Analytic strategies to detect linkage to a common disorder with genetically determined age of onset: Diabetes mellitus in Pima Indians

Segregation analysis suggests that the high prevalence of non-insulin-dependent diabetes mellitus in Pima Indians may be partially due to a single locus with a major effect on age of onset. A simulation study was conducted to evaluate the power of various age-adjustment strategies in linkage analysis to detect this putative gene in 1,862 sib-pairs from 264 potentially informative nuclear families. Simulations were performed at a recombination fraction (θ) of 0.05 for values of polymorphism information content (PIC) ranging from 0.38 to 1.00. Under the codominant age-of-onset model supported by segregation analysis, power to detect linkage (at P < 0.0001) at PIC = 1.00 was 75% for the Haseman-Elston (HE) sib-pair test and 63% for the affected sib-pair test (ASP) with no age adjustment. Substantial improvements in power were possible for the HE test by defining the trait as a survival analysis "residual" (power = 91%) and for the ASP test by use of an age-of-onset threshold above which individuals are not included in the analysis (power = 90%, for age of onset < 45 yrs). The parametric method of linkage analysis was most powerful, as long as both the analysis model and the simulation model involved a genetic effect on age of onset, regardless of whether dominance at the trait locus was misspecified. Methods of age adjustment based on the probability of eventually becoming affected only improved power when the genetic effect was on susceptibility rather than age of onset. The method of age adjustment in linkage analysis may depend on whether one anticipates a genetic effect primarily on age of onset or on ultimate susceptibility. Genet. Epidemiol. 15:299–315, 1998. © 1998 Wiley-Liss, Inc. This article is a US Government work and, as such, is in the public domain in the United States of America.     

Assessing genetic effects in survival data by correlating martingale residuals with an application to age at onset of Huntington disease

Genetic models for survival data are hard to formulate and hard to fit. For example, the popular gamma-frailty model for sib-pair data does not generalize easily to extended pedigrees and is not easy to fit. In this paper we show how martingale residuals from a (marginal) Cox model can be employed to estimate the presence of a genetic effect and to estimate genetic correlations depending on the genetic distance (kinship). The methodology is applied to age at onset of Huntington disease (HD) in carriers of the HD gene. The number of CAG repeats in the HD gene is a well-known predictor for age at onset of the disease. However, there is an indication that other genes might be involved as well; leading to unexplained familial clustering. Using our methodology, we found a clearly significant genetic association between the martingale residuals with correlations of about 0.6 for relatives that share 50 per cent of their genes (sib-pairs and parent-child) and about 0.3 for relatives that share 25 per cent of their genes (grandparent-grandchild, uncle/aunt-niece/nephew).     

Estimating familial effects on age at onset and liability to schizophrenia. II. Adjustment for censored data

Genetic studies of disorders with adult onset often contain individuals who have not completed their age at risk when last observed. Without correction for such censoring, correlation in ages at onset among relatives is substantially underestimated. Moreover, without correction for the effect of correlated ages at onset, the relationship between age at onset in the proband and liability in relatives is substantially overestimated. The present paper describes methods for correcting the effects of censoring on these estimates. In a companion paper [Kendler and MacLean, Genet Epidemiol 7:409-417, 1990] these methods are applied to a large family study of schizophrenia.     

Genomewide linkage scan reveals novel loci modifying age of onset of Huntington's disease in the Venezuelan HD kindreds

The age of onset of Huntington's disease (HD) is inversely correlated with the CAG length in the HD gene. The CAG repeat length accounts for 70% of the variability in HD age of onset. However, 90% of individuals worldwide with expanded alleles possess between 40 and 50 CAG repeat lengths in their HD gene. For these people, the size of their repeat only determines 44% of the variability in their age of onset. Once the effect of the CAG repeat has been accounted for, the residual variance in age of onset is a heritable trait. Targeted candidate gene studies and a genome scan have suggested some loci as potential modifiers of the age of onset of HD. We analyzed the large Venezuelan kindreds in which the HD gene was originally identified. These kindreds offer greater analytic power than standard sib-pair designs. We developed novel pedigree-member selection procedures to maximize power. Using a 5,858-single-nucleotide-polymorphism marker panel, we performed a genomewide linkage analysis. We discovered two novel loci on chromosome 2. Chromosome 2p25 (logarithm of the odds ratio (LOD)=4.29) and 2q35 (LOD=3.39) may contain genes that modify age of onset. A third linkage peak on chromosome 6q22 (LOD=2.48) may confirm the most promising locus from a previous genome scan. Two other candidate loci are suggestive on chromosome 5 (LOD=3.31 at 5p14 and LOD=3.14 at 5q32). All these regions harbor candidate genes that are potential HD modifier genes. Finding these modifier genes can reveal accessible and promising new therapeutic pathways and targets to ameliorate and cure HD.     

