Validation of an approximate approach to compute genetic correlations between longevity and linear traits

The estimation of genetic correlations between a nonlinear trait such as longevity and linear traits is computationally difficult on large datasets. A two-step approach was proposed and was checked via simulation. First, univariate analyses were performed to get genetic variance estimates and to compute pseudo-records and their associated weights. These pseudo-records were virtual performances free of all environmental effects that can be used in a BLUP animal model, leading to the same breeding values as in the (possibly nonlinear) initial analyses. By combining these pseudo-records in a multiple trait model and fixing the genetic and residual variances to their values computed during the first step, we obtained correlation estimates by AI-REML and approximate MT-BLUP predicted breeding values that blend direct and indirect information on longevity. Mean genetic correlations and reliabilities obtained on simulated data confirmed the suitability of this approach in a wide range of situations. When nonzero residual correlations exist between traits, a sire model gave nearly unbiased estimates of genetic correlations, while the animal model estimates were biased upwards. Finally, when an incorrect genetic trend was simulated to lead to biased pseudo-records, a joint analysis including a time effect could adequately correct for this bias.     

Effects of censoring on parameter estimates and power in genetic modeling.

Genetic and environmental influences on variance in phenotypic traits may be estimated with normal theory Maximum Likelihood (ML). However, when the assumption of multivariate normality is not met, this method may result in biased parameter estimates and incorrect likelihood ratio tests. We simulated multivariate normal distributed twin data under the assumption of three different genetic models. Genetic model fitting was performed in six data sets: multivariate normal data, discrete uncensored data, censored data, square root transformed censored data, normal scores of censored data, and categorical data. Estimates were obtained with normal theory ML (data sets 1-5) and with categorical data analysis (data set 6). Statistical power was examined by fitting reduced models to the data. When fitting an ACE model to censored data, an unbiased estimate of the additive genetic effect was obtained. However, the common environmental effect was underestimated and the unique environmental effect was overestimated. Transformations did not remove this bias. When fitting an ADE model, the additive genetic effect was underestimated while the dominant and unique environmental effects were overestimated. In all models, the correct parameter estimates were recovered with categorical data analysis. However, with categorical data analysis, the statistical power decreased. The analysis of L-shaped distributed data with normal theory ML results in biased parameter estimates. Unbiased parameter estimates are obtained with categorical data analysis, but the power decreases.     

Chorion type as a possible influence on the results and interpretation of twin study data.

The estimation of genetic effects from twin studies usually relies upon the equal environment assumption--that monozygous (MZ) and dizygous (DZ) twin pairs experience equal similarity of their environments from prenatal experiences through adulthood. However, the sharing of a chorion may make a subset of identical twins more similar, or in some cases, more different, than twins that do not share a chorion. Recent studies suggest monochorionic MZ twins resemble one another more than dichorionic MZ twins in cognitive abilities, personality, and risk for psychiatric disorder. To the extent that prenatal environment affects these characteristics, the traditional twin method will yield biased estimates of genetic and environmental influences. We develop models for quantifying this bias and estimating the influence of chorion type on estimates of heritability.     

Implications of absence of measurement invariance for detecting sex limitation and genotype by environment interaction.

Using univariate sum scores in genetic studies of twin data is common practice. This practice precludes an investigation of the measurement model relating the individual items to an underlying factor. Absence of measurement invariance across a grouping variable such as gender or environmental exposure refers to group differences with respect to the measurement model. It is shown that a decomposition of a sum score into genetic and environmental variance components leads to path coefficients of the additive genetic factor that are biased differentially across groups if individual items are non-invariant. The arising group differences in path coefficients are identical to what is known as "scalar sex limitation" when gender is the grouping variable, or as "gene by environment interaction" when environmental exposure is the grouping variable. In both cases the interpretation would be in terms of a group-specific effect size of the genetic factor. This interpretation may be incorrect if individual items are non-invariant.     

