Assessing familial aggregation of age at onset, by using estimating equations, with application to breast cancer.

In genetic research of chronic diseases, age-at-onset outcomes within families are often correlated. The nature of correlation of age-at-onset outcomes is indicative of common genetic and/or shared environmental risk factors among family members. Understanding patterns of such correlation may shed light on the disease etiology and, hence, is an important step to take prior to further searching for the responsible genes via segregation and linkage studies. Age-at-onset outcomes are different from those familiar quantitative or qualitative traits for which many statistical methods have been developed. In comparison with the quantitative traits, age-at-onset outcomes are often censored, i.e., instead of actual age-at-onset outcomes, only the current ages or ages at death are observed. They are also different from qualitative traits because of their continuity. Because of the complexity of correlated censored outcomes, few methods have yet been developed. A traditional approach is to impose a parametric joint distribution for the correlated age-at-onset outcomes, which has been criticized for requiring a stringent assumption about the entire distribution of age at onset. The purpose of this paper is to describe a method for assessing familial aggregation of correlated age-at-onset outcomes semiparametrically, by use of estimating equations. This method does not require any parametric assumption for modeling the age at onset. The estimates of parameters, including those quantifying the correlation within families, are consistent and have an asymptotic normal distribution that can be used to make inferences. To illustrate this new method, we analyzed two age-at-onset data sets that were obtained from studies conducted in the States of Washington and Hawaii, with the objective of quantifying the familial aggregations of age at onset of breast cancer.     

Linkage analysis for diseases with variable age of onset

We present a method for the multivariate linkage analysis of the age of onset of a disease. The approach allows the incorporation of covariates for the study of gene by environment interactions. It is applicable to general pedigrees. The likelihood of the data is expressed as a function of the number of alleles identical by descent at a marker, the censored ages of onset and disease status, and environmental exposures. In a simulation study, we compare the power to detect linkage under different sampling schemes for either a dominant or recessive trait when approximately 10% of individuals are gene carriers. The majority of the linkage information from a sample of randomly selected sib pairs was retained when the analyses were limited to sibships with one sibling having early-onset disease (<59 years old). Incorporating parental phenotypes could improve the power to detect the gene. When the sample consists of affected sib pairs (ASPs) having variable age of onset, the likelihood ratio (LR) test had higher power than the means (t(2)) test for detecting a locus with a large genetic relative risk (R(g) = 20). However, the power of the two tests was similar when ASPs are selected so that the proband has an early onset of disease. Lastly, the LR test had more power than the t(2) test to detect linkage in the presence of gene by environment interactions.     

Apo-E genotypes and cardiovascular diseases: a sensitivity study using cross-validatory criteria

The Apolipoprotein-E (Apo-E) gene, a gene that produces proteins which help to regulate lipid levels in the bloodstream, is of interest in the study of cardiovascular diseases. An approach to making inferences about the genetic effects of the Apo-E gene has been developed by Glickman and Gagnon (2002). The framework describes the role of genetic and risk factors on the onset ages of multiple diseases, and accounts for the possibility that an individual was censored for reasons related to the diseases of interest. The framework also allows for missing genetic information, so that subjects censored prior to genetic sampling, and therefore missing such information, may still be included in the analysis. We apply an extension to this framework to the original cohort of the Framingham Heart Study for measuring the effects of different Apo-E genotypes on the onset age of various cardiovascular disease events. In particular, we compare the fit of univariate versus multivariate onset age components to the model, whether to incorporate health covariates measured at baseline or at a point later in the study, and whether to assume a heritability model for Apo-E genotype frequencies. The results of the best fitting model are presented.     

Cox regression model with randomly censored covariates

This paper deals with a Cox proportional hazards regression model, where some covariates of interest are randomly right‐censored. While methods for censored outcomes have become ubiquitous in the literature, methods for censored covariates have thus far received little attention and, for the most part, dealt with the issue of limit‐of‐detection. For randomly censored covariates, an often‐used method is the inefficient complete‐case analysis (CCA) which consists in deleting censored observations in the data analysis. When censoring is not completely independent, the CCA leads to biased and spurious results. Methods for missing covariate data, including type I and type II covariate censoring as well as limit‐of‐detection do not readily apply due to the fundamentally different nature of randomly censored covariates. We develop a novel method for censored covariates using a conditional mean imputation based on either Kaplan–Meier estimates or a Cox proportional hazards model to estimate the effects of these covariates on a time‐to‐event outcome. We evaluate the performance of the proposed method through simulation studies and show that it provides good bias reduction and statistical efficiency. Finally, we illustrate the method using data from the Framingham Heart Study to assess the relationship between offspring and parental age of onset of cardiovascular events.     

