Measuring and partitioning the high-order linkage disequilibrium by multiple order Markov chains

A map of the background levels of disequilibrium between nearby markers can be useful for association mapping studies. In order to assess the background levels of linkage disequilibrium (LD), multilocus LD measures are more advantageous than pairwise LD measures because the combined analysis of pairwise LD measures is not adequate to detect simultaneous allele associations among multiple markers. Various multilocus LD measures based on haplotypes have been proposed. However, most of these measures provide a single index of association among multiple markers and does not reveal the complex patterns and different levels of LD structure. In this paper, we employ non-homogeneous, multiple order Markov Chain models as a statistical framework to measure and partition the LD among multiple markers into components due to different orders of marker associations. Using a sliding window of multiple markers on phased haplotype data, we compute corresponding likelihoods for different Markov Chain (MC) orders in each window. The log-likelihood difference between the lowest MC order model (MC0) and the highest MC order model in each window is used as a measure of the total LD or the overall deviation from the gametic equilibrium for the window. Then, we partition the total LD into lower order disequilibria and estimate the effects from two-, three-, and higher order disequilibria. The relationship between different orders of LD and the log-likelihood difference involving two different orders of MC models are explored. By applying our method to the phased haplotype data in the ENCODE regions of the HapMap project, we are able to identify high/low multilocus LD regions. Our results reveal that the most LD in the HapMap data is attributed to the LD between adjacent pairs of markers across the whole region. LD between adjacent pairs of markers appears to be more significant in high multilocus LD regions than in low multilocus LD regions. We also find that as the multilocus total LD increases, the effects of high-order LD tends to get weaker due to the lack of observed multilocus haplotypes. The overall estimates of first, second, third, and fourth order LD across the ENCODE regions are 64, 23, 9, and 3%.     

Under‐reported data analysis with INAR‐hidden Markov chains

In this work, we deal with correlated under‐reported data through INAR(1)‐hidden Markov chain models. These models are very flexible and can be identified through its autocorrelation function, which has a very simple form. A naïve method of parameter estimation is proposed, jointly with the maximum likelihood method based on a revised version of the forward algorithm. The most‐probable unobserved time series is reconstructed by means of the Viterbi algorithm. Several examples of application in the field of public health are discussed illustrating the utility of the models. Copyright © 2016 John Wiley & Sons, Ltd.     

Contrasting linkage disequilibrium as a multilocus family‐based association test

Linkage disequilibrium (LD) of genetic loci is routinely estimated and graphically illustrated in genetic association studies. It has been suggested that the information in LD is also useful for association mapping and genetic association can be detected by comparing LD patterns between cases and controls. Here, we extend this idea to analyze case‐parents data by comparing LD patterns between transmitted and nontransmitted genotypes. We provide the condition when contrasting LD is valid for testing gene‐gene interactions. A permutation procedure is given to assess statistical significance. One advantage of our proposed methods is that haplotype information is not required. Thus, the implementation of our methods is straightforward and the resulted tests are free from potential bias caused by assumptions made to estimate haplotypes in silico. Since our test statistics use pairwise LD measurements, they are less affected by missing data than many other multilocus methods. With simulated data, we demonstrate that examining LD patterns of case‐parents data is a useful multilocus association mapping strategy and it complements existing association mapping methods. The application of our methods to a Crohn's disease data set shows that our methods can detect multilocus association that might be missed by other association methods. Our permutation procedure can also be modified to allow multiple offspring from a family to be analyzed. Genet. Epidemiol. 2011. © 2011 Wiley‐Liss, Inc. 35: 487‐498, 2011     

Multipoint linkage disequilibrium mapping with particular reference to the African‐American population

A new approach to scanning the genome is presented to detect linkage disequilibrium caused specifically by population admixture. In contrast to current linkage genome scanning methods to find causal genes for complex diseases, this new method should be powerful to find genes for multilocus traits, particularly those genes that lead to the highest population attributable risk. Such a scan using the African‐American population is generally feasible for mapping common diseases. A conservative threshold is also provided for such association mapping. Genet. Epidemiol. 17:79–101, 1999. © 1999 Wiley‐Liss, Inc.     