Effects of data structure on the estimation of covariance functions to describe genotype by environment interactions in a reaction norm model

Covariance functions have been proposed to predict breeding values and genetic (co)variances as a function of phenotypic within herd-year averages (environmental parameters) to include genotype by environment interaction. The objective of this paper was to investigate the influence of definition of environmental parameters and non-random use of sires on expected breeding values and estimated genetic variances across environments. Breeding values were simulated as a linear function of simulated herd effects. The definition of environmental parameters hardly influenced the results. In situations with random use of sires, estimated genetic correlations between the trait expressed in different environments were 0.93, 0.93 and 0.97 while simulated at 0.89 and estimated genetic variances deviated up to 30% from the simulated values. Non random use of sires, poor genetic connectedness and small herd size had a large impact on the estimated covariance functions, expected breeding values and calculated environmental parameters. Estimated genetic correlations between a trait expressed in different environments were biased upwards and breeding values were more biased when genetic connectedness became poorer and herd composition more diverse. The best possible solution at this stage is to use environmental parameters combining large numbers of animals per herd, while losing some information on genotype by environment interaction in the data.     

A twin study of the etiology of prolonged fatigue and immune activation.

Risk factors to prolonged fatigue syndromes (PFS) are controversial. Pre-morbid and/or current psychiatric disturbance, and/or disturbed cell-mediated immunity (CMI), have been proposed as etiologic factors. Self-report measures of fatigue and psychologic distress and three in vitro measures of CMI were collected from 124 twin pairs. Crosstwin-crosstrait correlations were estimated for the complete monozygotic (MZ; 79 pairs) and dizygotic (DZ; 45 pairs) twin groups. Multivariate genetic and environmental models were fitted to explore the patterns of covariation between etiologic factors. For fatigue, the MZ correlation was more than double the DZ correlation (0.49 versus 0.16) indicating strong genetic control of familial aggregation. By contrast, for in vitro immune activation measures MZ and DZ correlations were similar (0.49-0.69 versus 0.42-0.53) indicating the etiologic role of shared environments. As small univariate associations were noted between prolonged fatigue and the in vitro immune measures (r = -0.07 to -0.12), multivariate models were fitted. Relevant etiologic factors included: a common genetic factor accounting for 48% of the variance in fatigue which also accounted for 4%, 6% and 8% reductions in immune activation; specific genetic factors for each of the in vitro immune measures; a shared environment factor influencing the three immune activation measures; and, most interestingly, unique environmental influences which increased fatigue but also increased markers of immune activation. PFS that are associated with in vitro measures of immune activation are most likely to be the consequence of current environmental rather than genetic factors. Such environmental factors could include physical agents such as infection and/or psychologic stress.     

Local estimation of age-dependent variance components from longitudinal twin data

In the study of longitudinal twin and family data, interest is often in the covariance structure of the data and the decomposition of this covariance structure into genetic and environmental components rather than in estimating the mean function. Various parametric models for covariance structures have been proposed but, e.g., in studies of children where growth spurts occur at various ages, it is difficult to a priori determine an appropriate parametric model for the covariance structure. In particular, there is a general lack of the visualization procedures, such as lowess, that are invaluable in the initial stages of constructing a parametric model for a mean function. Here we use kernel smoothing to modify a cross-sectional approach based on the sample covariance matrices to obtain smoothed estimates of the genetic and environmental variances and correlations for longitudinal twin data. The methods are proposed to be exploratory as an aid to parametric modeling rather than inferential, although approximate asymptotic standard errors are derived in the Appendix.     

Comparative genetic variance and heritability of dental occlusal variables in U.S. and Northwest Indian twins

Genetic variance analysis of 15 dental occlusal and arch variables is based on cross-cultural comparison of twin variances (U.S. Whites and Northwest Indian Punjabis). Both samples exhibit high genetic versus environmental partition of variance. However, monozygotes and dizygotes have unequal variance, which invalidates conventional genetic variance ratios. The pattern of environmental biases on the zygosities is quite different in the two groups. Revised estimates that acknowledge zygosity heterogeneity (hence unequal environmental influences) are generally much lower for occlusal traits, whereas arch size measurements are unaffected.     

The epidemiology and genetics of smoking initiation and persistence: crosscultural comparisons of twin study results.

