Extended validity of results for variance components models

SummaryThis paper reviews research situations in medicine, epidemiology and psychiatry, in psychological measurement and testing, and in sample surveys in which the observer(rater or interviewer) can be an important source of measurement error. Moreover, most of the statistical literature in observer variability is surveyed with attention given to a notational unification of the various models proposed. In the continuous data case, the usual analysis of variance (ANOVA) components of variance models are presented with an emphasis on the intraclass correlation coefficient as a measure of reliability. Other modified ANOVA models, response error models in sample surveys, and related multivariate extensions are also discussed. For the categorical data case, special attention is given to measures of agreement and tests of hypotheses when the data consist of dichotomous responses. In addition, similarities between the dichotomous and continous cases are illustrated in terms of intraclass correlation coefficients. Finally, measures of agreement, such as kappa and weighted‐kappa, are discussed in the context of nominal and ordinal data. A proposed unifying framework for the categorical data case is given in the form of concluding remarks.

Variance components models were used to analyze total IgE levels in families ascertained though the Collaborative Study of the Genetics of Asthma (CSGA) using a genome-wide array of polymorphic markers. While IgE levels are known to be associated with clinical asthma and recognized to be under strong genetic control (here the heritability was estimated at 44-60% in the three racial groups), specific genes influencing this trait are still largely unknown. Multipoint analysis of 323 markers yielded little indication of specific regions containing a trait locus controlling total serum IgE levels (adjusted for age and gender). Although a number of regions showed LOD statistics above 1.5 in Caucasian families (chromosome 4) and in African-American families (chromosomes 2 and 4), none yielded consistent evidence in all three racial groups. Analysis of total IgE adjusted for gender, age and Allergy Index (a quantitative score of skin test sensitivity to 14 common aeroallergens) was conducted on these data. In this analysis, a much stronger signal for a trait locus controlling adjusted log[total IgE] was seen on the telomeric end of chromosome 18, but only in Caucasian families. This region accounted for most of the genetic variation in log[total IgE], and may represent a quantitative trait locus for IgE levels independent of atopic response. Oligogenic analysis accounting simultaneously for the contribution of this locus on chromosome 18 and other chromosomal regions showing some evidence of linkage in these Caucasian families (on chromosomes 2, 4 and 20) failed to yield significant evidence for interaction.

Experimenters often make several observations on a given experimental unit. If these observations can be associated with some continuous variable, such as t)ime or temperature, they collectively form a curve. Wishart (1938) first recommended that a general regression model be fitted to each curve and that the effects of the experimental treatments be evaluated by analyzing the coefficients in the model. Univariate (Box, 1950) and multivariate analysis of variance (Cole and Grizzle, 1966) and principal component analysis (Church, 1966) are other techniques for the analysis of response curves. A discussion of these methods is presented and a new model, which combines the univariate analysis of variance and principal component analysis, is developed. This model overcomes some of the inadequacies of the available procedures and gives results which are easy to understand and interpret. Examples are presented which compare the various methods of analysis and illustrate the usefulness of this new model.

While variance components analysis has emerged as a powerful tool in complex trait genetics, existing methods for fitting variance components do not scale well to large-scale datasets of genetic variation. Here, we present a method for variance components analysis that is accurate and efficient: capable of estimating one hundred variance components on a million individuals genotyped at a million SNPs in a few hours. We illustrate the utility of our method in estimating and partitioning variation in a trait explained by genotyped SNPs (SNP-heritability). Analyzing 22 traits with genotypes from 300,000 individuals across about 8 million common and low frequency SNPs, we observe that per-allele squared effect size increases with decreasing minor allele frequency (MAF) and linkage disequilibrium (LD) consistent with the action of negative selection. Partitioning heritability across 28 functional annotations, we observe enrichment of heritability in FANTOM5 enhancers in asthma, eczema, thyroid and autoimmune disorders.