Relatedness mapping and tracts of relatedness for genome‐wide data in the presence of linkage disequilibrium

Estimates of relatedness have several applications such as the identification of relatives or in identifying disease related genes through identity by descent (IBD) mapping. Here we present a new method for identifying IBD tracts among individuals from genome‐wide single nucleotide polymorphisms data. We use a continuous time Markov model where the hidden states are the number of alleles shared IBD between pairs of individuals at a given position. In contrast to previous methods, our method accurately accounts for linkage disequilibrium using pairwise haplotype probabilities. The method provides a map of the local relatedness along the genome. We illustrate the potential of the method for mapping disease genes on a real data set, and show that the method has the potential to map causative disease mutations using only a handful of affected individuals. The new IBD mapping method provides considerable improvement in mapping power in natural populations compared to standard association mapping methods. Genet. Epidemiol. 2009. © 2008 Wiley‐Liss, Inc.     

Bounds and normalization of the composite linkage disequilibrium coefficient

The composite linkage disequilibrium (LD) measure is often calculated for two-locus genotypic data, especially when coupling and repulsion double heterozygotes cannot be distinguished. This measure was reported to have good statistical properties and was suggested for routine testing of LD, regardless of Hardy-Weinberg equilibrium at either of two loci. However, the bounds for this measure have not been yet reported. These bounds are derived here as functions of one-locus genotype or allele frequencies. They provide standardized measures of composite linkage disequilibrium, defined as the proportion of its maximum attainable value, given observed allele or genotype frequencies.     

Comparing the power of linkage detection by the transmission disequilibrium test and the identity-by-descent test

The aim of this study is to compare the power of the transmission disequilibrium test (TDT) to that of the identity-by-descent (IBD) distribution test. The relative powers of these tests depend both on the underlying genetic model and on the available family data. Families with two affected sibs are always more informative than those with one affected child and one unaffected child. The IBD test is always more powerful in the first situation and, contrary to the TDT, is independent of the presence of gametic disequilibrium. When there is strong linkage disequilibrium, the TDT can be more powerful than the IBD test. In that case, linkage can be detected by the TDT even in families with only one affected child. ©1995 Wiley-Liss, Inc.     

Extent and distribution of linkage disequilibrium in the Old Order Amish

Knowledge of the extent and distribution of linkage disequilibrium (LD) is critical to the design and interpretation of gene mapping studies. Because the demographic history of each population varies and is often not accurately known, it is necessary to empirically evaluate LD on a population‐specific basis. Here we present the first genome‐wide survey of LD in the Old Order Amish (OOA) of Lancaster County Pennsylvania, a closed population derived from a modest number of founders. Specifically, we present a comparison of LD between OOA individuals and US Utah participants in the International HapMap project (abbreviated CEU) using a high‐density single nucleotide polymorphism (SNP) map. Overall, the allele (and haplotype) frequency distributions and LD profiles were remarkably similar between these two populations. For example, the median absolute allele frequency difference for autosomal SNPs was 0.05, with an inter‐quartile range of 0.02–0.09, and for autosomal SNPs 10–20 kb apart with common alleles (minor allele frequency≥0.05), the LD measure r² was at least 0.8 for 15 and 14% of SNP pairs in the OOA and CEU, respectively. Moreover, tag SNPs selected from the HapMap CEU sample captured a substantial portion of the common variation in the OOA (～88%) at r²≥0.8. These results suggest that the OOA and CEU may share similar LD profiles for other common but untyped SNPs. Thus, in the context of the common variant‐common disease hypothesis, genetic variants discovered in gene mapping studies in the OOA may generalize to other populations. Genet. Epidemiol. 34: 146–150, 2010. © 2009 Wiley‐Liss, Inc.     

A modified forward multiple regression in high‐density genome‐wide association studies for complex traits

Genome‐wide association studies (GWAS) have been widely used to identify genetic effects on complex diseases or traits. Most currently used methods are based on separate single‐nucleotide polymorphism (SNP) analyses. Because this approach requires correction for multiple testing to avoid excessive false‐positive results, it suffers from reduced power to detect weak genetic effects under limited sample size. To increase the power to detect multiple weak genetic factors and reduce false‐positive results caused by multiple tests and dependence among test statistics, a modified forward multiple regression (MFMR) approach is proposed. Simulation studies show that MFMR has higher power than the Bonferroni and false discovery rate procedures for detecting moderate and weak genetic effects, and MFMR retains an acceptable‐false positive rate even if causal SNPs are correlated with many SNPs due to population stratification or other unknown reasons. Genet. Epidemiol. 33:518–525, 2009. © 2009 Wiley‐Liss, Inc.     

