Epigenetics,heritability and longitudinal analysis

Background

Longitudinal data and repeated measurements in epigenome-wide association studies (EWAS) provide a rich resource for understanding epigenetics. We summarize 7 analytical approaches to the GAW20 data sets that addressed challenges and potential applications of phenotypic and epigenetic data. All contributions used the GAW20 real data set and employed either linear mixed effect (LME) models or marginal models through generalized estimating equations (GEE). These contributions were subdivided into 3 categories: (a) quality control (QC) methods for DNA methylation data; (b) heritability estimates pretreatment and posttreatment with fenofibrate; and (c) impact of drug response pretreatment and posttreatment with fenofibrate on DNA methylation and blood lipids.

Results

Two contributions addressed QC and identified large statistical differences with pretreatment and posttreatment DNA methylation, possibly a result of batch effects. Two contributions compared epigenome-wide heritability estimates pretreatment and posttreatment, with one employing a Bayesian LME and the other using a variance-component LME. Density curves comparing these studies indicated these heritability estimates were similar. Another contribution used a variance-component LME to depict the proportion of heritability resulting from a genetic and shared environment. By including environmental exposures as random effects, the authors found heritability estimates became more stable but not significantly different. Two contributions investigated treatment response. One estimated drug-associated methylation effects on triglyceride levels as the response, and identified 11 significant cytosine-phosphate-guanine (CpG) sites with or without adjusting for high-density lipoprotein. The second contribution performed weighted gene coexpression network analysis and identified 6 significant modules of at least 30 CpG sites, including 3 modules with topological differences pretreatment and posttreatment.

Conclusions

Four conclusions from this GAW20 working group are: (a) QC measures are an important consideration for EWAS studies that are investigating multiple time points or repeated measurements; (b) application of heritability estimates between time points for individual CpG sites is a useful QC measure for DNA methylation studies; (c) drug intervention demonstrated strong epigenome-wide DNA methylation patterns across the 2 time points; and (d) new statistical methods are required to account for the environmental contributions of DNA methylation across time. These contributions demonstrate numerous opportunities exist for the analysis of longitudinal data in future epigenetic studies.

     

Estimating quantitative genetic parameters in wild populations: a comparison of pedigree and genomic approaches

The estimation of quantitative genetic parameters in wild populations is generally limited by the accuracy and completeness of the available pedigree information. Using relatedness at genomewide markers can potentially remove this limitation and lead to less biased and more precise estimates. We estimated heritability, maternal genetic effects and genetic correlations for body size traits in an unmanaged long‐term study population of Soay sheep on St Kilda using three increasingly complete and accurate estimates of relatedness: (i) Pedigree 1, using observation‐derived maternal links and microsatellite‐derived paternal links; (ii) Pedigree 2, using SNP‐derived assignment of both maternity and paternity; and (iii) whole‐genome relatedness at 37 037 autosomal SNPs. In initial analyses, heritability estimates were strikingly similar for all three methods, while standard errors were systematically lower in analyses based on Pedigree 2 and genomic relatedness. Genetic correlations were generally strong, differed little between the three estimates of relatedness and the standard errors declined only very slightly with improved relatedness information. When partitioning maternal effects into separate genetic and environmental components, maternal genetic effects found in juvenile traits increased substantially across the three relatedness estimates. Heritability declined compared to parallel models where only a maternal environment effect was fitted, suggesting that maternal genetic effects are confounded with direct genetic effects and that more accurate estimates of relatedness were better able to separate maternal genetic effects from direct genetic effects. We found that the heritability captured by SNP markers asymptoted at about half the SNPs available, suggesting that denser marker panels are not necessarily required for precise and unbiased heritability estimates. Finally, we present guidelines for the use of genomic relatedness in future quantitative genetics studies in natural populations.     