Application of a rank-based genetic association test to age-at-onset data from the Collaborative Study on the Genetics of Alcoholism study

Association studies of quantitative traits have often relied on methods in which a normal distribution of the trait is assumed. However, quantitative phenotypes from complex human diseases are often censored, highly skewed, or contaminated with outlying values. We recently developed a rank-based association method that takes into account censoring and makes no distributional assumptions about the trait. In this study, we applied our new method to age-at-onset data on ALDX1 and ALDX2. Both traits are highly skewed (skewness > 1.9) and often censored. We performed a whole genome association study of age at onset of the ALDX1 trait using Illumina single-nucleotide polymorphisms. Only slightly more than 5% of markers were significant. However, we identified two regions on chromosomes 14 and 15, which each have at least four significant markers clustering together. These two regions may harbor genes that regulate age at onset of ALDX1 and ALDX2. Future fine mapping of these two regions with densely spaced markers is warranted.     

Score tests of genetic association in the presence of linkage based on the additive genetic gamma frailty model

Nuclear families with multiple affected sibs are often collected for genetic linkage analysis of complex diseases. Once linkage evidence is established, dense markers are often typed in the linked region for genetic association analysis based on linkage disequilibrium (LD). Detection of association in the presence of linkage localizes disease genes more accurately than the methods that rely on linkage alone. However, test of association due to LD in the linked region needs to account for dependency of the allele transmissions to different sibs within a family. In this paper, we define a joint model for genetic linkage and association and derive the corresponding joint survival function of age of onset for the sibs within a sibship. The joint survival function is a function of both the inheritance vector and the genotypes at the candidate marker locus. Based on this joint survival function, we derive score tests for genetic association. The proposed methods utilize the phenotype data of all the sibs and have the advantages of family-based designs which can avoid the potential spurious association caused by population admixture. In addition, the methods can account for variable age of onset or age at censoring and possible covariate effects, and therefore provide important tools for modelling disease heterogeneity. Simulation studies and application to the data sets from the 12th Genetic Analysis Workshop indicate that the proposed methods have correct type 1 error rates and increased power over other existing methods for testing allelic association.     

The amyloid precursor protein locus and very-late-onset Alzheimer disease

Although mutations in the amyloid-beta precursor protein (APP) gene are known to confer high risk of Alzheimer disease (AD) to a small percentage of families in which it has early onset, convincing evidence of a major role for the APP locus in late-onset AD has not been forthcoming. In this report, we have used a covariate-based affected-sib-pair linkage method to analyze the chromosome 21 clinical and genetic data obtained on affected sibships by the National Institute of Mental Health Alzheimer Disease Genetics Initiative. The baseline model (without covariates) gave a LOD score of 0.02, which increases to 1.43 when covariates representing the additive effects of E2 and E4 are added. Larger increases in LOD scores were found when age at last examination/death (LOD score 5.54; P=.000002) or age at onset plus disease duration (LOD score 5.63; P=.000006) were included in the linkage model. We conclude that the APP locus may predispose to AD in the very elderly.     

A tobit variance-component method for linkage analysis of censored trait data

Variance-component (VC) methods are flexible and powerful procedures for the mapping of genes that influence quantitative traits. However, traditional VC methods make the critical assumption that the quantitative-trait data within a family either follow or can be transformed to follow a multivariate normal distribution. Violation of the multivariate normality assumption can occur if trait data are censored at some threshold value. Trait censoring can arise in a variety of ways, including assay limitation or confounding due to medication. Valid linkage analyses of censored data require the development of a modified VC method that directly models the censoring event. Here, we present such a model, which we call the "tobit VC method." Using simulation studies, we compare and contrast the performance of the traditional and tobit VC methods for linkage analysis of censored trait data. For the simulation settings that we considered, our results suggest that (1) analyses of censored data by using the traditional VC method lead to severe bias in parameter estimates and a modest increase in false-positive linkage findings, (2) analyses with the tobit VC method lead to unbiased parameter estimates and type I error rates that reflect nominal levels, and (3) the tobit VC method has a modest increase in linkage power as compared with the traditional VC method. We also apply the tobit VC method to censored data from the Finland-United States Investigation of Non-Insulin-Dependent Diabetes Mellitus Genetics study and provide two examples in which the tobit VC method yields noticeably different results as compared with the traditional method.     

Recursive partitioning models for linkage in COGA data

We have developed a recursive-partitioning (RP) algorithm for identifying phenotype and covariate groupings that interact with the evidence for linkage. This data-mining approach for detecting gene x environment interactions uses genotype and covariate data on affected relative pairs to find evidence for linkage heterogeneity across covariate-defined subgroups. We adapted a likelihood-ratio based test of linkage parameterized with relative risks to a recursive partitioning framework, including a cross-validation based deviance measurement for choosing optimal tree size and a bootstrap sampling procedure for choosing robust tree structure. ALDX2 category 5 individuals were considered affected, categories 1 and 3 unaffected, and all others unknown. We sampled non-overlapping affected relative pairs from each family; therefore, we used 144 affected pairs in the RP model. Twenty pair-level covariates were defined from smoking status, maximum drinks, ethnicity, sex, and age at onset. Using the all-pairs score in GENEHUNTER, the nonparametric linkage tests showed no regions with suggestive linkage evidence. However, using the RP model, several suggestive regions were found on chromosomes 2, 4, 6, 14, and 20, with detection of associated covariates such as sex and age at onset.     

