Genetic linkage analysis of a dichotomous trait incorporating a tightly linked quantitative trait in affected sib pairs

Many complex diseases are usually considered as dichotomous traits but are also associated with quantitative biological markers or quantitative risk factors. For such dichotomous traits, although their associated quantitative traits may not directly underly the diagnosis of the disease status, if the associated quantitative trait is also linked to the chromosomal regions linked to the dichotomous trait, then joint analysis of dichotomous and quantitative traits should be more efficient than consideration of them separately. Previous studies have focused on the situation when a dichotomous trait can be modeled by a threshold process acting on a single underlying normal liability distribution. However, for many complex disorders, including most psychiatric disorders, diagnosis is generally based on a set of binary or discrete criteria. These traits cannot be modeled on the basis of a threshold process acting on an underlying continuous trait. We propose a likelihood-based method that efficiently combines such a discrete trait and an associated quantitative trait in the analysis, using affected-sib-pair data. Our simulation studies suggest that joint analysis increases the power to detect linkage of dichotomous traits. We also apply the proposed new method to an asthma genome-scan data set and incorporate the total serum immunoglobulin E level in the analysis.     

Segregation analysis of restless legs syndrome: possible evidence for a major gene in a family study using blinded diagnoses

OBJECTIVE: The objective of this study was to ascertain the most likely inheritance pattern of restless legs syndrome (RLS) using segregation analysis. METHODS: Probands were RLS patients presenting to the Neurology and Sleep clinics of the Johns-Hopkins Bayview medical center with willing first and second degree relatives. Blinded diagnosis was made in those who exhibited the four diagnostic features of RLS. Analysis was performed on RLS as a dichotomous trait and considering age of onset models on 590 phenotyped subjects from 77 pedigrees. RESULTS: All non-genetic models were rejected considering RLS as a dichotomous trait. A single locus Mendelian dominant model with gender as a covariate had best fit with allele frequency of 0.077 and complete penetrance. RLS frequency in non-carrier subjects was estimated to be 0.14. Two underlying distributions of age of onset, with a possible dichotomy at 26.3 years, were identified. Contrary to the results for RLS as a dichotomous trait, age of onset models did not indicate single major gene inheritance. CONCLUSION: This segregation analysis suggests that the pattern of segregation is consistent with that of a single major locus, when RLS is treated as a dichotomous trait without considering age of onset. The high rate of phenocopies matches known population frequencies and taken with significant residual familial effects and the lack of evidence for a major gene controlling age of onset, indicates that non-genetic causes of RLS may exist and RLS is a complex disorder.     

Genetic basis of acanthosis nigricans in Mexican Americans and its association with phenotypes related to type 2 diabetes

Acanthosis nigricans (AN) is a skin condition associated with hyperinsulinemia and insulin resistance and has been shown to be a risk factor for type 2 diabetes. The influence of genetic factors on AN and the basis of its association with type 2 diabetes and its risk factors are unknown. Using data from 397 participants from two Mexican American family studies, we investigated the heritability of AN and its genetic correlation with other diabetes risk factors. AN was examined as both a continuous trait and a dichotomous trait by means of a previously described validated scale. The results indicated that the heritability (h2) for AN, when examined as a continuous trait, was high (0.58+/-0.10) and statistically significant (P<0.001). The h2 for AN as a dichotomous trait was estimated to be moderate (0.23+/-0.05) and was also significant (P=0.018). The additive genetic correlations between AN (either as a continuous trait or a dichotomous trait) and type 2 diabetes and its risk factors, including body mass index and fasting insulin, were high or moderately high and statistically significant. The random environmental correlations, by contrast, were low and statistically insignificant. These data suggest that genes that influence AN have pleiotropic effects on diabetes and its risk factors.     