There appears to be no standard method of constructing confidence regions for the variance components and ratios of a random or mixed model; however, with regard to point estimation and tests of hypotheses the analysis of variance has become somewhat routine. This study derives confidence regions by using the AOV mean squares with Kimball's result. These confidence regions are conservative, that is, the actual confidence level cannot be less than any pre-set value and are polygonal and easy to construct. They determine simultaneous confidence intervals for the variance ratios, but these intervals (one-sided) have the defect that the end-point may be negative, a property similar to that of the AOV estimators of variance components. Confidence regions are demonstrated for the two-way classification and three-stage nested model and a numerical example is included.

One of the main concerns in the family studies of complex diseases is the effect that ascertainment and correction for it may have on test procedures and estimators. Elston and Sobel [1979] and Hopper and Mathews [1982] proposed two ways to correct for ascertainment in the study of quantitative trait data. For single ascertainment, using a variance components approach, we present results of simulation studies comparing estimates from these two methods for different selection criteria. We also show results from simulations when ascertained families are analyzed either at random or by correcting for ascertainment. For discordant sibpairs, we compare a variance components model that incorporates ascertainment correction with the extreme discordant sib pairs (EDSP) design proposed by Risch and Zhang [1995]. Our results show that there is minimal difference between the two methods of ascertainment correction. In the presence of effects from a large genetic background and the segregation of a rare gene, both ascertainment affected the polygenic and environmental components of variance but had rather little impact on the estimate of the linked major gene component of variance. The results also show the EDSP is slightly more powerful the variance components procedures for common alleles, and the variance components procedure is much more powerful than using EDSP when there is a rare allele segregating in the population.

FRI0043 Heritability assessment of cartilage collagen metabolism. a twin study on circulating pro-collagen iia n-terminal pro-peptide (piianp)

The Analysis of Variance technique estimates variance components by comparing their mean squares to their expected values. Nevertheless, this method could give variance component estimates that are found outside the parameter space, i.e. negative estimates. In a bid to overcome this deficiency, alternate approaches are essential, and likelihood-based approaches have become common over time. Bayesian techniques have also been proposed and Bayes factors developed for examining various models. We applied the Bayes factor proposed by Faulkenberry (2018) to a Balanced Two Way ANOVA under three (3) cases, namely Case 1: the levels of the two factors are fixed; Case 2: the levels of the two factors are random; and Case 3: the levels of one factor are considered as fixed, while the levels of the other factor are considered as random. We realized that when the levels of the two factors are fixed, the Bayesian conclusion about the variability in the effects is in line with that of a frequentist. But when the same data set was considered to be wholly or partly as sample observations drawn randomly from a given population of interest, the Bayesian conclusion differed slightly from that of the frequentist. Keywords: Bayes Factor; Bayesian; Frequentist, Fixed; Random.

This study aims to expand our understanding of the genetic architecture of crown morphology in the human diphyodont dentition. Here, we present bivariate genetic correlation estimates for deciduous and permanent molar traits and evaluate the patterns of pleiotropy within (e.g., m1–m2) and between (e.g., m2–M1) dentitions. Morphology was observed and scored from dental models representing participants of an Australian twin and family study (deciduous n = 290, permanent n = 339). Data collection followed Arizona State University Dental Anthropology System standards. Genetic correlation estimates were generated using maximum likelihood variance components analysis in SOLAR v.8.1.1. Approximately 23% of deciduous variance components models and 30% of permanent variance components models yielded significant genetic correlation estimates. By comparison, over half (56%) of deciduous–permanent homologues (e.g., m2 hypocone–M1 hypocone) were significantly genetically correlated. It is generally assumed that the deciduous and permanent molars represent members of a meristic molar field emerging from the primary dental lamina. However, stronger genetic integration among m2–M1/M2 homologues than among paired deciduous traits suggests the m2 represents the anterior-most member of a “true” molar field. The results indicate genetic factors act at distinct points throughout development to generate homologous molar form, starting with the m2, which is later replaced by a permanent premolariform crown.