We examined whether there are crosscultural differences in the magnitude of genetic and environmental contributions to risk of becoming a regular smoker and of persistence in smoking in men and women. Standard methods of epidemiologic and genetic analysis were applied to questionnaire data on history of cigarette use obtained from large samples of male and female like-sex twins from three different countries: Australia (N = 2284 pairs), Sweden (N = 8651 pairs), and Finland (N = 10,948 pairs). Samples were subdivided into three age groups (AG), 18-25 years, 26-35 years, and 36-46 years of age. The magnitude of genetic influence for lifetime smoking was found to be consistent across country and AG for women (46%) and men (57%), and estimates of the contribution from environmental influences shared by twin and co-twin could be equated across all countries by AG for the women (from youngest to oldest AG: 45%, 35%, and 26%), but not for men, with separate estimates obtained for the Scandinavian (33%, 29%, and 19%) and the Australian men (26%, 9%, and 11%). There was no evidence for an important role for shared environmental influences on persistent smoking, and the genetic contribution was found to be consistent in magnitude in men and women, and the same across country and AG (52%). There are strong genetic influences on smoking behavior, and that risk of becoming a smoker (but not persistence in smoking) may be modified by experiences shared by twins that differ by AG and, at least for men, cultural background.     

Resolution of genetic and cultural inheritance in twin families by path analysis: application to HDL-cholesterol.

A path model and associated statistical method for the analysis of data on twin families are introduced and applied to high density lipoprotein cholesterol (HDL-c) observations in the Swedish Twin Family Study. The proposed path model incorporates both genetic and environmental sources of familial resemblance, maternal environmental effects, intergenerational differences in heritabilities, marital resemblance due to either primary or secondary phenotypic homogamy, and twin residual environmental correlations. Application of the model to HDL-c levels resulted in parameter estimates consistent with those reported in earlier reviews and in the analysis of nuclear family and twin data. Genetic heritability was estimated as h2 = .363 +/- .243, cultural heritability as c2 = .187 +/- .082, and the proportion of phenotypic variance due to residual environmental effects as r2 = .450 +/- .207. Although the parameter estimates were comparable, the statistical tests of hypotheses were, relative to other designs, of low statistical power. It appears that environmental indices are necessary for powerful tests of hypotheses.     

Method for Evaluating Multiple Mediators: Mediating Effects of Smoking and COPD on the Association between the CHRNA5-A3 Variant and Lung Cancer Risk

A mediation model explores the direct and indirect effects between an independent variable and a dependent variable by including other variables (or mediators). Mediation analysis has recently been used to dissect the direct and indirect effects of genetic variants on complex diseases using case-control studies. However, bias could arise in the estimations of the genetic variant-mediator association because the presence or absence of the mediator in the study samples is not sampled following the principles of case-control study design. In this case, the mediation analysis using data from case-control studies might lead to biased estimates of coefficients and indirect effects. In this article, we investigated a multiple-mediation model involving a three-path mediating effect through two mediators using case-control study data. We propose an approach to correct bias in coefficients and provide accurate estimates of the specific indirect effects. Our approach can also be used when the original case-control study is frequency matched on one of the mediators. We employed bootstrapping to assess the significance of indirect effects. We conducted simulation studies to investigate the performance of the proposed approach, and showed that it provides more accurate estimates of the indirect effects as well as the percent mediated than standard regressions. We then applied this approach to study the mediating effects of both smoking and chronic obstructive pulmonary disease (COPD) on the association between the CHRNA5-A3 gene locus and lung cancer risk using data from a lung cancer case-control study. The results showed that the genetic variant influences lung cancer risk indirectly through all three different pathways. The percent of genetic association mediated was 18.3% through smoking alone, 30.2% through COPD alone, and 20.6% through the path including both smoking and COPD, and the total genetic variant-lung cancer association explained by the two mediators was 69.1%.     

Simulation analysis to test the influence of model adequacy and data structure on the estimation of genetic parameters for traits with direct and maternal effects

Simulations were used to study the influence of model adequacy and data structure on the estimation of genetic parameters for traits governed by direct and maternal effects. To test model adequacy, several data sets were simulated according to different underlying genetic assumptions and analysed by comparing the correct and incorrect models. Results showed that omission of one of the random effects leads to an incorrect decomposition of the other components. If maternal genetic effects exist but are neglected, direct heritability is overestimated, and sometimes more than double. The bias depends on the value of the genetic correlation between direct and maternal effects. To study the influence of data structure on the estimation of genetic parameters, several populations were simulated, with different degrees of known paternity and different levels of genetic connectedness between flocks. Results showed that the lack of connectedness affects estimates when flocks have different genetic means because no distinction can be made between genetic and environmental differences between flocks. In this case, direct and maternal heritabilities are under-estimated, whereas maternal environmental effects are overestimated. The insufficiency of pedigree leads to biased estimates of genetic parameters.     