Modeling linkage disequilibrium between a polymorphic marker locus and a locus affecting complex dichotomous traits in natural populations

Linkage disequilibrium is an important topic in evolutionary and population genetics. An issue yet to be settled is the theory required to extend the linkage disequilibrium analysis to complex traits. In this study, we present theoretical analysis and methods for detecting or estimating linkage disequilibrium (LD) between a polymorphic marker locus and any one of the loci affecting a complex dichotomous trait on the basis of samples randomly or selectively collected from natural populations. Statistical properties of these methods were investigated and their powers were compared analytically or by use of Monte Carlo simulations. The results show that the disequilibrium may be detected with a power of 80% by using phenotypic records and marker genotype when both the trait and marker variants are common (30%) and the LD is relatively high (40-100% of the theoretical maximum). The maximum-likelihood approach provides accurate estimates of the model parameters as well as detection of linkage disequilibrium. The likelihood method is preferred for its higher power and reliability in parameter estimation. The approaches developed in this article are also compared to those for analyzing a continuously distributed quantitative trait. It is shown that a larger sample size is required for the dichotomous trait model to obtain the same level of power in detecting linkage disequilibrium as the continuous trait analysis. Potential use of these estimates in mapping the trait locus is also discussed.     

KELVIN: a software package for rigorous measurement of statistical evidence in human genetics

This paper describes the software package KELVIN, which supports the PPL (posterior probability of linkage) framework for the measurement of statistical evidence in human (or more generally, diploid) genetic studies. In terms of scope, KELVIN supports two-point (trait-marker or marker-marker) and multipoint linkage analysis, based on either sex-averaged or sex-specific genetic maps, with an option to allow for imprinting; trait-marker linkage disequilibrium (LD), or association analysis, in case-control data, trio data, and/or multiplex family data, with options for joint linkage and trait-marker LD or conditional LD given linkage; dichotomous trait, quantitative trait and quantitative trait threshold models; and certain types of gene-gene interactions and covariate effects. Features and data (pedigree) structures can be freely mixed and matched within analyses. The statistical framework is specifically tailored to accumulate evidence in a mathematically rigorous way across multiple data sets or data subsets while allowing for multiple sources of heterogeneity, and KELVIN itself utilizes sophisticated software engineering to provide a powerful and robust platform for studying the genetics of complex disorders.     

A recoding scheme for X-linked and pseudoautosomal loci to be used with computer programs for autosomal LOD-score analysis

We present a recoding scheme that allows for a parametric multipoint X-chromosomal linkage analysis of dichotomous traits in the context of a computer program for autosomes that can use trait models with imprinting. Furthermore, with this scheme, it is possible to perform a joint multipoint analysis of X-linked and pseudoautosomal loci. It is required that (1) the marker genotypes of all female nonfounders are available and that (2) there are no male nonfounders who have daughters in the pedigree. The second requirement does not apply if the trait locus is pseudoautosomal. The X-linked marker loci are recorded by adding a dummy allele to the males' hemizygous genotypes. For modelling an X-linked trait locus, five different liability classes are defined, in conjunction with a paternal imprinting model for male nonfounders. The formulation aims at the mapping of a diallelic trait locus relative to an arbitrary number of codominant markers with known genetic distances, in cases where a program for a genuine X-chromosomal analysis is not available.     

Variations in form of the hypoglossal canal

Variation in the nature and extent of division of the hypoglossal canal can be classified by a simple scoring scheme. Applied to three series of crania of differing provenance, the results indicate a continuity in expression of the trait rather than the dichotomous character utilized in previous studies. The similarity in results in these three populations, of widely differing environment, suggests fairly strict canalization of development.     

Disequilibrium mapping of a quantitative-trait locus in an expanding population.

Linkage disequilibrium (LD) mapping can be successful if there is strong nonrandom association between marker alleles and an allele affecting a trait of interest. The principles of LD mapping of dichotomous traits are well understood, but less is known about LD mapping of a quantitative-trait locus (QTL). It is shown in this report that selective genotyping can increase the power to detect and map a rare allele of large effect at a QTL. Two statistical tests of the association between an allele and a quantitative character are proposed. These tests are approximately independent, so information from them can be combined. Analytic theory is developed to show that these two tests are effective in detecting the presence of a low-frequency allele with a relatively large effect on the character when the QTL is either already a candidate locus or closely linked to a marker locus that is in strong LD with the QTL. The latter situation is expected in a rapidly growing population in which the allele of large effect was present initially in one copy. Therefore, the proposed tests are useful under the same conditions as those for successful LD mapping of a dichotomous trait or disease. Simulations show that, for detection of the presence of a QTL, these tests are more powerful than a simple t-test. The tests also provide a basis for defining a measure of association, gamma, between a low-frequency allele at a putative QTL and a low-frequency allele at a marker locus.     

