levels due to reduced sun exposure, higher obesity prevalence and higher pollution levels represent the main risk factors in influencing MS risk. These findings emphasize the importance of accounting for environmental factors linked to geographical location in the investigation of MS risk factors, as well as to further explore the influence of GxE interactions in modifying genetic risk.

Multiple Sclerosis Heritability Estimation on Sardinian Ascertained Extended Families Using Bayesian Liability Threshold Model

Heritability studies represent an important tool to investigate the main sources of variability for complex diseases, whose etiology involves both genetics and environmental factors. In this paper, we aimed to estimate multiple sclerosis (MS) narrow-sense heritability (h2), on a liability scale, using extended families ascertained from affected probands sampled in the Sardinian province of Nuoro, Italy. We also investigated the sources of MS liability variability among shared environment effects, sex, and categorized year of birth (<1946, ≥1946). The latter can be considered a proxy for different early environmental exposures. To this aim, we implemented a Bayesian liability threshold model to obtain posterior distributions for the parameters of interest adjusting for ascertainment bias. Our analysis highlighted categorized year of birth as the main explanatory factor, explaining ~70% of MS liability variability (median value = 0.69, 95% CI: 0.64, 0.73), while h2 resulted near to 0% (median value = 0.03, 95% CI: 0.00, 0.09). By performing a year of birth-stratified analysis, we found a high h2 only in individuals born on/after 1946 (median value = 0.82, 95% CI: 0.68, 0.93), meaning that the genetic variability acquired a high explanatory role only when focusing on this subpopulation. Overall, the results obtained highlighted early environmental exposures, in the Sardinian population, as a meaningful factor involved in MS to be further investigated.

Heritability curves: A local measure of heritability in family models

Classical heritability models for family data split the phenotype variance into genetic and environmental components. For instance, the ACE model in twin studies assumes the phenotype variance decomposes as a²  + c²  + e² , representing (additive) genetic effects, common (shared) environment, and residual environment, respectively. However, for some phenotypes it is biologically plausible that the genetic and environmental components may vary over the range of the phenotype. For instance, very large or small values of the phenotype may be caused by "sporadic" environmental factors, whereas the mid-range phenotype variation may be more under the control of common genetic factors. This article introduces a "local" measure of heritability, where the genetic and environmental components are allowed to depend on the value of the phenotype itself. Our starting point is a general formula for local correlation between two random variables. For estimation purposes, we use a multivariate Gaussian mixture, which is able to capture nonlinear dependence and respects certain distributional constraints. We derive an analytical expression for the associated correlation curve, and show how to decompose the correlation curve into genetic and environmental parts, for instance, a² (y) + c² (y) + e² (y) for the ACE model, where we estimate the components as functions of the phenotype y. Furthermore, our model allows switching, for instance, from the ACE model to the ADE model within the range of the same phenotype. When applied to birth weight (BW) data on Norwegian mother-father-child trios, we conclude from the model that low and high BW are less heritable traits than medium BW. We also demonstrate switching between the ACE and ADE model when studying body mass index in adult monozygotic and dizygotic twins.

Human Birth Weight and Reproductive Immunology: Testing for Interactions between Maternal and Offspring KIR and HLA-C Genes

BACKGROUND/AIMS

Maternal and offspring cell contact at the site of placentation presents a plausible setting for maternal-fetal genotype (MFG) interactions affecting fetal growth. We test hypotheses regarding killer cell immunoglobulin-like receptor (KIR) and HLA-C MFG effects on human birth weight by extending the quantitative MFG (QMFG) test.

METHODS

Until recently, association testing for MFG interactions had limited applications. To improve the ability to test for these interactions, we developed the extended QMFG test, a linear mixed-effect model that can use multi-locus genotype data from families.

RESULTS

We demonstrate the extended QMFG test's statistical properties. We also show that if an offspring-only model is fit when MFG effects exist, associations can be missed or misattributed. Furthermore, imprecisely modeling the effects of both KIR and HLA-C could result in a failure to replicate if these loci's allele frequencies differ among populations. To further illustrate the extended QMFG test's advantages, we apply the extended QMFG test to a UK cohort study and the Norwegian Mother and Child Cohort (MoBa) study.

CONCLUSION

We find a significant KIR-HLA-C interaction effect on birth weight. More generally, the QMFG test can detect genetic associations that may be missed by standard genome-wide association studies for quantitative traits.

A hierarchical frailty model applied to two-generation melanoma data

We present a hierarchical frailty model based on distributions derived from non-negative Lévy processes. The model may be applied to data with several levels of dependence, such as family data or other general clusters, and is an alternative to additive frailty models. We present several parametric examples of the model, and properties such as expected values, variance and covariance. The model is applied to a case-cohort sample of age at onset for melanoma from the Swedish Multi-Generation Register, organized in nuclear families of parents and one or two children. We compare the genetic component of the total frailty variance to the common environmental term, and estimate the effect of birth cohort and gender.

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.