Utilizing Propensity Scores to Estimate Causal Treatment Effects with Censored Time-Lagged Data

Observational studies frequently are conducted to compare long-term effects of treatments. Without randomization, patients receiving one treatment are not guaranteed to be prognostically comparable to those receiving another treatment. Furthermore, the response of interest may be right-censored because of incomplete follow-up. Statistical methods that do not account for censoring and confounding may lead to biased estimates. This article presents a method for estimating treatment effects in nonrandomized studies with right-censored responses. We review the assumptions required to estimate average causal effects and derive an estimator for comparing two treatments by applying inverse weights to the complete cases. The weights are determined according to the estimated probability of receiving treatment conditional on covariates and the estimated treatment-specific censoring distribution. By utilizing martingale representations, the estimator is shown to be asymptotically normal and an estimator for the asymptotic variance is derived. Simulation results are presented to evaluate the properties of the estimator. These methods are applied to an observational data set of acute coronary syndrome patients from Duke University Medical Center to estimate the effect of a treatment strategy on the mean 5-year medical cost.     

The heritability of insomnia: A meta-analysis of twin studies

Twin studies of insomnia exhibit heterogeneity in estimates of heritability. This heterogeneity is likely because of sex differences, age of the sample, the reporter and the definition of insomnia. The aim of the present study was to systematically search the literature for twin studies investigating insomnia disorder and insomnia symptoms and to meta-analyse the estimates of heritability derived from these studies to generate an overall estimate of heritability. We further examined whether heritability was moderated by sex, age, reporter and insomnia symptom. A systematic literature search of five online databases was completed on 24 January 2020. Two authors independently screened 5644 abstracts, and 160 complete papers for the inclusion criteria of twin studies from the general population reporting heritability statistics on insomnia or insomnia symptoms, written in English, reporting data from independent studies. We ultimately included 12 papers in the meta-analysis. The meta-analysis focussed on twin intra-class correlations for monozygotic and dizygotic twins. Based on these intra-class correlations, the meta-analytic estimate of heritability was estimated at 40%. Moderator analyses showed stronger heritability in females than males; and for parent-reported insomnia symptoms compared with self-reported insomnia symptoms. There were no other significant moderator effects, although this is likely because of the small number of studies that were comparable across levels of the moderators. Our meta-analysis provides a robust estimate of the heritability of insomnia, which can inform future research aiming to uncover molecular genetic factors involved in insomnia vulnerability.     

Epigenetics,heritability and longitudinal analysis

Background

Longitudinal data and repeated measurements in epigenome-wide association studies (EWAS) provide a rich resource for understanding epigenetics. We summarize 7 analytical approaches to the GAW20 data sets that addressed challenges and potential applications of phenotypic and epigenetic data. All contributions used the GAW20 real data set and employed either linear mixed effect (LME) models or marginal models through generalized estimating equations (GEE). These contributions were subdivided into 3 categories: (a) quality control (QC) methods for DNA methylation data; (b) heritability estimates pretreatment and posttreatment with fenofibrate; and (c) impact of drug response pretreatment and posttreatment with fenofibrate on DNA methylation and blood lipids.

Results

Two contributions addressed QC and identified large statistical differences with pretreatment and posttreatment DNA methylation, possibly a result of batch effects. Two contributions compared epigenome-wide heritability estimates pretreatment and posttreatment, with one employing a Bayesian LME and the other using a variance-component LME. Density curves comparing these studies indicated these heritability estimates were similar. Another contribution used a variance-component LME to depict the proportion of heritability resulting from a genetic and shared environment. By including environmental exposures as random effects, the authors found heritability estimates became more stable but not significantly different. Two contributions investigated treatment response. One estimated drug-associated methylation effects on triglyceride levels as the response, and identified 11 significant cytosine-phosphate-guanine (CpG) sites with or without adjusting for high-density lipoprotein. The second contribution performed weighted gene coexpression network analysis and identified 6 significant modules of at least 30 CpG sites, including 3 modules with topological differences pretreatment and posttreatment.

Conclusions

Four conclusions from this GAW20 working group are: (a) QC measures are an important consideration for EWAS studies that are investigating multiple time points or repeated measurements; (b) application of heritability estimates between time points for individual CpG sites is a useful QC measure for DNA methylation studies; (c) drug intervention demonstrated strong epigenome-wide DNA methylation patterns across the 2 time points; and (d) new statistical methods are required to account for the environmental contributions of DNA methylation across time. These contributions demonstrate numerous opportunities exist for the analysis of longitudinal data in future epigenetic studies.

