Genetic variance components estimation for binary traits using multiple related individuals

Understanding and modeling genetic or nongenetic factors that influence susceptibility to complex traits has been the focus of many genetic studies. Large pedigrees with known complex structure may be advantageous in epidemiological studies since they can significantly increase the number of factors whose influence on the trait can be estimated. We propose a likelihood approach, developed in the context of generalized linear mixed models, for modeling dichotomous traits based on data from hundreds of individuals all of whom are potentially correlated through either a known pedigree or an estimated covariance matrix. Our approach is based on a hierarchical model where we first assess the probability of each individual having the trait and then formulate a likelihood assuming conditional independence of individuals. The advantage of our formulation is that it easily incorporates information from pertinent covariates as fixed effects and at the same time takes into account the correlation between individuals that share genetic background or other random effects. The high dimensionality of the integration involved in the likelihood prohibits exact computations. Instead, an automated Monte Carlo expectation maximization algorithm is employed for obtaining the maximum likelihood estimates of the model parameters. Through a simulation study we demonstrate that our method can provide reliable estimates of the model parameters when the sample size is close to 500. Implementation of our method to data from a pedigree of 491 Hutterites evaluated for Type 2 diabetes (T2D) reveal evidence of a strong genetic component to T2D risk, particularly for younger and leaner cases.     

Empirical significance values for linkage analysis: trait simulation using posterior model distributions from MCMC oligogenic segregation analysis

Variance-components (VC) linkage analysis is a powerful model-free method for assessing linkage, but the distribution of VC logarithm of the odds ratio (LOD) scores may deviate substantially from the assumed asymptotic distribution. Typically, the null distribution of the VC-LOD score and other linkage statistics has been estimated by generating new genotype data independently of the trait data, and computing a linkage statistic for many such marker-simulated data sets. However, marker simulation is susceptible to errors in the assumed marker and map model and is computationally intensive. Here, we describe a method for generating posterior distributions of linkage statistics through simulation of trait data based on the original sample and on results from an initial scan using a Bayesian Markov-chain Monte Carlo (MCMC) approach for oligogenic segregation analysis. We use samples of oligogenic trait models taken from the posterior distribution to generate new samples of trait data, which were paired with the original marker data for analysis. Empirical P-values obtained from trait and marker simulation were similar when derived for several strong linkage signals from published linkage scans, and for analysis of data with a known, simulated, trait model. Furthermore, trait simulation produces the expected null distribution of VC-LOD scores and is computationally fast when marker identity-by-descent estimates from the original data could be reused. These results suggest that trait simulation gives valid estimates of statistical significance of linkage signals. Finally, these results also demonstrate the feasibility of obtaining empirical significance levels for evaluating Bayesian oligogenic linkage signals with either marker or trait simulation.     

Genetic Analysis Workshop II: combined segregation, linkage, and association analysis

A combined segregation, linkage, and association analysis using the program COMBIN was performed on the simulated pedigree data prepared for the Second Genetic Analysis Workshop. The model used in COMBIN is described and the presented results illustrate its effectiveness in the analysis of such data. Linkage analysis was performed and maps for each linkage group are presented.     

Analysis of pedigree data in populations with multiple ancestries: Strategies for dealing with admixture in Caribbean Hispanic families from the ADSP

Multipoint linkage analysis is an important approach for localizing disease‐associated loci in pedigrees. Linkage analysis, however, is sensitive to misspecification of marker allele frequencies. Pedigrees from recently admixed populations are particularly susceptible to this problem because of the challenge of accurately accounting for population structure. Therefore, increasing emphasis on use of multiethnic samples in genetic studies requires reevaluation of best practices, given data currently available. Typical strategies have been to compute allele frequencies from the sample, or to use marker allele frequencies determined by admixture proportions averaged over the entire sample. However, admixture proportions vary among pedigrees and throughout the genome in a family‐specific manner. Here, we evaluate several approaches to model admixture in linkage analysis, providing different levels of detail about ancestral origin. To perform our evaluations, for specification of marker allele frequencies, we used data on 67 Caribbean Hispanic admixed families from the Alzheimer's Disease Sequencing Project. Our results show that choice of admixture model has an effect on the linkage analysis results. Variant‐specific admixture proportions, computed for individual families, provide the most detailed regional admixture estimates, and, as such, are the most appropriate allele frequencies for linkage analysis. This likely decreases the number of false‐positive results, and is straightforward to implement.     