Multilocus linkage disequilibrium mapping by the decay of haplotype sharing with samples of related individuals

We consider the problem of multilocus linkage disequilibrium (LD) mapping of a trait-associated variant from case-control samples in which some individuals may be related. Our method, which we call DHS-R, is an extension of the decay of haplotype sharing (DHS) method of McPeek and Strahs and Strahs and McPeek. The DHS-R method shares the main features of the DHS method: (1) it allows construction of a confidence interval for the location of a trait-associated variant; (2) it allows for missing observations and unphased genotype data, with the uncertainty in the haplotypes taken into account in the analysis; and (3) it allows for heterogeneity, mutation, recombination, and background LD. The main advances of the DHS-R are (1) the ability to include individuals of arbitrary known relationship (including inbreeding) in the case and control samples; (2) an extension to allow partially-phased haplotypes derived from case-parent trio genotype data; and (3) an extension to allow for genotyping error in the model. Our method, which uses a hidden Markov model for likelihood calculation and maximization, has the advantage of being computationally feasible even in a large, complex pedigree. Simulations based on a 13-generation, 1,623-member Hutterite pedigree demonstrate accurate coverage of the confidence intervals for location of the variant. We apply the method to fine-mapping of a susceptibility locus for bronchial hyperresponsiveness (BHR) in the Hutterites. The results confirm the importance of taking into account the relatedness of individuals in LD mapping.     

A multiple imputation approach to disclosure limitation for high‐age individuals in longitudinal studies

Disclosure limitation is an important consideration in the release of public use data sets. It is particularly challenging for longitudinal data sets, since information about an individual accumulates with repeated measures over time. Research on disclosure limitation methods for longitudinal data has been very limited. We consider here problems created by high ages in cohort studies. Because of the risk of disclosure, ages of very old respondents can often not be released; in particular, this is a specific stipulation of the Health Insurance Portability and Accountability Act (HIPAA) for the release of health data for individuals. Top‐coding of individuals beyond a certain age is a standard way of dealing with this issue, and it may be adequate for cross‐sectional data, when a modest number of cases are affected. However, this approach leads to serious loss of information in longitudinal studies when individuals have been followed for many years. We propose and evaluate an alternative to top‐coding for this situation based on multiple imputation (MI). This MI method is applied to a survival analysis of simulated data, and data from the Charleston Heart Study (CHS), and is shown to work well in preserving the relationship between hazard and covariates. Copyright © 2010 John Wiley & Sons, Ltd.     

Two common polymorphisms in the APO A-IV coding gene: their evolution and linkage disequilibrium.

Human apolipoprotein A-IV (APO A-IV) exhibits a common protein polymorphism detectable by isoelectric focusing (IEF) due to a single base substitution at codon 360 which replaces the frequently occurring glutamine residue (allele 1) with histidine (allele 2). Recently, sequence analysis of the APO A-IV coding region has revealed another common nucleotide substitution at codon 347 which converts the commonly present threonine residue (allele A) into serine (allele T). In order to investigate the extent of genetic variation at codon 347, we screened DNA samples from 192 unrelated individuals using a polymerase chain reaction based assay. The frequencies of the two alleles, A-IV*A and A-IV*T, were 0.81 and 0.19, respectively, with average heterozygosity 0.31. Genetic screening of the corresponding 192 plasma samples by IEF gave frequencies of 0.922 and 0.078 for the A-IV*1 and A-IV*2 alleles, respectively, at codon 360 with average heterozygosity 0.14. Genotype data at the two polymorphic sites were used to assign unequivocal haplotypes to all the 384 chromosomes. Of the expected four haplotypes (A1, T1, A2, and T2) only three were observed and their frequencies were 0.732 for A1, 0.190 for T1 and 0.078 for A2, with average heterozygosity 0.42. Although our data indicate significant linkage disequilibrium between the two sites (chi 21 = 7.65, P < 0.006, standardized disequilibrium constant phi = -0.14) the degree of nonrandom association varied between alleles at the two sites. Based upon allele frequency data and variable linkage disequilibrium between alleles, we propose that the A2 and T1 haplotypes may have evolved from the parental A1 haplotype by two independent mutations.     