Evolutionary transitions between mechanisms of sex determination in vertebrates

Sex in many organisms is a dichotomous phenotype--individuals are either male or female. The molecular pathways underlying sex determination are governed by the genetic contribution of parents to the zygote, the environment in which the zygote develops or interaction of the two, depending on the species. Systems in which multiple interacting influences or a continuously varying influence (such as temperature) determines a dichotomous outcome have at least one threshold. We show that when sex is viewed as a threshold trait, evolution in that threshold can permit novel transitions between genotypic and temperature-dependent sex determination (TSD) and remarkably, between male (XX/XY) and female (ZZ/ZW) heterogamety. Transitions are possible without substantive genotypic innovation of novel sex-determining mutations or transpositions, so that the master sex gene and sex chromosome pair can be retained in ZW-XY transitions. We also show that evolution in the threshold can explain all observed patterns in vertebrate TSD, when coupled with evolution in embryonic survivorship limits.     

Power loss for linkage analysis due to the dichotomization of trichotomous phenotypes

OBJECTIVES: Some traits, while naturally polychotomous, are routinely dichotomized for genetic analysis. Dichotomization, intuitively, leads to a loss of power to detect linkage, as some phenotypic variability is discarded. This paper examines this power loss in the context of a trichotomous trait. METHODS: To examine this power loss, we performed a simulation study where a trichotomous trait was simulated in a sample of 1,000 sib-pairs under various genetic models. The study was replicated 1,000 times. Linkage analysis using a variance components method, as implemented in Mx, was then performed on the trichotomous trait and compared with that on a dichotomized version of the trait. RESULTS: A comparison of the power and false positive rates of the analyses shows that power to detect linkage was increased by up to 22 percentage points simply by examining the trait as a trichotomy instead of a dichotomy. Under all models examined, the trichotomous analysis outperformed the dichotomous version. CONCLUSIONS: Comparable levels of false positive rates under both methods confirm that this power gain comes solely from the information lost upon dichotomization. Thus, dichotomizing tri- or poly-chotomous traits can lead to crippling power loss, especially in the case of many loci of small effect.     

Genomewide scan of hoarding in sib pairs in which both sibs have Gilles de la Tourette syndrome

A genome scan of the hoarding phenotype (a component of obsessive-compulsive disorder) was conducted on 77 sib pairs collected by the Tourette Syndrome Association International Consortium for Genetics (TSAICG). All sib pairs were concordant for a diagnosis of Gilles de la Tourette syndrome (GTS). However, the analyses reported here were conducted for hoarding as both a dichotomous trait and a quantitative trait. Not all sib pairs in the sample were concordant for hoarding. Standard linkage analyses were performed using GENEHUNTER and Haseman-Elston methods. In addition, novel analyses with a recursive-partitioning technique were employed. Significant allele sharing was observed for both the dichotomous and the quantitative hoarding phenotypes for markers at 4q34-35 (P=.0007), by use of GENEHUNTER, and at 5q35.2-35.3 (P=.000002) and 17q25 (P=.00002), by use of the revisited Haseman-Elston method. The 4q site is in proximity to D4S1625, which was identified by the TSAICG as a region linked to the GTS phenotype. The recursive-partitioning technique examined multiple markers simultaneously. Results suggest joint effects of specific loci on 5q and 4q, with an overall P value of.000003. Although P values were not adjusted for multiple comparison, nearly all were much smaller than the customary significance level of.0001 for genomewide scans.     