Genetic Analysis Workshop II: segregation and linkage analysis

Familial segregation and linkage analyses were performed on two sets of the Genetic Analyses Workshop II data. The salient features of the mode of inheritance of the disease trait and its linkage/association with polymorphic markers and also marker-marker linkages were delineated using statistical-genetic techniques.     

Genetic Analysis Workshop II: segregation and three-locus linkage analysis

Data stimulated for Genetic Analysis Workshop II were analyzed using PAP. Segregation analysis showed a simple recessive mode of inheritance for data set 2 while no conclusions could be made about the mode of inheritance for data set 3. Pairwise linkage analysis suggested three linkage groups, but three-locus analysis did not provide strong evidence for the gene order within these groups. For three of the four three-locus comparisons performed, three-locus analysis suggested the simulated order. In only one case did the pairwise analysis suggest the simulated order, indicating the necessity for multi-locus analysis for gene order.     

Genetic Analysis Workshop II: multiple-locus segregation analysis incorporating linkage markers

The workshop data were examined using a newly developed methodology (MILINK, Risch, 1984) for combined segregation, linkage, and association analysis of a complex disease trait in pedigree data. Results from problems two and three suggest that the method is powerful both for determining mode of disease inheritance and for resolution of linkage disequilibrium versus pleiotrophy (with epistasis) of marker alleles.     

On planning of samples for linkage analysis: Two ways of a sample size reduction

The sample size required for a given type I and type II errors of linkage decision is determined by using the earlier proposed method of the linkage test power estimation [Ginsburg et al., 1996]. Dependence of the sample size on the heterozygotic genotype penetrance is investigated. Two approaches to sample size reduction are considered: the choice of marker gene and the special extension of analyzed pedigree structures. Their effects are quantitatively evaluated in some illustrative situations. It is shown that a practical reduction in sample size can be achieved only when the added part of a pedigree has a special set of phenotypic characteristics in its members. © 1996 Wiley-Liss, Inc.     

Genetic Analysis Workshop II: results of incorporating a linkage disequilibrium parameter

The corporation of a linkage disequilibrium parameter, delta, into linkage analysis is illustrated for data from Genetic Analysis Workshop II. Points from a joint likelihood surface are calculated and displayed on a recombination fraction-linkage disequilibrium grid using a simple modification of LIPED. The approach is shown to increase the power of linkage analysis and the power of tests for heterogeneity of linkage for the simulated examples.     

Haplotype sharing analysis with SNPs in candidate genes: the Genetic Analysis Workshop 12 example

Haplotype sharing analysis was used to investigate the association of affection status with single nucleotide polymorphism (SNP) haplotypes within candidate gene 1 in one sample each from the isolated and the general population of Genetic Analysis Workshop (GAW) 12 simulated data. Gene 1 has direct influence on affection and harbors more than 70 SNPs. Haplotype sharing analysis depends heavily on previous haplotype estimation. Using GENEHUNTER haplotypes, strong evidence was found for most SNPs in the isolated population sample, thus providing evidence for an involvement of this gene, but the maximum -log(10)(p) values for the haplotype sharing statistics (HSS) test statistic did not correspond to the location of the true variant in either population. In comparison, transmission disequilibrium test (TDT) analysis showed the strongest results at the disease-causing variant in both populations, and these were outstanding in the general population. In this example, TDT analysis appears to perform better than HSS in identifying the disease-causing variant, using SNPs within a candidate gene in an outbred population. Simulations showed that the performance of HSS is hampered by closely spaced SNPs in strong linkage disequilibrium with the functional variant and by ambiguous haplotypes.     

