Practical Application of Residuals from Survival Models in Quantitative Trait Linkage Analysis

A number of familial diseases have an age‐of‐onset component, which can be considered as a censored quantitative trait. However, few software resources are available for the use of time‐to‐event endpoints in linkage analysis. The purpose of this analysis was to examine the use of martingale residuals from Cox survival models as quantitative traits for familial diseases with variable age at onset. We used these residuals as quantitative traits in variance components linkage scans for the 50 replicates of the general population simulated data for chromosomes 6 and 7. The region on chromosome 6 containing markers D06G034 and D06G035 demonstrated evidence for linkage, consistent with the underlying genetic model. This analysis demonstrates the applicability of using martingale residuals as a quantitative trait in linkage analyses of diseases that depend on age of onset. © 2001 Wiley‐Liss, Inc.     

Incorporating Age at Onset Information into the Transmission/Disequilibrium Test

In this paper, we proposed two approaches for incorporating the age at onset into the transmission/disequilibrium test (TDT). Trios (affected offspring and their parents) were extracted from the first four replicate data sets of the general population type. Focusing on chromosome 6 where MG6 and MG7 reside, we compared the usual TDT with the newly proposed tests in terms of gene localization. © 2001 Wiley‐Liss, Inc.     

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.

     

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.     

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.     

Sex‐ and Age‐of‐Onset‐Based Locus Heterogeneity in Asthma

Asthma is a complex disease with a genetic component. The results of genome‐wide linkage studies imply that locus heterogeneity is likely to be an important feature of the genetics of asthma. To attempt to reduce locus heterogeneity, we hypothesized that the following may form the bases for locus heterogeneity at some asthma susceptibility loci: sex of affected individuals, parental origin of alleles shared by affected sib pairs, and age of onset of wheeze. Analysis of such strata may assist in the identification of novel susceptibility loci, or reveal the basis for locus heterogeneity at previously identified loci. Genotype and phenotype data from genome‐wide linkage searches for asthma susceptibility loci from three populations were analyzed. Some regions demonstrated evidence for linkage to affected individuals of a particular sex. There was evidence for excess maternal allele sharing at regions on chromosomes 9 and 11. Regions on chromosomes 2 and 6 were linked to late and early age at onset of wheeze in asthma, respectively. These analyses suggest that the bases that we selected for stratification may be appropriate at certain susceptibility loci for asthma, and may therefore assist in the fine mapping of such loci. Differences in such variables between studies may explain apparent nonreplication of linkage results. © 2001 Wiley‐Liss, Inc.     

Estimating effects of probands' characteristics on familial risk: I. Adjustment for censoring and correlated ages at onset.

Family studies with age at onset of the disease as the endpoint face two important problems: censoring and correlation of age at onset among relatives. We present a multivariate survival model for ages at onset of relatives which incorporates the problems cited above. The interpretations of regression coefficients and association parameter in the context of family studies are emphasized. The present paper describes a statistical method for estimating these parameters. In a companion paper [Pulver and Liang, Genet Epidemiol 8:339-350, 1991] this model is applied to a genetic epidemiologic study of schizophrenia.     

Tests for genetic association using family data.

We use likelihood-based score statistics to test for association between a disease and a diallelic polymorphism, based on data from arbitrary types of nuclear families. The Nonfounder statistic extends the transmission disequilibrium test (TDT) to accommodate affected and unaffected offspring, missing parental genotypes, phenotypes more general than qualitative traits, such as censored survival data and quantitative traits, and residual correlation of phenotypes within families. The Founder statistic compares observed or inferred parental genotypes to those expected in the general population. Here the genotypes of affected parents and those with many affected offspring are weighted more heavily than unaffected parents and those with few affected offspring. We illustrate the tests by applying them to data on a polymorphism of the SRD5A2 gene in nuclear families with multiple cases of prostate cancer. We also use simulations to compare the power of these family-based statistics to that of the score statistic based on Cox's partial likelihood for censored survival data, and find that the family-based statistics have considerably more power when there are many untyped parents. The software program FGAP for computing test statistics is available at http://www.stanford.edu/dept/HRP/epidemiology/FGAP.     

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.     

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.     

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.     

Association and Linkage for Age at Onset of a Common Oligogenic Disease Using Genetic Variance Component Models

The aims of our analysis were: (1) to investigate association of single nucleotide polymorphisms (SNPs) and other covariates with age at onset in the simulated Genetic Analysis Workshop (GAW) 12 general population data, and (2) to use the polygenic random effects estimated during model fitting (sigma squared A random effects) as input to a Haseman‐Elston linkage analysis. The association analyses used genetic variance component models in a generalized linear mixed models framework and were fitted using Gibbs sampling. This method successfully detected the only three sequenced genes that were also major genes. The single‐point linkage analysis used all markers provided. Regions of linkage were found close to all four of the sites of major genes that explained a non‐trivial component of the variance of age at onset. In all four cases the linkage peak fell within 5 cM of the true location. In three cases the peak significance was p < 0.01. © 2001 Wiley‐Liss, Inc.