Linkage of type 2 diabetes mellitus and of age at onset to a genetic location on chromosome 10q in Mexican Americans

Since little is known about chromosomal locations harboring type 2 diabetes-susceptibility genes, we conducted a genomewide scan for such genes in a Mexican American population. We used data from 27 low-income extended Mexican American pedigrees consisting of 440 individuals for whom genotypic data are available for 379 markers. We used a variance-components technique to conduct multipoint linkage analyses for two phenotypes: type 2 diabetes (a discrete trait) and age at onset of diabetes (a truncated quantitative trait). For the multipoint analyses, a subset of 295 markers was selected on the basis of optimal spacing and informativeness. We found significant evidence that a susceptibility locus near the marker D10S587 on chromosome 10q influences age at onset of diabetes (LOD score 3.75) and is also linked with type 2 diabetes itself (LOD score 2.88). This susceptibility locus explains 63.8%+/-9.9% (P=. 000016) of the total phenotypic variation in age at onset of diabetes and 65.7%+/-10.9% (P=.000135) of the total variation in liability to type 2 diabetes. Weaker evidence was found for linkage of diabetes and of age at onset to regions on chromosomes 3p, 4q, and 9p. In conclusion, our strongest evidence for linkage to both age at onset of diabetes and type 2 diabetes itself in the Mexican American population was for a region on chromosome 10q.     

Chromosome 14 and late-onset familial Alzheimer disease (FAD)

Familial Alzheimer disease (FAD) is genetically heterogeneous. Two loci responsible for early-onset FAD have been identified: the amyloid precursor protein gene on chromosome 21 and the as-yet-unidentified locus on chromosome 14. The genetics of late-onset FAD is unresolved. Maximum-likelihood, affected-pedigree-member (APM), and sib-pair analyses were used, in 49 families with a mean age at onset ≥60 years, to determine whether the chromosome 14 locus is responsible for late-onset FAD. The markers used were D14S53, D14S43, and D14S52. The LOD score method was used to test for linkage of late-onset FAD to the chromosome 14 markers, under three different models: age-dependent penetrance, an affected-only analysis, and age-dependent penetrance with allowance for possible age-dependent sporadic cases. No evidence for linkage was obtained under any of these conditions for the late-onset kindreds, and strong evidence against linkage (LOD score ≤ –2.0) to this region was obtained. Heterogeneity tests of the LOD score results for the combined group of families (early onset, Volga Germans, and late onset) favored the hypothesis of linkage to chromosome 14 with genetic heterogeneity. The positive results are primarily from early-onset families. APM analysis gave significant evidence for linkage of D14S43 and D14S52 to FAD in early-onset kindreds (P < .02). No evidence for linkage was found for the entire late-onset family group. Significant evidence for linkage to D14S52, however, was found for a subgroup of families of intermediate age at onset (mean age at onset ≥60 years and <70 years). These results indicate that the chromosome 14 locus is not responsible for Alzheimer disease in most late-onset FAD kindreds but could play a role in a subset of these kindreds.     

Heterogeneity analysis of breast cancer families by using age at onset as a covariate.

An extension of the usual mixture model of heterogeneity (two family types, one with and one without linkage) is proposed by introducing age at onset as a covariate. The extended model defines age-dependent penetrances where the exact parametrization of age-at-onset distributions depends on the given genotype and family type (linked or unlinked). This extension was applied to breast cancer families. We postulated that the mean age at onset in individuals affected by the linked gene was lower than the mean age at onset in all other affected individuals. Linkage heterogeneity for breast cancer families was detected at a significance level of .003.     

Chromosome 17q linkage studies of 18 Utah breast cancer kindreds.

In this paper we present linkage results from the analysis of 18 Utah breast cancer kindreds, for three 17q markers. Four kindreds had LOD scores greater than 1.0 for at least one of the marker loci. One of these kindreds has a LOD score of 6.07 with D17S579, and we believe it to be the most informative 17q family reported to date. Among the kindreds which appear unlinked to 17q were an early-onset breast cancer family, a large breast-ovarian family, and a kindred with mixed age at onset. Analysis of individual recombinants in the linked families localizes the BRCA1 gene between THRA1 and D17S579 (Mfd188). A comparison of the Cancer and Steroid Hormone Study (CASH) model and a model which assumes a rare dominant susceptibility locus with low penetrance and no phenocopies stresses the difficulties in assessing linkage if the assumptions of the CASH model in terms of age at onset of breast cancer are not appropriate for the BRCA1 locus. A hypothetical breast cancer pedigree is used to calculate gene carrier probabilities under the CASH model, thereby illustrating some of our concerns regarding the use of this model to detect and exclude 17q linkage in breast cancer families.     