     

Turning the analysis of obesity–mortality associations upside down: Modeling years of life lost through conditional distributions

Objective:

We demonstrate the utility of parametric survival analysis. The analysis of longevity as a function of risk factors such as body mass index (BMI; kg/m²), activity levels, and dietary factors is a mainstay of obesity research. Modeling survival through hazard functions, relative risks, or odds of dying with methods such as Cox proportional hazards or logistic regression are the most common approaches and have many advantages. However, they also have disadvantages in terms of the ease of interpretability, especially for non‐statisticians; the need for additional data to convert parameter estimates to estimates of years of life lost (YLL); debates about the appropriate time scale in the model; and an inability to estimate median survival time when the censoring rate is too high.

Design and Methods:

We will conduct parametric survival analyses with multiple distributions, including distributions that are known to be poor fits (Gaussian), as well as a newly discovered “Compressed Gaussian”'' distribution.

Results:

Parametric survival analysis models were able to accurately estimate median survival times in a population‐based data set of 15,703 individuals, even for distributions that were not good fits and the censoring rate was high, due to the central limit theorem.

Conclusions:

Parametric survival models are able to provide more direct answers, and in our analysis of an obesity‐related data set, gave consistent YLL estimates regardless of the distribution used. We recommend increased consideration of parametric survival models in chronic disease and risk factor epidemiology.     

Seed size, shape and vertical distribution in the soil: indicators of seed longevity

1. We investigated the vertical distribution of seeds in the soil, using data from nine studies in five European countries. We discovered significant correlations between seed shape and distribution in the soil.
2. The classification of the longevity of seeds of plant species has been improved by the introduction of a 'longevity index', expressing on a continuous scale the most recent information on seed longevity represented as the proportion of non-transient seed bank records in the database of Thompson et al. (1997 ). Remarkably, no difference in seed longevity was found if the index was based on direct observations only when compared with the index based on the complete data set where indirect, 'depth-derived' observations were included.
3. Seed longevity was best estimated using a multiple regression model with an integrated measure of seed size and shape and depth distribution of seeds.
4. The shape of seeds, known to be a consistent character of species, was shown to be constant within species, whereas depth distribution of seeds was highly variable among sites. This is consistent with the variability of seed longevity found in published seed bank data.     

Phenotypic and genetic parameters compared during repeated measures of longissimus muscle area and subcutaneous fat thickness in Nelore cattle

Real-time ultrasound is currently used for in vivo carcass evaluation of beef cattle. We estimated heritability and repeatability coefficients for ultrasound-measured carcass traits in Nelore cattle. We measured longissimus muscle area, backfat thickness, and rump fat thickness in male and female animals ranging in age from 10 to 26 months. The variance components were estimated by single-trait analysis using the derivative-free restricted maximum likelihood method, under an animal model. The complete data file included 3077 records of 1172 animals born between 2003 and 2008. Two analyses were performed using a repeatability model: a) all records of longissimus muscle area, backfat thickness, and rump fat thickness of animals aged 10 to 26 months, and b) considering two age periods (11 to 17 and 18 to 24 months). The heritability estimates ranged from 0.33 to 0.46 for longissimus muscle area, from 0.20 to 0.26 for backfat, and from 0.26 to 0.29 for rump fat, demonstrating that direct selection for these traits can provide genetic gain. The repeatability estimates were moderate, ranging from 0.42 to 0.73. The highest repeatability estimates were obtained for longissimus muscle area in both the first (0.70) and second (0.73) analyses. The repeatability estimates suggest that ultrasound measures are precise; higher precision was obtained for longissimus muscle area than for subcutaneous fat thickness. The latter could be obtained during periods of greater feed availability to increase precision.     

Effects of Multiple Retrovirus Insertions on Quantitative Traits of Mice

To assess the potential to generate quantitative genetic variation by insertional mutagenesis in a vertebrate, lines of mice in which many provirus vector inserts segregated at a low initial frequency on an inbred background (insert lines) were subjected to divergent artificial selection on body weight at 6 weeks and responses and heritability estimates compared to control lines lacking inserts. Heritability estimates were more than 1.5 times greater in the insert lines than in the controls, but because the phenotypic variance was substantially higher in the insert lines the genetic variance was about 3 times greater. Realized heritability estimates tended to be lower than heritabilities estimated by an animal model which utilizes information in covariances between all relatives in the data set. A surprisingly large response to selection occurred in the inbred control line. Insert lines were about 20% less fertile than controls. Division of the selection lines into inbred sublines in the later generations of the experiment revealed substantially greater variation among sublines of the insert lines than among the controls. Heritabilities were similar to typical estimates for the trait in outbred populations. In conclusion, there was clear evidence of extra variation deriving from inserts, which has yet to be attributed to individual genes.     