Cost-effectiveness analysis of a multinational RCT with a binary measure of effectiveness and an interacting covariate

In a recent multinational randomized clinical trial, 1356 patients from 14 countries were randomized between two arms. The primary measure of effectiveness was 30-day survival. Health care utilization was collected on all patients and was combined with a single country's price weights to provide patient-level cost data. The purpose of this paper is to report the results of the cost-effectiveness analysis for the country that provided the cost weights, so as to provide a case study for illustrating recently proposed methodologies that account for skewed cost data, the between-country variation in treatment effects, possible interactions between treatment and baseline covariates, and the difficulty of estimated adjusted risk differences. A hierarchal model is used to account for the two sources of variation (between country and between patients, within a country). The model, which uses gamma distributions for cost data and recent methods for estimating adjusted risk differences, provides overall and country-specific estimates of treatment effects. Model estimation is facilitated by Markov chain Monte Carlo methods using the WinBUGS software. In addition, the theory of expected value of information is used to determine if the data provided by the trial are sufficient for decision making.     

Genetic Analysis Workshop II: study of Problem 2 linkage relationships by different methods

Segregation and linkage analyse were performed on Problem 2 simulated data. Segregation analysis showed evidence for nearly recessive major susceptibility locus with parameter estimates close to the simulation input values. Linkage between this susceptibility locus (X) and the ten marker loci (A to J) led us to propose the following map: X-G-F-B.     

Genetic Analysis Workshop II: further consideration of segregation and linkage analyses in Problem 3

We analyzed disease-marker associations in Problem 3 for the Genetic Analysis Workshop II, using PAP for segregation analysis and LIPED for linkage analysis. In this report we present aspects of our analyses that are not reported in the summary [MacCluer et al, 1984]. Certain features that we added to the running of LIPED to facilitate the analysis are discussed. Furthermore, we tested for Mendelian transmission in the hypothetical trait locus and we calculated modified relative risks for marker-trait genotypes. Some of the problems involved in analyzing complex associations among loci are discussed.     

Genetic Analysis Workshop II: results of segregation analyses using POINTER and linkage analyses using LIPED

Genetic Analysis Workshop II Problems 2 and 3 were analyzed using the segregation analysis program, POINTER and the linkage analysis program LIPED. Results of the segregation analyses were acceptable with respect to both parameter estimation and hypothesis testing. Results of the linkage analyses were also good. Although it was noted that the linkage and population association data were sometimes compatible with more than one hypothesis, the correct relationships among the trait and marker loci were generally among those found compatible with the data.     

Preliminary Implementation of New Data Mining Techniques for the Analysis of Simulation Data from Genetic Analysis Workshop 12: Problem 2

We introduce a new data mining method applicable to complex disease genetics. Our approach is suited to a broad spectrum of diseases, identifying the noteworthy sharing of combinations of alleles in unrelated affected individuals. Furthermore, this approach may be extended to comprise the common types of genotype data, including single‐nucleotide polymorphisms, candidate‐gene sequences, etc. Using a method derived from data‐mining computer algorithms, we analyze a data set of unrelated affected individuals chosen from the simulated pedigrees of problem 2 of the Genetics Analysis Workshop 12. We observe that most marker subsets containing a flanking marker for each of six or seven of the disease‐gene loci yield significant numbers of individuals manifesting substantially similar genotypes. However, initial attempts (blind to the generating model) to identify the predisposing loci have not been successful. Refining our methods so that such loci may routinely be found and validated is underway. © 2001 Wiley‐Liss, Inc.     