The genetics of phenotypic plasticity. XI. Joint evolution of plasticity and dispersal rate

In a spatially heterogeneous environment, the rate at which individuals move among habitats affects whether selection favors phenotypic plasticity or genetic differentiation, with high dispersal rates favoring trait plasticity. Until now, in theoretical explorations of plasticity evolution, dispersal rate has been treated as a fixed, albeit probabilistic, characteristic of a population, raising the question of what happens when the propensity to disperse and trait plasticity are allowed to evolve jointly. We examined the effects of their joint evolution on selection for plasticity using an individual-based computer simulation model. In the model, the environment consisted of a linear gradient of 50 demes with dispersal occurring either before or after selection. Individuals consisted of loci whose phenotypic expression either are affected by the environment (plastic) or are not affected (nonplastic), plus a locus determining the propensity to disperse. When dispersal rate and trait plasticity evolve jointly, the system tends to dichotomous outcomes of either high trait plasticity and high dispersal, or low trait plasticity and low dispersal. The outcome strongly depended on starting conditions, with high trait plasticity and dispersal favored when the system started at high values for either trait plasticity or dispersal rate (or both). Adding a cost of plasticity tended to drive the system to genetic differentiation, although this effect also depended on initial conditions. Genetic linkage between trait plasticity loci and dispersal loci further enhanced this strong dichotomy in evolutionary outcomes. All of these effects depended on organismal life history pattern, and in particular whether selection occurred before or after dispersal. These results can explain why adaptive trait plasticity is less common than might be expected.     

Prediction of Selection Response for Threshold Dichotomous Traits

This paper presents a formula to predict expected response to one generation of truncation selection for a dichotomous trait under polygenic additive inheritance. The derivation relies on the threshold liability concept and on the normality assumption of the joint distribution of additive genetic values and their predictors used as selection criteria. This formula accounts for asymmetry of response when both the prevalence of the trait and the selection rate differ from 1/2 via a bivariate normal integral term. The relationship with the classical formula R = iota rho sigma G is explained with a Taylor expansion about a zero value of the correlation factor. Properties are illustrated with an example of sire selection based on progeny test performance which shows a departure from usual predictions up to 15-20% at low (0.05) or high (0.95) selection rates. Univariate approximations and extensions to several paths of genetic change are also discussed.     

AnthropMMD: An R package with a graphical user interface for the mean measure of divergence

The mean measure of divergence is a dissimilarity measure between groups of individuals described by dichotomous variables. It is well suited to datasets with many missing values, and it is generally used to compute distance matrices and represent phenograms. Although often used in biological anthropology and archaeozoology, this method suffers from a lack of implementation in common statistical software. A package for the R statistical software, AnthropMMD, is presented here. Offering a dynamic graphical user interface, it is the first one dedicated to Smith's mean measure of divergence. The package also provides facilities for graphical representations and the crucial step of trait selection, so that the entire analysis can be performed through the graphical user interface. Its use is demonstrated using an artificial dataset, and the impact of trait selection is discussed. Finally, AnthropMMD is compared to three other free tools available for calculating the mean measure of divergence, and is proven to be consistent with them.     

A Gibbs sampling approach to linkage analysis.

We present a Monte Carlo approach to estimation of the recombination fraction theta and the profile likelihood for a dichotomous trait and a single marker gene with 2 alleles. The method is an application of a technique known as 'Gibbs sampling', in which random samples of each of the unknowns (here genotypes, theta and nuisance parameters, including the allele frequencies and the penetrances) are drawn from their posterior distributions, given the data and the current values of all the other unknowns. Upon convergence, the resulting samples derive from the marginal distribution of all the unknowns, given only the data, so that the uncertainty in the specification of the nuisance parameters is reflected in the variance of the posterior distribution of theta. Prior knowledge about the distribution of theta and the nuisance parameters can be incorporated using a Bayesian approach, but adoption of a flat prior for theta and point priors for the nuisance parameters would correspond to the standard likelihood approach. The method is easy to program, runs quickly on a microcomputer, and could be generalized to multiple alleles, multipoint linkage, continuous phenotypes and more complex models of disease etiology. The basic approach is illustrated by application to data on cholesterol levels and an a low-density lipoprotein receptor gene in a single large pedigree.     