A linkage analysis of the Gm locus and multiple sclerosis

We conducted linkage analyses of immunoglobulin G heavy chain marker (Gm) phenotypes and multiple sclerosis (MS) in 30 families, each having at least two first-degree relatives with definite/probable MS. These families yielded positive evidence for linkage to human leukocyte antigen (HLA) loci in previous analyses. In the present analysis, however, the results for Gm were negative. Most lod scores were negative, particularly at the smaller recombination values (theta). We explored the possibility of heterogeneity by subgrouping our data on the basis of specific HLA types (A3, B7) and Gm types (Gm1, Gm1,2) within the pedigrees. The results were again negative with no substantial differences in estimates of theta between subgroups.     

Re‐structuring the negotiated order of the hospital

Researchers continue to lament the lack of organisational focus in the sociology of health and illness. Although studies have increasingly focused on boundaries between organizations, little such research has focused on the formal boundaries within the hospital itself. Given its dramatic compartmentalisation, and continuing prevalence in health systems, the lack of organisational perspective in hospital research limits insights into the effects (as well as the construction) of the order of health work and care. With a greater emphasis on ‘ordering’ in the concept of negotiated order, the aim of this study is to examine the manifestation and consequences of the formal boundaries of hospital departments. Fieldwork featured 12 months of ethnography, including formal and informal observations, 80 audio‐recorded, semi‐structured interviews, and 56 field interviews, in the Emergency Departments (EDs) of two tertiary referral hospitals. Compared with in‐patient hospital departments, the ED has limited legitimacy claims of organ‐specific knowledge to transfer patients out of the ED. The manifestation of specialised knowledge hierarchies in organisational structures disadvantages patients who are older and who have chronic conditions, underpinning the argument that effects as well as the negotiation of stable organisational orders deserve increased attention in the sociology of health and illness.     

A logistic regression extension of the transmission disequilibrium test for continuous traits: application to linkage disequilibrium between alcoholism and the candidate genes DRD2 and ADH3

The transmission disequilibrium test (TDT) recently has become a popular method of testing for linkage in the presence of association due to its simplicity and advantages over other within-family analytic methods. In this paper, we describe a logistic regression extension to the TDT that can be used to test for differences in linkage disequilibrium as a function of one or more continuous and/or categorical explanatory variables. We highlight important features of this method and demonstrate some of its possible uses. We applied these analyses to test for linkage disequilibrium between the dopamine receptor D2 (DRD2) and alcohol dehydrogenase 3 (ADH3) genes and both diagnostic and quantitative indices of alcoholism. Using data from the Collaborative Study on the Genetics of Alcoholism data set, we found evidence suggesting linkage disequilibrium between DRD2 and ADH3 and quantitative indices of alcoholism and correlated phenotypes corresponding to smoking and personality. None of the evidence for linkage disequilibrium varied by sex or age.     

A joint logistic regression and covariate‐adjusted continuous‐time Markov chain model

The use of longitudinal measurements to predict a categorical outcome is an increasingly common goal in research studies. Joint models are commonly used to describe two or more models simultaneously by considering the correlated nature of their outcomes and the random error present in the longitudinal measurements. However, there is limited research on joint models with longitudinal predictors and categorical cross‐sectional outcomes. Perhaps the most challenging task is how to model the longitudinal predictor process such that it represents the true biological mechanism that dictates the association with the categorical response. We propose a joint logistic regression and Markov chain model to describe a binary cross‐sectional response, where the unobserved transition rates of a two‐state continuous‐time Markov chain are included as covariates. We use the method of maximum likelihood to estimate the parameters of our model. In a simulation study, coverage probabilities of about 95%, standard deviations close to standard errors, and low biases for the parameter values show that our estimation method is adequate. We apply the proposed joint model to a dataset of patients with traumatic brain injury to describe and predict a 6‐month outcome based on physiological data collected post‐injury and admission characteristics. Our analysis indicates that the information provided by physiological changes over time may help improve prediction of long‐term functional status of these severely ill subjects. Copyright © 2017 John Wiley & Sons, Ltd.