A comparison of methods to estimate cross-environment genetic correlations

Advanced techniques for quantitative genetic parameter estimation may not always be necessary to answer broad genetic questions. However, simpler methods are often biased, and the extent of this determines their usefulness. In this study we compare family mean correlations to least squares and restricted error maximum likelihood (REML) variance component approaches to estimating cross-environment genetic correlations. We analysed empirical data from studies where both types of estimates were made, and from studies in our own laboratories. We found that the agreement between estimates was better when full-sib rather than half-sib estimates of cross-environment genetic correlations were used and when mean family size increased. We also note biases in REML estimation that may be especially important when testing to see if correlations differ from 0 or 1. We conclude that correlations calculated from family means can be used to test for the presence of genetic correlations across environments, which is sufficient for some research questions. Variance component approaches should be used when parameter estimation is the objective, or if the goal is anything other than determining broad patterns.     

A note on the effect of observations with missing data on genetic correlation estimates

Summary Various studies have estimated covariance components as half the difference between the variance component of the sum of the variable values, for each observation, and the sum of the corresponding variable variance components. Although the variance components for the separate variables can be computed using all available data, the variance components of the sum can be computed only from those observations with records for both variables. Previous studies have suggested eliminating observations with missing data, because of possible selection bias. The effect of missing data on estimates of covariance components and genetic correlations was tested on sample beef cattle data and simulated data by randomly deleting differing proportions of records of one variable for each pair of variables analyzed. Estimates of genetic correlations computed with observations with missing data eliminated, were more accurate than estimates computed using all available data. Furthermore, when observations with missing data were included, estimates of genetic correlation far outside the parameter space were common. Therefore, this method should be used only if observations with missing data have been eliminated.     

Genetic correlations and their dependence on environmental similarity—Insights from livestock data

Genetic correlations for a trait across environments are predicted to decrease as environments diverge. However, estimates of genetic correlations from natural populations are typically defined across a limited environmental range and prone to very large standard errors, making it difficult to test this prediction. We address the importance of environmental distance on genetic correlations by employing data from domestic cattle in which abundant and accurate estimates are available from a wide range of environments. Three production traits related to milk yield show a clear decrease in genetic correlations with increasing environmental divergence. This pattern was also evident for growth traits and other yield traits but not for traits related to reproduction, morphology, physiology, or disease. We suspect that this reflects weaker selection on these latter trait classes compared to production traits, or alternatively the effects of selection are constrained by unfavorable genetic correlations between traits. The results support the notion that traits that historically have been under strong directional selection in a small range of frequently encountered environments will evolve high genetic correlations across these environments, while exposure to uncommon (and dissimilar) environments lead to a reranking of gene effects and a decrease in genetic correlations across environments.     

Within- and between-zygosity variance in oral traits among US and Punjabi twins

Cross-cultural comparison of twin variances reveals widespread heterogeneity among zygosities for dental occlusal traits, implying various biases in calculation of genetic variance or heritability estimates. These estimates are fairly robust for dental size traits, however. Differences in pattern between Punjabi (Northwest Indian) and American twins highlight the environmental differences that affect heritability determinations.     

Dominance and environmental variances: their effect on heritabilities estimated from twin data

A method for partitioning genetic variance estimated from twin data into additive and dominance variances was presented using Falconer's variance component model. The effects of dominance and environmental variances on a number of heritability estimates were also reviewed. A heritability estimate, based on the analysis of variance and the genetic variance estimates presented by HASEMAN and ELSTON and CHRISTIAN et al. which utilizes all available information from twin data, was proposed and discussed. This estimate seems to be the least affected by fluctuations in the magnitudes of dominance and environmental variances.     