Description of a large pedigree with an adverse lipoprotein cholesterol phenotype: the Bogalusa Heart Study

A large pedigree (N = 356) with a high prevalence of heart disease and associated adverse lipoprotein phenotype was studied. The adverse lipoprotein phenotype is characterized by both low levels of high-density-lipoprotein cholesterol (HDL-C) alone (16.3%) and in combination with other adverse lipoprotein levels (12.8%). In all, 44.2% of all pedigree members had at least one adverse lipoprotein level. Analysis of mating types showed that all lipids and lipoproteins possess familial clustering with 25-36% of offspring above median levels when both parents had levels below the median, while 67-83% had levels above the median when both parents had levels above the median. Using adjusted lipid and lipoprotein levels, a statistically significant linear trend was found between the degree of relationship to pedigree members with heart disease, and both the low-density-lipoprotein cholesterol/high-density-lipoprotein cholesterol (LDL-C/HDL-C) ratio (P less than .05), and the very-low-density-lipoprotein cholesterol (VLDL-C; P less than .01) level. A similar analysis using the prevalence of adverse lipoprotein levels as the dependent variable and degree of relationship to heart diseased pedigree numbers as the independent variable showed significant (P less than .05) relationships with VLDL-C and the LDL-C/HDL-C ratio. Further genetic analyses of this pedigree may reveal genetic mechanisms responsible for the familiality of lipoprotein levels in this pedigree.     

Genetic analysis of Alzheimer's disease: A summary of contributions to GAW8

Participants in the Alzheimer's disease component of GAW8 had access to three collections of pedigrees, complete with marker data from chromosomes 19 and 21. There were a total of 94 independent pedigrees and more than 2,000 individuals. Onset of the disorder varied widely among pedigrees. These data are briefly summarized along with a discussion of the problems associated with performing genetic analyses of Alzheimer's disease. The majority of the workshop participants performed an analysis either with some of the data contributed to the workshop or with data simulated on pedigrees of the same structure and disease status as were contributed. There were also a few purely methodological contributions. The contributions are summarized in three general areas: family association and phenotype, linkage analysis, and heterogeneity tests. © 1993 Wiley-Liss, Inc.     

Twin concordance for a binary trait: III. A bivariate analysis of hay fever and asthma

Self-reported histories of hay fever and asthma were obtained from 3,808 pairs of adult twins 18 years and over registered with the Australian National Health Medical Research Council Twin Registry (1232 MZF, 567 MZM, 751 DZF, 352 DZM, 906 DZO). The prevalence of hay fever and asthma was 0.32 and 0.13, respectively, with little variation with zygosity, sex, and age. The associations between twin pairs for these two traits were analysed, under the assumption of constant prevalences, as a special case of a log-linear model for binary traits in pedigrees using the statistical package GLIM. The model assumption that there are no second- or higher-order interactions was tested in the 2 X 2 X 2 X 2 table of twin by disease outcomes without revealing strong evidence of departure, even in this large data set. The log-linear modelling showed that only three first-order interactions, namely 1) between hay fever in a twin pair, 2) asthma in a twin pair, and 3) hay fever and asthma in the same twin, were necessary to describe the data. The first two interaction terms were significantly larger in identical pairs; the third was independent of zygosity. Under this parsimonious model, there was a significant difference between identical and fraternal pairs in marginal correlation, both in asthma and hay fever, and in the cross-correlation between hay fever in one twin and asthma in the other. This suggests that genetic factors are implicated in both hay fever and asthma and that some of these genetic factors are common (at least among a subgroup of individuals) to both traits.     

The sequential analysis of repeated binary responses: a score test for the case of three time points

In this paper a robust method is developed for the analysis of data consisting of repeated binary observations taken at up to three fixed time points on each subject. The primary objective is to compare outcomes at the last time point, using earlier observations to predict this for subjects with incomplete records. A score test is derived. The method is developed for application to sequential clinical trials, as at interim analyses there will be many incomplete records occurring in non-informative patterns. Motivation for the methodology comes from experience with clinical trials in stroke and head injury, and data from one such trial is used to illustrate the approach. Extensions to more than three time points and to allow for stratification are discussed.     

Genetic analysis of a common oligogenic trait with quantitative correlates: Summary of GAW9 results

The statistical genetic analyses of a simulated data set for Genetic Analysis Workshop 9 Problem 2 are summarized. A diverse set of methods are evaluated with regard to the success with which they were able to determine the mode of inheritance and locate the genes underlying an oligogenically determined disease and four related quantitative traits. © 1995 Wiley-Liss, Inc.