Identity-by-descent-based heritability analysis in the Northern Finland Birth Cohort

For most complex traits, only a small proportion of heritability is explained by statistically significant associations from genome-wide association studies (GWAS). In order to determine how much heritability can potentially be explained through larger GWAS, several different approaches for estimating total narrow-sense heritability from GWAS data have recently been proposed. These methods include variance components with relatedness estimates from allele-sharing, variance components with relatedness estimates from identity-by-descent (IBD) segments, and regression of phenotypic correlation on relatedness estimates from IBD segments. These methods have not previously been compared on real or simulated data. We analyze the narrow-sense heritability of nine metabolic traits in the Northern Finland Birth Cohort (NFBC) using these methods. We find substantial estimated heritability for several traits, including LDL cholesterol (54 % heritability), HDL cholesterol (46 % heritability), and fasting glucose levels (39 % heritability). Estimates of heritability from the regression-based approach are much lower than variance component estimates in these data, which may be due to the presence of strong population structure. We also investigate the accuracy of the competing approaches using simulated phenotypes based on genotype data from the NFBC. The simulation results substantiate the downward bias of the regression-based approach in the presence of population structure.     

Estimation of genetic parameters for partial egg production periods by means of random regression models

We estimated genetic parameters for egg production in different periods by means of random regression models, aiming at selection based on partial egg production from a generation of layers. The production was evaluated for each individual by recording the number of eggs produced from 20 to 70 weeks of age, with partial records taken every three weeks for a total of 17 periods. The covariance functions were estimated with a random regression model by the restricted maximum likelihood method. A model composed of third-order polynomials for the additive effect, ninth-order polynomials for the permanent environment, and a residual variance structure with five distinct classes, was found to be most suitable for adjusting the egg production data for laying hens. The heritability estimates varied from 0.04 to 0.14. The genetic correlations were all positive, varying from 0.10 to 0.99. Selection applied in partial egg production periods will result in greater genetic profit for the adjacent periods. However, as the distance in time between periods increases, selection becomes less efficient. Selection based on the second period (23 to 25 weeks of age), where greater heritability was estimated, would note benefit the final egg-laying cycle periods.     

Heritability estimates from genomewide relatedness matrices in wild populations: Application to a passerine,using a small sample size

Genomic developments have empowered the investigation of heritability in wild populations directly from genomewide relatedness matrices (GRM). Such GRM‐based approaches can in particular be used to improve or substitute approaches based on social pedigree (PED‐social). However, measuring heritability from GRM in the wild has not been widely applied yet, especially using small samples and in nonmodel species. Here, we estimated heritability for four quantitative traits (tarsus length, wing length, bill length and body mass), using PED‐social, a pedigree corrected by genetic data (PED‐corrected) and a GRM from a small sample (n = 494) of blue tits from natural populations in Corsica genotyped at nearly 50,000 filtered SNPs derived from RAD‐seq. We also measured genetic correlations among traits, and we performed chromosome partitioning. Heritability estimates were slightly higher when using GRM compared to PED‐social, and PED‐corrected yielded intermediate values, suggesting a minor underestimation of heritability in PED‐social due to incorrect pedigree links, including extra‐pair paternity, and to lower information content than the GRM. Genetic correlations among traits were similar between PED‐social and GRM but credible intervals were very large in both cases, suggesting a lack of power for this small data set. Although a positive linear relationship was found between the number of genes per chromosome and the chromosome heritability for tarsus length, chromosome partitioning similarly showed a lack of power for the three other traits. We discuss the usefulness and limitations of the quantitative genetic inferences based on genomic data in small samples from wild populations.     