Genetic association tests with age at onset

Many diseases or traits exhibit a varying age at onset. Recent data examples of prostate cancer and childhood diabetes show that compared to simply treating the disease outcome as affected vs. unaffected, incorporation of age-at-onset information into the transmission/disequilibrium type of test (TDT) does not appear to change the results much. In this paper, we evaluate the power of TDT as a function of age at onset, and show that age-at-onset information is most useful when the disease is common, or the relative risk associated with the high-risk genotype varies with age. Moreover, an extremely old unaffected subject can contribute substantially to the power of the TDT, sometimes as much as old-onset subjects. We propose a modified test statistic for testing no association between the marker at the candidate locus and age at onset. The simulation study was conducted to evaluate the finite sample properties of proposed and the TDT test statistics under various sampling schemes for trios of parents and offspring, as well as for sibling clusters where unaffected siblings were used as controls.     

Two-stage global search designs for linkage analysis using pairs of affected relatives

We investigate the two-stage procedure proposed by Elston [(1992) Proceedings of the XVIth International Biometric Conference, Hamilton, New Zealand, December 7–11, 1992, pp 39–51, and (1994) “Genetic Approaches to Mental Disorders.” Washington, DC: American Psychiatric Press, pp 3–21] for performing a global search of the genome to locate disease genes by linkage analysis using affected relative pairs. The optimal design depends on the type of pairs studied, the effect of the disease locus, the relative costs of recruiting affected persons and typing markers, how informative the markers are, and the amount of genetic heterogeneity. It is specified by the initial number of markers to use, the number of affected relative pairs to study, the initial significance level α^* to use at the first stage, and the number of flanking markers to use at the second stage around markers significant at the first stage. Asymptotically, the optimal design does not depend separately on either the desired final significance level or power, but rather on a function of the two. Both as the effect of the disease locus increases and as the relative cost of recruiting a subject increases, the optimal number of initial markers increases and the optimal number of pairs decreases. The expected cost of the study decreases as the effect of the disease locus increases, but increases as the relative cost of recruiting a subject increases. The optimal initial number of markers decreases but the number of pairs increases when there is genetic heterogeneity present; conversely, the optimal initial number of markers increases when markers are less than fully informative. Compared to a one-stage procedure, a two-stage procedure typically halves the cost of a study. © 1996 Wiley-Liss, Inc.     

Estimating familial effects on age at onset and liability to schizophrenia. I. Results of a large sample family study

Previous analyses of age at onset in schizophrenia, which is highly variable and appears to be influenced by familial factors, have neglected to consider either (1) the impact of censoring on correlations in age at onset in affected relatives or (2) the impact of correlated ages at onset on the relationship between age at onset in the proband and risk in relatives. In this report, using methods outlined in the companion paper [MacLean et al., Genet Epidemiol 7:419-426, 1990] we examine these questions in the large family data set of schizophrenia collected by Lindelius [Acta Psychiat Scand (Suppl) 216:1-125, 1970]. Ages at onset are positively correlated in pairs of affected relatives (parent-offspring approximately equal to siblings greater than nieces/nephews) and these correlations are substantially higher after correction for censoring. Early age at onset is associated with higher risk of illness in siblings and nieces/nephrews but not in children. These results are consistent with the hypothesis that age at onset in schizophrenia is influenced by familial factors which are probably genetic and which are mostly unrelated to factors influencing disease liability.     

Removing phenotypic distribution assumptions from tests of linkage disequilibrium for quantitative traits

The transmission disequilibrium test (TDT) has become a family-based method of reference to search for linkage disequilibrium (LD). Although it was first developed for dichotomous traits, numerous approaches have extended the TDT to quantitative phenotypes that either rely on regression or variance component techniques. Both of these approaches are based on some phenotypic distribution assumptions, the violation of which can lead to inflation of type I error rates, and derive information from phenotypic variability, so that their power is very low under some selection schemes (e.g., one-tailed selection). We propose a new family-based test of association for quantitative traits, denoted maximum-likelihood-binomial (MLB)-QTDT, which addresses the two previous issues by incorporating a latent binary variable that captures the LD information between the marker allele and the quantitative phenotype. The method can be understood as a classical TDT for binary traits that would include pure affected and pure unaffected children, and the probability for a child to be affected or unaffected depends on his/her quantitative phenotypic value. Simulation studies under the null hypothesis show that the MLB-QTDT provides very consistent type I errors even in small and/or selected samples. Under the alternative hypothesis, the MLB-QTDT has good power to analyze one-tailed selected samples, and performs as well as a classical approach in other designs. The MLB-QTDT is a flexible distribution-free method to test for LD with quantitative phenotypes in nuclear families, and can easily incorporate previous extensions developed in the context of family-based association studies with binary traits.     

