Modeling and dissection of longitudinal blood pressure and hypertension phenotypes in genetic epidemiological studies.

We discuss analyses of the Genetic Analysis Workshop 13 data from the Framingham Heart Study and simulations based on this study. We summarize analyses that investigated measures of systolic blood pressure or hypertension as the main phenotype, with the main focus being the modeling of this complex longitudinal phenotype. The approaches include familial aggregation methods and one-stage and two-stage linkage methods. For one-stage linkage methods, phenotype modeling is carried out jointly with the linkage analysis or incorporated in the analysis design. For two-stage linkage methods, phenotypes are first modeled in order to develop summary measures that are then analyzed in a subsequent linkage analysis. Results depend on phenotype selection and on how analyses account for longitudinality, treatment effects, and heterodasticity.

A meta-analytic investigation of linkage and association of common leptin receptor (LEPR) polymorphisms with body mass index and waist circumference.

METHODS: We analyzed data pooled from nine studies on the human leptin receptor (LEPR) gene for the association of three alleles (K109R, Q223R and K656N) of LEPR with body mass index (BMI; kg/m(2)) and waist circumference (WC). A total of 3263 related and unrelated subjects from diverse ethnic backgrounds including African-American, Caucasian, Danish, Finnish, French Canadian and Nigerian were studied. We tested effects of individual alleles, joint effects of alleles at multiple loci, epistatic effects among alleles at different loci, effect modification by age, sex, diabetes and ethnicity, and pleiotropic genotype effects on BMI and WC. RESULTS: We found that none of the effects were significant at the 0.05 level. Heterogeneity tests showed that the variations of the non-significant effects are within the range of sampling variation. CONCLUSIONS: We conclude that, although certain genotypic effects could be population-specific, there was no statistically compelling evidence that any of the three LEPR alleles is associated with BMI or WC in the overall population.

Pooling analysis of genetic data: the association of leptin receptor (LEPR) polymorphisms with variables related to human adiposity.

Analysis of raw pooled data from distinct studies of a single question generates a single statistical conclusion with greater power and precision than conventional metaanalysis based on within-study estimates. However, conducting analyses with pooled genetic data, in particular, is a daunting task that raises important statistical issues. In the process of analyzing data pooled from nine studies on the human leptin receptor (LEPR) gene for the association of three alleles (K109R, Q223R, and K656N) of LEPR with body mass index (BMI; kilograms divided by the square of the height in meters) and waist circumference (WC), we encountered the following methodological challenges: data on relatives, missing data, multivariate analysis, multiallele analysis at multiple loci, heterogeneity, and epistasis. We propose herein statistical methods and procedures to deal with such issues. With a total of 3263 related and unrelated subjects from diverse ethnic backgrounds such as African-American, Caucasian, Danish, Finnish, French-Canadian, and Nigerian, we tested effects of individual alleles; joint effects of alleles at multiple loci; epistatic effects among alleles at different loci; effect modification by age, sex, diabetes, and ethnicity; and pleiotropic genotype effects on BMI and WC. The statistical methodologies were applied, before and after multiple imputation of missing observations, to pooled data as well as to individual data sets for estimates from each study, the latter leading to a metaanalysis. The results from the metaanalysis and the pooling analysis showed that none of the effects were significant at the 0.05 level of significance. Heterogeneity tests showed that the variations of the nonsignificant effects are within the range of sampling variation. Although certain genotypic effects could be population specific, there was no statistically compelling evidence that any of the three LEPR alleles is associated with BMI or waist circumference in the general population.

A tournament of linkage tests in complex inheritance.

The performance of some weakly parametric linkage tests in common use was compared on 200 replicates of oligogenic inheritance from Genetic Analysis Workshop 10. Each random sample for the quantitative trait was dichotomized at different thresholds and also selected through 2 affected sibs, generating 8 combinations of sample and variable. The variance component program SOLAR performed best with a continuous trait, even in selected samples, when the population mean was used. The sib-pair program SIBPAL2 was best in most other cases when the phenotype product, population mean, and empirical estimates of pair correlations were used. The BETA program that introduced phenotype products was slightly more powerful than maximum likelihood scores under the null hypothesis and approached but did not exceed SIBPAL2 under its optimal conditions. Type I errors generally exceeded expectations from a chi(2) test, but were conservative with respect to bounds on lods. All methods can be improved by use of the population mean, empirical correlations, logistic representation for affection status, and correct lods for samples that favour the null hypothesis. It remains uncertain whether all information can be extracted by weakly parametric methods and whether correction for ascertainment bias demands a strongly parametric model. Performance on a standard set of simulated data is indispensable for recognising optimal methods.

Pooling data and linkage analysis in the chromosome 5q candidate region for asthma.