Genetic relationship of discrete-time survival with fertility and production in dairy cattle using bivariate models

Bivariate analyses of functional longevity in dairy cattle measured as survival to next lactation (SURV) with milk yield and fertility traits were carried out. A sequential threshold-linear censored model was implemented for the analyses of SURV. Records on 96 642 lactations from 41 170 cows were used to estimate genetic parameters, using animal models, for longevity, 305 d-standardized milk production (MY305), days open (DO) and number of inseminations to conception (INS) in the Spanish Holstein population; 31% and 30% of lactations were censored for DO and INS, respectively. Heritability estimates for SURV and MY305 were 0.11 and 0.27 respectively; while heritability estimates for fertility traits were lower (0.07 for DO and 0.03 for INS). Antagonist genetic correlations were estimated between SURV and fertility (-0.78 and -0.54 for DO and INS, respectively) or production (-0.53 for MY305), suggesting reduced functional longevity with impaired fertility and increased milk production. Longer days open seems to affect survival more than increased INS. Also, high productive cows were more problematic, less functional and more liable to being culled. The results suggest that the sequential threshold model is a method that might be considered at evaluating genetic relationship between discrete-time survival and other traits, due to its flexibility.     

Near real-time surveillance of the SARS-CoV-2 epidemic with incomplete data

When responding to infectious disease outbreaks, rapid and accurate estimation of the epidemic trajectory is critical. However, two common data collection problems affect the reliability of the epidemiological data in real time: missing information on the time of first symptoms, and retrospective revision of historical information, including right censoring. Here, we propose an approach to construct epidemic curves in near real time that addresses these two challenges by 1) imputation of dates of symptom onset for reported cases using a dynamically-estimated “backward” reporting delay conditional distribution, and 2) adjustment for right censoring using the NobBS software package to nowcast cases by date of symptom onset. This process allows us to obtain an approximation of the time-varying reproduction number (R_t) in real time. We apply this approach to characterize the early SARS-CoV-2 outbreak in two Spanish regions between March and April 2020. We evaluate how these real-time estimates compare with more complete epidemiological data that became available later. We explore the impact of the different assumptions on the estimates, and compare our estimates with those obtained from commonly used surveillance approaches. Our framework can help improve accuracy, quantify uncertainty, and evaluate frequently unstated assumptions when recovering the epidemic curves from limited data obtained from public health systems in other locations.     

NATURAL HERITABILITIES: CAN THEY BE RELIABLY ESTIMATED IN THE LABORATORY?

The validity of the assumption, that laboratory estimates of heritabilities will tend to overestimate natural heritabilities, due to a reduction in environmental variability and thus the phenotypic variance of traits, is examined. One hundred sixty-five field estimates of narrow sense heritabilities derived from the literature are compared with 189 estimates from laboratory studies on wild, outbred animal populations derived from the data set of Mousseau and Roff. The results indicate that 84% of field heritabilities are significantly different from zero and that for morphological, behavioral, and life-history traits there are no significant differences between laboratory and field estimates of heritability. Unexpectedly, mean heritabilities for morphological and life-history traits are actually higher in the field than in the lab. Twenty-two cases were found for which both laboratory and natural heritabilities had been estimated on the same traits. For this subset of the data, laboratory heritabilities tended to be higher than field estimates, but the difference was not significant. Also, the correlation between lab and field estimates was high (r = 0.6, P < 0.001), and the regression slope did not differ significantly from one. The major implications of this study are that laboratory estimates of heritability should generally provide reasonable estimations of both the magnitude and the significance of heritabilities in nature.     

The accuracy of a heritability estimator using molecular information

The heritability of a quantitative trait is a key parameter to quantify the genetic variation present in a population. Although estimates of heritability require accurate information on the genetic relationship among individuals, pedigree data is generally lacking in natural populations. Nowadays, the increasing availability of DNA markers is making possible the estimation of coancestries from neutral molecular information. In 1996, K. Ritland developed an approach to estimate heritability from the regression of the phenotypic similarity on the marker-based coancestry. We carried out simulations to analyze the accuracy of the estimates of heritability obtained by this method using information from a variable number of neutral codominant markers. Because the main application of the estimator is on populations with no family structure, such as natural populations, its accuracy was tested under this scenario. However, the method was also investigated under other scenarios, in order to test the influence of different factors (family structure, assortative mating and phenotypic selection) on the precision. Our results suggest that the main factor causing a directional bias in the estimated heritability is the presence of phenotypic selection, and that very noisy estimates are obtained in the absence of a familiar structure and for small population sizes. The estimated heritabilities from marker-based coancestries showed lower accuracy than the estimated heritabilities from genealogical coancestries. However, a large amount of bias occurred even in the most favourable situation where genealogical coancestries are known. The results also indicate that the molecular markers are more suitable to infer coancestry than inbreeding.     