Extensions to sib-pair linkage tests applicable to disorders characterized by delayed onset

Extensions of the approach to sib-pair linkage tests developed by Haseman and Elston [Behav Genet 2:3-19, 1972] are proposed which incorporate information on age of onset and age at examination. Alternate sources for the age of onset corrections are described, including models for the estimation of parameters associated with the age of onset distribution. Simulation is used to examine the performance of the approach when applied to a dominant disorder of late onset for a range of recombination fractions ranging from very tight linkage to free recombination. For each set of genetic parameters, 2,000 samples of 50 four-member sibships were generated under a complete ascertainment model to investigate power and Type I error, and to compare variants of the proposed technique. Results with and without age-of-onset correction are compared to each other and to those obtainable if penetrance were complete, i.e., if there were no intervening age-of-onset phenomenon. Results from simulation studies show that significance probabilities are enhanced in the presence of linkage when age-of-onset extensions are used. The proposed methods are associated with acceptable levels of Type I error, and substantive gains in power are obtained when data related to age of onset and age at examination are incorporated into the analysis.     

Linkage of Alzheimer's disease to chromosome 21 and chromosome 19 markers: Effect of age of onset assumptions

Age of onset heterogeneity in Alzheimer's disease families was modelled by allowing for different liability classes for affected individuals according to their age of onset when calculating lod scores to chromosome 21 and chromosome 19 markers. Linkage to chromosome 21 was supported in the Boston data set, and the method of age correction did not greatly change the lod scores when only affected individuals were analyzed. The location of a gene on chromosome 19 for late age of onset illness was affected by the assumptions about early onset individuals. © 1993 Wiley-Liss, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

     

Sample size calculations for linkage analysis using extreme sib pairs based on segregation analysis with the quantitative phenotype body weight as an example

One approach to establish linkage is based on allele-sharing methods for sib pairs. Recently, the use of extreme sib pairs (ESP) has been proposed to increase power for mapping quantitative traits in humans. Several approaches have been discussed. In this study, we calculate sample sizes for the various ESP approaches using segregation analyses of quantitative traits. We illustrate this approach by using previously published segregation analyses of body weight despite the fact that the assumptions imposed by these analyses do not hold up for this quantitative phenotype. Genet. Epidemiol. 15:577–593,1998. © 1998 Wiley-Liss, Inc.     

Score test for detecting linkage to complex traits in selected samples

We present a unified approach to selection and linkage analysis of selected samples, for both quantitative and dichotomous complex traits. It is based on the score test for the variance attributable to the trait locus and applies to general pedigrees. The method is equivalent to regressing excess IBD sharing on a function of the traits. It is shown that when population parameters for the trait are known, such inversion does not entail any loss of information. For dichotomous traits, pairs of pedigree members of different phenotypic nature (e.g., affected sib pairs and discordant sib pairs) can easily be combined as well as populations with different trait prevalences.     

A time-dependent logistic hazard function for modeling variable age of onset in analysis of familial diseases

The paper presents an extension of the regressive logistic models proposed by Bonney [Biometrics 42:611-625, 1986], to address the problems of variable age-of-onset and time-dependent covariates in analysis of familial diseases. This goal is achieved by using failure time data analysis methods, and partitioning the time of follow up in K mutually exclusive intervals. The conditional probability of being affected within the kth interval (k = 1...K) given not affected before represents the hazard function in this discrete formulation. A logistic model is used to specify a regression relationship between this hazard function and a set of explanatory variables including genotype, phenotypes of ancestors, and other covariates which can be time dependent. The probability that a given person either becomes affected within the kth interval (i.e., interval k includes age of onset of the person) or remains unaffected by the end of the kth interval (i.e., interval k includes age at examination of the person) are derived from the general results of failure time data analysis and used for the likelihood formulation. This proposed approach can be used in any genetic segregation and linkage analysis in which a penetrance function needs to be defined. Application of the method to familial leprosy data leads to results consistent with our previous analysis performed using the unified mixed model [Abel and Demenais, Am J Hum Genet 42:256-266, 1988], i.e., the presence of a recessive major gene controlling susceptibility to leprosy. Furthermore, a simulation study shows the capability of the new model to detect major gene effects and to provide accurate parameter estimates in a situation of complete ascertainment.     