We investigated a variety of methods for pooling data from eight data sets (n = 5,424 subjects) to validate evidence for linkage of markers in the cytokine cluster on chromosome 5q31-33 to asthma and asthma-associated phenotypes. Chromosome 5 markers were integrated into current genetic linkage and physical maps, and a consensus map was constructed to facilitate effective data pooling. To provide more informative phenotypes with better distributional properties, variance component models were fitted using Gibbs sampling methods in order to generate residual additive genetic effects, or sigma-squared-A-random-effects (SSARs), which were used as derived phenotypes in subsequent linkage analyses. Multipoint estimates of alleles shared identically by descent (IBD) were computed for all full sibling pairs. Linkage analyses were performed with a new Haseman-Elston method that uses generalized-least-squares and a weighted combination of the mean-corrected trait-sum squared and trait-difference squared as the dependent variable. Analyses were performed with all data sets pooled together, and also separately with the resulting linkage statistics pooled by several meta-analytic methods. Our results provide no significant evidence that loci conferring susceptibility to asthma affection or atopy, as measured by total serum IgE levels, are present in the 5q31-33 region. This study has provided a clearer understanding of the significance, or lack of significance, of the 5q31-33 region in asthma genetics for the phenotypes studied.

Improved evidence for linkage on 6p and 5p with retrospective pooling of data from three asthma genome screens.

To improve our ability to identify genes for complex diseases, evaluation of new methods that retrospectively pool genotype and phenotype data collected by multiple centers is important. Availability of three whole-genome screens enabled us to compare two methods, pooling raw data and meta-analysis. Multipoint linkage analyses were performed on two outcomes, total serum IgE levels and asthma affection status, using an improved Haseman-Elston algorithm. Two regions showed stronger evidence for linkage using covariate-adjusted pooled data, compared with any individual sample. Both methods for pooling data identified strong linkage to Z-transformed logeIgE levels at a location between D6S1019 and D6S426, and to the asthma trait at D5S268. In conclusion, retrospective analysis of pooled genome scan data is a potentially powerful and useful method to examine both positive and negative evidence for linkage of quantitative and categorical phenotypes across populations.

Genome-wide linkage analysis in a general population sample using sigma 2A random effects (SSARs) fitted by Gibbs sampling.

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.

Meta-analysis for linkage to asthma and atopy in the chromosome 5q31-33 candidate region.

Asthma is a common, complex human disease. Gene discovery in asthma has been complicated by substantial etiological heterogeneity, the possibility of genes of small effect and the concomitant requirement for large sample sizes. Linkage to asthma phenotypes has been investigated most intensively in the 5q chromosomal region, although results have been inconsistent across studies and all studies have had modest sample sizes. One potential solution to these issues is to combine data from multiple studies in a retrospective meta-analysis by pooling either summary statistics or raw data. The International Consortium on Asthma Genetics combined data from 11 data sets (n = 6277 subjects) to investigate evidence for linkage of 35 markers spanning the cytokine cluster on chromosome 5q31­33 to 'asthma' dichotomy and total serum immunoglobulin E (IgE) levels. Chromosome 5q markers typed in different centers were integrated into a consensus map to facilitate effective data pooling. Multipoint linkage analyses using a new Haseman­Elston method were performed with all data sets pooled together, and also separately with the resulting linkage statistics pooled by meta-analytic methods. Our results did not provide any evidence significant at the 5% level that loci conferring susceptibility to asthma or atopy are present in the 5q31­33 region; however, there was some weak evidence (empirical P = 0.077) of linkage to asthma affection. This study suggests that loci in 5q31­33 have at most a modest effect on susceptibility to asthma or total serum IgE levels, may not be detectable or present in all human populations and are difficult to detect even using combined linkage evidence from 2400­2600 full sibling pairs.

Genome scan of human systemic lupus erythematosus by regression modeling: evidence of linkage and epistasis at 4p16-15.2.

Systemic lupus erythematosus (SLE) is a complex autoimmune disorder involving at least hormonal, environmental, and genetic factors. Familial aggregation, a 2%-3% sibling recurrence rate, monozygotic twin concordance >20%, association with several candidate genes, as well as the results of five genome scans support a genetic component. We present here the results of a genome scan of 126 pedigrees multiplex for SLE, including 469 sibling pairs (affected and unaffected) and 175 affected relative pairs. Using the revised multipoint Haseman-Elston regression technique for concordant and discordant sibling pairs and a conditional logistic regression technique for affected relative pairs, we identify a novel linkage to chromosome 4p16-15.2 (P=.0003 and LOD=3.84) and present evidence of an epistatic interaction between chromosome 4p16-15.2 and chromosome 5p15 in our European American families. We confirm the evidence of linkage to chromosome 4p16-15.2 in European American families using data from an independent pedigree collection. In addition, our data support the published results of three independent studies for nine purportedly linked regions and agree with the previously published results from a subset of these data for three regions. In summary, results from two new analytical techniques establish and confirm linkage with SLE at 4p16-15.2, indicate epistasis between 4p16-15.2 and 5p15, and confirm other linkage effects with SLE that have been reported elsewhere.