We used variance components analysis to investigate the underlying determinants of the quantitative phenotypes (Q1-Q5) and their interrelationships in replicate 42 of the Genetic Analysis Workshop 12 simulated general population. Variance components models were fitted using Gibbs sampling in WinBUGS v1.3. Sigma-squared-A-random-effects (SSARs) were estimated for each phenotype, and were used as derived phenotypes in subsequent linkage analyses. Whole-genome, multipoint linkage analyses were based upon a new Haseman-Elston identity-by descent sib-pair method that takes a weighted combination of the trait-sum and trait-difference. The five quantitative traits simulated were closely correlated with each other and with affection status. The whole-genome screen of quantitative traits associated with the simulated complex disease suggested that one or more major loci regulating Q1 localizes to chromosome 2p and that one or more major loci regulating Q5 may localize to chromosome 1p.

: Exact tests are derived for testing hypotheses concerning the variance components of the main effects in an unbalanced random two-way crossed classification with interaction model. The tests are based on four sums of squares which are distributed independently as scalar multiples of chi-squared variates. These sums of squares can also be used to find an exact test concerning the interaction variance component, and to obtain simultaneous confidence intervals on all continuous functions of the model's variance components. A study is made concerning the power of the proposed tests, including a comparison with other approximate tests. (Author)

Pulse pressure (PP) is an independent risk factor for cardiovascular disease. PP rises with age, more so in women. We examined sex differences in the correlations and variance components of PP in adult subjects from 767 nuclear families, enriched with those containing twins, from the Victorian Family Heart Study. After adjusting for age, we found no significant differences in the means or variances of PP in males and females. Under the assumption of no sex differences, the proportions of variance due to shared genes, shared environment, and individual-specific environment were 20%, 23% and 57%, respectively. However, same-sex relative pairs had significantly higher correlations than opposite-sex pairs (P = 0.005), implying the existence of sex-dependent effects. Extensions to the simple variance components model suggested three possible explanations for these differences: smaller genetic correlation between opposite-sex pairs (rhoG,MF = 0.45, P = 0.007); smaller environmental correlation between opposite-sex pairs (P = 0.0003); or different environmental and genetic correlations obtained by estimating genetic, environmental, and individual variance components separately for males and females (not nested, Akaike's Information Criterion (AIC) smaller by 6.69). Under the last model, the genetic component of PP variance is greater for males (1.62 vs 0.33) while the environmental component is greater for females (1.84 vs 0), which would have implications for the planning of gene discovery studies, since heritability would be higher in males. However, the second (environmental) approach best fits the data according to the AIC. Genetic explanations for sex differences in phenotypic correlations may be misleading unless shared environmental factors are also considered. PP illustrates a phenotype in which sex dependency represents an important component of phenotypic determination that can be revealed by detailed variance components modelling.

A note on non-negative minimum bias MINQE in variance components model

Variance components modeling has emerged as a powerful method for quantitative trait loci (QTL) linkage analysis. However, the power to detect a gene of minor effect is low. Many complex traits are affected by environmental as well as genetic factors, and one strategy to increase power is to reduce nongenetic phenotypic variance by adjusting for environmental covariates. In this paper, we investigate the power of three approaches to covariate adjustment in variance components linkage analysis: (i) incorporate covariates in the means model, (ii) incorporate covariates in the covariance matrix, and (iii) perform analysis on residual statistics. These approaches are compared to an analysis without adjustment. The results show that in the absence of correlation between the covariate and the QTL effect, adjusting for covariates indeed increases power to detect an underlying QTL. As this correlation increases, however, the power decreases. In the presence of a causal association between QTL and covariates, not adjusting for covariates appeared to be more powerful. The three approaches for adjusting for covariate: residual statistics, the means model, and the covariance model, had equal power to detect a QTL.

ABSTRACTTwenty judges performed a variety of chemosensory tasks in order to select the best scores to form a panel for coffee evaluation. An average of correct responses (P%), one‐way analysis of variance (ANOVA) and principal components analysis (PCA) were compared. The tests involved: ability to recognize the four basic tastes, identification and matching of odors, taste intensity evaluation and perception of small differences in taste. P% accounted for 71.17 ± 4.34% and 10 of the judges had scores greater than the final average. ANOVA and PCA resulted in 2 different panels consisting of 9 and 12 judges, respectively. The panel was composed by the nine panelists selected by the three methods. The other three panelists that were doubtful could improve to the point of acceptance with additional training. These methods should be used simultaneously to have more security in the acceptance or rejection of panelists.