Robust genetic linkage analysis based on a score test of homogeneity: The weighted pairwise correlation statistic

In testing genetic linkage using large or complex pedigrees, robust methods may be preferred to the Lod-score method. The affected-pedigree-member method is robust but does not use the information available in nonaffected subjects, which results in a loss of power. We propose a new test of genetic linkage based on a score test of homogeneity derived from a random effect model. The statistic is simple and uses only pairs of subjects. In contrast with the affected-pedigree-method, it uses all the available pairs and does not depend on the marker alleles frequencies. A rank version of this weighted pairwise correlation statistic is proposed, its exact first and second moment derived. We show that for age-dependent diseases, it provides a simple nonparametric test. © 1994 Wiley-Liss, Inc.     

Estimating effects of proband characteristics on familial risk: II. The association between age at onset and familial risk in the Maryland schizophrenia sample.

In this report we apply methods outlined in the companion paper [Liang, Genet Epidemiol 8:329-338, 1991] to study the association between proband age at onset and familial risk among first-degree relatives of 374 schizophrenic probands. The analyses take into consideration the potential problems of censoring and correlation of age at onset within families. All analyses were done by gender of the proband; age at onset was dichotomized. The results of the analyses of the male probands suggest that there is an increased risk of schizophrenia among the relatives of male probands who have an onset prior to age 17 when compared to relatives of male probands who have an onset later than 16. We did not find an association between age at onset and familial risk among the female probands, but this may be due to the smaller number of female probands and the lower power associated with the analyses.     

Bivariate survival models for analysis of genetic and environmental effects in twins

Classic methods in genetics for the analysis of binary attributes, based on an assumption of a "threshold" on a normally distributed latent variable called "liability," estimate the strength of genetic and environmental effects from differences in correlations between relatives of differing genetic relatedness. Two problems that are not easily addressed by these methods are the need to take the age of onset into account (particularly in chronic diseases in which incidence rates vary considerably with age and the lengths of time at risk can vary between individuals) and the desirability of incorporating measured covariates (genetic or environmental). The standard methods of cohort analysis used in epidemiology allow for both of these features, but until recently have been restricted to independent individuals. Recent developments in survival analysis have extended the widely used "proportional hazards" model of Cox by the addition of latent variable, epsilon, reflecting the shared susceptibility of related subjects because of their shared genes or shared environment. We show how this approach can be combined with more traditional models of gene-environment interaction to allow the main effects of measured genetic markers and environmental variables to be estimated, as well as the residual variance of genetic and environment and their interactions. The approaches are applied to a cohort of female twin births in Sweden from 1886 to 1958, linked with the Swedish cancer registry from 1961 to 1982.     

The predictive usefulness of age and kind of onset in discriminating psychogenic from organic impotence

It is well known in clinical practice that psychogenic impotence affects younger patients than organic impotence and with a more acute onset. In the present study the authors evaluated the predictive usefulness and discriminating power of the following sociodemographic and clinical variables: age, kind of onset (acute or gradual), civil status, number of partners, duration of illness. The sample was made of 133 patients suffering from erectile dysfunction for at least three months, consecutively admitted to the Multidisciplinary Centre for the Diagnosis and Treatment of Impotence of the Scientific Institute San Raffaele of Milan from May 1992 to April 1993. All patients underwent a thorough clinical and laboratory evaluation: 72 (54.5%) were psychogenic (mean age 42.6±11.2); 60 (45.5%) organic (mean age 56.3±9.8). Stepwise logistic regression model identified age and kind of onset as significant predictors of kind of impotence. According to the logistic regression classification table, sensitivity for psychogenic impotence was 778, specificity was. 750, positive predictive power was .789, and negative predictive power was .738. These results indicate that age and kind of onset proved to be significant predictors of psychogenic impotence and to have a good clinical functioning as both inclusion and exclusion criteria. These results suggest that a patient in his forties and with an acute onset of impotence should be firstly assessed from a psychological point of view; and on the opposite, a 50 year old patient with a gradual onset presents a rationale for a thorough clinical evaluation.     