Heritability of resting metabolic rate in a wild population of blue tits

We report the first study with the aim to estimate heritability in a wild population, a nest box breeding population of blue tits. We estimated heritability as well as genetic and phenotypic correlations of resting metabolic rate (RMR), body mass and tarsus length with an animal model based on data from a split cross‐fostering experiment with brood size manipulations. RMR and body mass, but not tarsus length, showed significant levels of explained variation but for different underlying reasons. In body mass, the contribution to the explained variation is mainly because of a strong brood effect, while in RMR it is mainly because of a high heritability. The additive variance in RMR was significant and the heritability was estimated to 0.59. The estimates of heritability of body mass (0.08) and tarsus length (0.00) were both low and based on nonsignificant additive variances. Thus, given the low heritability (and additive variances) in body mass and tarsus length the potential for direct selection on RMR independent of the two traits is high in this population. However, the strong phenotypic correlation between RMR and mass (0.643 ± 0.079) was partly accounted for by a potentially strong, although highly uncertain, genetic correlation (1.178 ± 0.456) between the two traits. This indicates that the additive variance of body mass, although low, might still somewhat constrain the independent evolvability of RMR.     

Bias correction in the hierarchical likelihood approach to the analysis of multivariate survival data

Frailty models are useful for measuring unobserved heterogeneity in risk of failures across clusters, providing cluster-specific risk prediction. In a frailty model, the latent frailties shared by members within a cluster are assumed to act multiplicatively on the hazard function. In order to obtain parameter and frailty variate estimates, we consider the hierarchical likelihood (H-likelihood) approach (Ha, Lee and Song, 2001. Hierarchical-likelihood approach for frailty models. Biometrika 88, 233-243) in which the latent frailties are treated as "parameters" and estimated jointly with other parameters of interest. We find that the H-likelihood estimators perform well when the censoring rate is low, however, they are substantially biased when the censoring rate is moderate to high. In this paper, we propose a simple and easy-to-implement bias correction method for the H-likelihood estimators under a shared frailty model. We also extend the method to a multivariate frailty model, which incorporates complex dependence structure within clusters. We conduct an extensive simulation study and show that the proposed approach performs very well for censoring rates as high as 80%. We also illustrate the method with a breast cancer data set. Since the H-likelihood is the same as the penalized likelihood function, the proposed bias correction method is also applicable to the penalized likelihood estimators.     

The heritability of human longevity: A population-based study of 2872 Danish twin pairs born 1870–1900

The aim of this study was to explore, in a large and non-censored twin cohort, the nature (i.e., additive versus non-additive) and magnitude (i.e., heritability) of genetic influences on inter-individual differences in human longevity. The sample comprised all identified and traced non-emigrant like-sex twin pairs born in Denmark during the period 1870–1900 with a zygosity diagnosis and both members of the pairs surviving the age of 15 years. A total of 2872 pairs were included. Age at death was obtained from the Danish Central Person Register, the Danish Cause-of-Death Register and various other registers. The sample was almost non-censored on the date of the last follow-up (May 1, 1994), all but 0.6% had died, leaving a total of 2872 pairs for analysis. Proportions of variance attributable to genetic and environmental factors were assessed from variance-covariance matrices using the structural equation model approach. The most parsimonious explanation of the data was provided by a model that included genetic dominance (non-additive genetic effects caused by interaction within gene loci) and non-shared environmental factors (environmental factors that are individual-specific and not shared in a family). The heritability of longevity was estimated to be 0.26 for males and 0.23 for females. The small sex-difference was caused by a greater impact of non-shared environmental factors in the females. Heritability was found to be constant over the three 10-year birth cohorts included. Thus, longevity seems to be only moderately heritable. The nature of genetic influences on longevity is probably non-additive and environmental influences non-shared. There is no evidence for an impact of shared (family) environment.