Haseman and Elston revisited.

Haseman and Elston (H-E) [1972] proposed a method to detect quantitative trait loci by linkage to a marker. The squared sib-pair trait difference is regressed on the proportion of marker alleles the pair is estimated to share identical by descent: a significantly negative regression coefficient suggests linkage. It has been shown that a maximum likelihood method that directly models the sib-pair covariance has more power. This increase in power can also be obtained using the H-E regression procedure by changing the dependent variable from the squared difference to the mean-corrected product of the sibs' trait values. Multiple sibs in a sibship can be accommodated by allowing for the correlations between pairs of products in a generalized least squares procedure. Multiple trait loci, including epistatic interactions, involve only multiple linear regression. Multivariate traits can use the method of Amos et al. [1990] to find the linear function of the traits that maximizes the evidence for linkage, which now leads more simply to a test of significance. Multiple markers can be the basis of a multipoint analysis. Results of simulation studies for a continuous trait are presented that investigate Type I error and power. A similar general scheme can be used to study affected sib pairs, testing whether their identity by descent sharing probabilities are greater than would be expected in the absence of linkage, and to study other types of relative pairs.

Multilocus linkage tests based on affected relative pairs.

For complex diseases, recent interest has focused on methods that take into account joint effects at interacting loci. Conditioning on effects of disease loci at known locations can lead to increased power to detect effects at other loci. Moreover, use of joint models allows investigation of the etiologic mechanisms that may be involved in the disease. Here we present a method for simultaneous analysis of the joint genetic effects at several loci that uses affected relative pairs. The method is a generalization of the two-locus LOD-score analysis for affected sib pairs proposed by Cordell et al. We derive expressions for the relative risk, lambdaR, to a relative of an affected individual, in terms of the additive and epistatic components of variance at an arbitrary number of disease loci, and we show how these can be used to fit a likelihood model to the identity-by-descent sharing among pairs of affected relatives in extended pedigrees. We implement the method by use of a stepwise strategy in which, given evidence of linkage to disease at m-1 locations on the genome, we calculate the conditional likelihood curve across the genome for an mth disease locus, using multipoint methods similar to those proposed by Kruglyak et al. We evaluate the properties of our method by use of simulated data and present an application to real data from families with insulin-dependent diabetes mellitus.

Model-based and model-free multipoint genome-wide linkage analysis of alcoholism.

We analyzed a subset of the Collaborative Study on the Genetics of Alcoholism (COGA) data set as provided by the 11th Genetic Analysis Workshop (GAW11). Linkage analyses were performed using each of the diagnostic criteria for alcoholism included in the data: the COGA criteria (DSM-III-R plus the Feighner criteria) and the narrower World Health Organization diagnosis ICD-10 criteria. Formal segregation analysis using these data was not attempted because only a subset of all the originally ascertained families was made available. Nevertheless, an attempt was made to estimate the best one-locus two-allele genetic model for these data. Model-based multipoint linkage analysis was performed using the results of our trait model fitting, and model-free multipoint linkage analysis was performed with an improved version of the Haseman and Elston linkage method for sib pairs.

Improving the power for disease locus detection in affected-sib-pair studies by using two-locus analysis and multiple regression methods.

In this paper we present a summary of an analysis of the simulated data (Problem 2) for GAW11. We used sib-pair and affected-sib-pair (ASP) methods to evaluate linkage to the mild form of disease at markers across the genome, in data sets of realistic moderate size (containing between 100 and 300 families selected from the simulated replicates). The true 'answers' were known in advance. Although in most cases we were successful in detecting linkage to disease in the correct regions, it was often difficult to distinguish these results from false positives elsewhere in the genome. We used two-locus methods to see whether the significance was improved by simultaneously modeling linkage to two disease loci, and found a modest increase in significance using two-locus methods in several cases.

Exact transmission-disequilibrium tests with multiallelic markers.

The transmission-disequilibrium (TD) test is a powerful method for detecting linkage between marker and disease loci in the presence of linkage disequilibrium. For multiallelic markers, we propose the use of exact tests, which are implemented using both an exact algorithm and Markov chain Monte Carlo simulation. Simulation studies show that exact tests improve both the small sample validity and the power of the TD method. We also compared the usual single-affected-offspring sampling scheme to one in which pairs of affected siblings are sampled. Affected-sib-pair sampling greatly increases the power of the TD method and will be most useful when a sample of affected sib pairs is available from prior linkage studies.