Estimates of correlations among yield traits and somatic cell score with different models to adjust for bovine somatotropin effects on Holstein dairy cows

Records of Holstein cows from the Dairy Records Processing Center at Raleigh, NC were edited to obtain three data sets: 65,720 first, 50,694 second, and 65,445 later lactations. Correlations among yield traits and somatic cell score were estimated with three different models: 1) bovine somatotropin (bST) administration ignored, 2) bST administration as a fixed effect and 3) administration of bST as part of the contemporary group (herd-year-month-bST). Heritability estimates ranged from 0.13 to 0.17 for milk, 0.12 to 0.20 for fat, 0.14 to 0.16 for protein yields, and 0.08 to 0.09 for somatic cell score. Estimates were less for later than first lactations. Estimates of genetic correlations among yields ranged from 0.35 to 0.85 with no important differences between estimates with the 3 models. Estimates for lactation 2 agreed with estimates for lactation 1. Estimates of genetic correlations for later lactations were generally greater than for lactations 1 and 2 except between milk and protein yields. Estimates of genetic correlations between yields and somatic cell score were mostly negative or small (-0.45 to 0.11). Estimates of environmental correlations among yield traits were similar with all models (0.77 to 0.97). Estimates of environmental correlations between yields and somatic cell score were negative (-0.22 to -0.14). Estimates of phenotypic correlations among yield traits ranged from 0.70 to 0.95. Estimates of phenotypic correlations between yields and somatic cell score were small and negative. For all three data sets and all traits, no important differences in estimates of genetic parameters were found for the two models that adjusted for bST and the model that did not.     

The contribution of risk factors to blood pressure heritability estimates in young adults: the East flanders prospective twin study.

The heritability of blood pressure estimated in previous studies may be confounded by the influence of potential blood pressure risk factors. We applied the classical twin design to estimate the contribution of these covariates to blood pressure heritability. The study consisted of 173 dizygotic and 251 monozygotic twin pairs aged 18-34 years, randomly selected from the East Flanders Prospective Twin Survey. In a standardized examination, blood pressure and anthropometry was measured, a questionnaire was completed, and a fasting blood sample was taken. In univariate and bivariate modeling, diastolic and systolic heritability were estimated both unadjusted and adjusted for potential risk factors. Also, covariate interaction was modeled. Bivariate analysis gave heritability estimates of 0.63 (95%CI 0.55-0.59), 0.74 (95%CI: 0.68-0.79), and 0.78 (95%CI: 0.70-0.84) for diastolic, systolic, and cross-trait heritability, respectively. The remaining variances could be attributed to unique environmental influences. These heritability estimates did not change substantially in univariate analyses or after adjustment for risk factors. A sex-limitation model showed that the heritability estimates for women were significantly higher than for men, but the same genetic factors were operating across sexes. Sex and cigarette smoking appeared to be statistically significant interaction terms. The heritability of blood pressure is relatively high in young adults. Potential risk factors of blood pressure do not appear to confound the heritability estimates. However, gene by sex by smoking interaction is indicated.     

The genetics of middle-age spread in middle-class males.

This study provides findings to assist in identifying factors that contribute to the current clinical and public health debate of the obesity epidemic. The study examined the genetics of adult-onset weight change in middle-aged male-male twins controlling for weight in early adulthood, lifetime history of tobacco use and alcohol dependence, and aimed to estimate the proportion of genetic factors that influence weight change between early adulthood and middle age in white middle-class males. The study was a classic longitudinal twin design and used Body Mass Index (BMI) for three waves of data collection from the Vietnam Era Twin Registry--induction physicals (approximately 1968), 1987 and 1990--or periods corresponding between young adulthood and middle age. Univariate heritability estimates for BMI at all three data periods were conducted as well as a Cholesky longitudinal genetic analysis for weight change controlling for BMI at military induction, smoking and alcohol use. Frequency data indicated that the sample was on average classified as normal BMI in their 20s; but BMI gradually increased during the next twenty years. Univariate data for each data period indicated that additive genetic factors accounted for between 63% and 69% of total variance in BMI. The Cholesky longitudinal genetic analysis of BMI87 and BMI90, controlling for BMI at military induction, indicated that more than half of the change in BMI from early adulthood to middle age remains heritable. No shared environmental factors were identified, thus the remainder of the variance was accounted for by nonshared, or unique, environmental factors and error. The data analysis suggests that treatments and public health interventions need to recognize the magnitude of genetic factors if short-term and long-term interventions are to be effective.