Risk factors for weight faltering in infancy according to age at onset

Olsen EM, Skovgaard AM, Weile B, Petersen J, Jørgensen T. Risk factors for weight faltering in infancy according to age at onset. Paediatric and Perinatal Epidemiology 2010. The aim of this study was to identify risk factors for failure to thrive (FTT) or weight faltering according to age of onset. The study is part of a Danish longitudinal population study of early risk mechanisms in child psychiatric disorders, The Copenhagen Child Cohort, which consists of a birth cohort of 6090 children born during the year 2000 and followed prospectively from birth. Weight faltering/FTT was defined as slow conditional weight gain, and divided into subtypes according to age of onset in the first year of life: birth to 2 weeks, 2 weeks to 4 months, and 4–8 months. Regardless of the age of onset, slow weight gain was found to be strongly associated with feeding problems, but the risk factors involved differed according to age of onset. Thus, onset within the first weeks of life clearly differed from faltering later on, the former being strongly associated with low birthweight and gestational age, with single parenthood and with mother having smoked during pregnancy. Onset between 2 weeks and 4 months was associated with congenital disorders and serious somatic illness, and with deviant mother–child relationship, whereas, onset between 4 and 8 months seemed to represent a group of children with feeding problems arising de novo in otherwise healthy children. In conclusion, weight faltering in infancy is clearly associated with contemporary measured feeding problems, but the risk mechanisms involved differ in early vs. late onset.     

Mixture models for linkage analysis of affected sibling pairs and covariates.

To determine the genetic etiology of complex diseases, a common study design is to recruit affected sib/relative pairs (ASP/ARP) and evaluate their genome-wide distribution of identical by descent (IBD) sharing using a set of highly polymorphic markers. Other attributes or environmental exposures of the ASP/ARP, which are thought to affect liability to disease, are sometimes collected. Conceivably, these covariates could refine the linkage analysis. Most published methods for ASP/ARP linkage with covariates can be conceptualized as logistic models in which IBD status of the ASP is predicted by pair-specific covariates. We develop a different approach to the problem of ASP analysis in the presence of covariates, one that extends naturally to ARP under certain conditions. For ASP linkage analysis, we formulate a mixture model in which a disease mutation is segregating in only a fraction alpha of the sibships, with 1 - alpha sibships being unlinked. Covariate information is used to predict membership within groups; in this report, the two groups correspond to the linked and unlinked sibships. For an ASP with covariate(s) Z = z and multilocus genotype X = x, the mixture model is alpha(z)g(x; lambda) + [1 - alpha(z)]g(0)(x), in which g(0)(x) follows the distribution of genotypes under the null IBD distribution and g(x; lambda) allows for increased IBD sharing. Two mixture models are developed. The pre-clustering model uses covariate information to form probabilistic clusters and then tests for excess IBD sharing independent of the covariates. The Cov-IBD model determines probabilistic group membership by joint consideration of covariate and IBD values. Simulations show that incorporating covariates into linkage analysis can enhance power substantially. A feature of our conceptualization of ASP linkage analysis, with covariates, is that it is apparent how data analysis might evaluate covariates prior to the linkage analysis, thus avoiding the loss of power described by Leal and Ott [2000] when data are stratified.     

Ordered subset analysis in genetic linkage mapping of complex traits

Etiologic heterogeneity is a fundamental feature of complex disease etiology; genetic linkage analysis methods to map genes for complex traits that acknowledge the presence of genetic heterogeneity are likely to have greater power to identify subtle changes in complex biologic systems. We investigate the use of trait-related covariates to examine evidence for linkage in the presence of heterogeneity. Ordered-subset analysis (OSA) identifies subsets of families defined by the level of a trait-related covariate that provide maximal evidence for linkage, without requiring a priori specification of the subset. We propose that examining evidence for linkage in the subset directly may result in a more etiologically homogeneous sample. In turn, the reduced impact of heterogeneity will result in increased overall evidence for linkage to a specific region and a more distinct lod score peak. In addition, identification of a subset defined by a specific trait-related covariate showing increased evidence for linkage may help refine the list of candidate genes in a given region and suggest a useful sample in which to begin searching for trait-associated polymorphisms. This method provides a means to begin to bridge the gap between initial identification of linkage and identification of the disease predisposing variant(s) within a region when mapping genes for complex diseases. We illustrate this method by analyzing data on breast cancer age of onset and chromosome 17q [Hall et al., 1990, Science 250:1684-1689]. We evaluate OSA using simulation studies under a variety of genetic models.