Type I error and the power of the s-test: old lessons from a new,analytically justified statistical test for phylogenies

We present a new procedure for assessing the statistical significance of the most likely unrooted dichotomous topology inferrable from four DNA sequences. The procedure calculates directly a P-value for the support given to this topology by the informative sites congruent with it, assuming the most likely star topology as the null hypothesis. Informative sites are crucial in the determination of the maximum likelihood dichotomous topology and are therefore an obvious target for a statistical test of phylogenies. Our P-value is the probability of producing through parallel substitutions on the branches of the star topology at least as much support as that given to the maximum likelihood dichotomous topology by the aforementioned informative sites, for any of the three possible dichotomous topologies. The degree of statistical significance is simply the complement of this P-value. Ours is therefore an a posteriori testing approach, in which no dichotomous topology is specified in advance. We implement the test for the case in which all sites behave identically and the substitution model has a single parameter. Under these conditions, the P-value can be easily calculated on the basis of the probabilities of change on the branches of the most likely star topology, because under these assumptions, each site can become informative independently from every other site; accordingly, the total number of informative sites of each kind is binomially distributed. We explore the test's type I error by applying it to data produced in star topologies having all branches equally long, or having two short and two long branches, and various degrees of homoplasy. The test is conservative but we demonstrate, by means of a discreteness correction and progressively assumption-free calculations of the P-values, that (1) the conservativeness is mostly due to the discrete nature of informative sites and (2) the P-values calculated empirically are moreover mostly quite accurate in absolute terms. Applying the test to data produced in dichotomous topologies with increasing internal branch length shows that, despite the test's "conservativeness," its power is much higher than that of the bootstrap, especially when the relevant informative sites are few.     

Selection strategies for linkage studies using twins.

Genetic linkage analysis for complex diseases offers a major challenge to geneticists. In these complex diseases multiple genetic loci are responsible for the disease and they may vary in the size of their contribution; the effect of any single one of them is likely to be small. In many situations, like in extensive twin registries, trait values have been recorded for a large number of individuals, and preliminary studies have revealed summary measures for those traits, like mean, variance and components of variance, including heritability. Given the small effect size, a random sample of twins will require a prohibitively large sample size. It is well known that selective sampling is far more efficient in terms of genotyping effort. In this paper we derive easy expressions for the information contributed by sib pairs for the detection of linkage to a quantitative trait locus (QTL). We consider random samples as well as samples of sib pairs selected on the basis of their trait values. These expressions can be rapidly computed and do not involve simulation. We extend our results for quantitative traits to dichotomous traits using the concept of a liability threshold model. We present tables with required sample sizes for height, insulin levels and migraine, three of the traits studied in the GenomEUtwin project.     

Evidence for Genetic Variation in Human Mate Preferences for Sexually Dimorphic Physical Traits

Intersexual selection has been proposed as an important force in shaping a number of morphological traits that differ between human populations and/or between the sexes. Important to these accounts is the source of mate preferences for such traits, but this has not been investigated. In a large sample of twins, we assess forced-choice, dichotomous mate preferences for height, skin colour, hair colour and length, chest hair, facial hair, and breast size. Across the traits, identical twins reported more similar preferences than nonidentical twins, suggesting genetic effects. However, the relative magnitude of estimated genetic and environmental effects differed greatly and significantly between different trait preferences, with heritability estimates ranging from zero to 57%.     

Elementary methods of cohort analysis with several exposure levels.

This paper proposes an extension of the Mantel-Haenszel rate ratio for the dichotomous exposure to the multiple exposure levels. This extension is based on the unbiased estimating function approach and yields closed-form Mantel-Haenszel rate ratio estimators. Dually consistent variance and covariance estimators of the estimating functions are given and a quasi-score-based confidence interval for individual common rate ratio is provided. A similar extension to the common rate difference case is also given.