Influences of FTO gene on onset age of adult overweight

FTO affects changes in BMI during both childhood and adulthood. However, its effect on onset age of overweight in adulthood is not known. To address this question, we conducted a study to examine effects of FTO tag SNPs on censored age of overweight in the longitudinal Bogalusa Heart Study (BHS) cohort, which began in 1973–1974. Of participating subjects, 658 whites (308 males and 350 females) with genotype data were selected for the study. The FTO gene was examined by a survival analysis of 30 tag SNPs regarding their association with left, interval and right-censored adult overweight. After adjustment for birth weight and sex, SNP rs9939609 has a small nominal p value of 0.004 for the association with onset age, which has an expected proportion of false positives of 9.6?% after adjusting for multiple tests. It was estimated that genotypes AA, AT and TT have onset age (standard error) of 22.82 (1.07), 28.96 (1.04) and 27.76 (1.04)?years, respectively, for a 50?% cumulative proportion of overweight in the population. Genotypes AA, AT and TT, respectively, have estimated survival probability of 65.8, 78.7 and 76.8?% at the age of 18; and survival probability of 6.5, 11.8 and 10.7?% at the age of 60. The odds ratios of survival beyond age ≥18?years are 0.52 for AA versus AT and 0.58 for AA versus TT. We thus concluded that risk genetic variants at FTO gene can accelerate the onset age and influence the survival odds of overweight in younger adults.     

Cox proportional hazards models with left truncation and time‐varying coefficient: Application of age at event as outcome in cohort studies

When analyzing time‐to‐event cohort data, two different ways of choosing a time scale have been discussed in the literature: time‐on‐study or age at onset of disease. One advantage of choosing the latter is interpretability of the hazard ratio as a function of age. To handle the analysis of age at onset in a principled manner, we present an analysis of the Cox Proportional Hazards model with time‐varying coefficient for left‐truncated and right‐censored data. In the analysis of Northern Manhattan Study (NOMAS) with age at onset of stroke as outcome, we demonstrate that well‐established risk factors may be important only around a certain age span and less established risk factors can have a strong effect in a certain age span.     

Multivariate survival models induced by genetic frailties,with application to linkage analysis

We derive a multivariate survival model for age of onset data of a sibship from an additive genetic gamma frailty model constructed basing on the inheritance vectors, and investigate the properties of this model. Based on this model, we propose a retrospective likelihood approach for genetic linkage analysis using sibship data. This test is an allele-sharing-based test, and does not require specification of genetic models or the penetrance functions. This new approach can incorporate both affected and unaffected sibs, environmental covariates and age of onset or age at censoring information and, therefore, provides a practical solution for mapping genes for complex diseases with variable age of onset. Small simulation study indicates that the proposed method performs better than the commonly used allele-sharing-based methods for linkage analysis, especially when the population disease rate is high. We applied this method to a type 1 diabetes sib pair data set and a small breast cancer data set. Both simulated and real data sets also indicate that the method is relatively robust to the misspecification to the baseline hazard function.     

PARK3 influences age at onset in Parkinson disease: a genome scan in the GenePD study

Parkinson disease (PD) is a late-onset neurodegenerative disorder. The mean age at onset is 61 years, but the disease can range from juvenile cases to cases in the 8th or 9th decade of life. The parkin gene on chromosome 6q and loci on chromosome 1p35-36 and 1p36 are responsible for some cases of autosomal recessive early-onset parkinsonism, but they do not appear to influence susceptibility or variability of age at onset for idiopathic PD. We have performed a genomewide linkage analysis using variance-component methodology to identify genes influencing age at onset of PD in a population of affected relatives (mainly affected sibling pairs) participating in the GenePD study. Four chromosomal loci showed suggestive evidence of linkage: chromosome 2p (maximum multipoint LOD [MaxLOD] = 2.08), chromosome 9q (MaxLOD = 2.00), chromosome 20 (MaxLOD = 1.82), and chromosome 21 (MaxLOD = 2.21). The 2p and 9q locations that we report here have previously been reported as loci influencing PD affection status. Association between PD age at onset and allele 174 of marker D2S1394, located on 2p13, was observed in the GenePD sample (P=.02). This 174 allele is common to the PD haplotype observed in two families that show linkage to PARK3 and have autosomal dominant PD, which suggests that this allele may be in linkage disequilibrium with a mutation influencing PD susceptibility or age at onset of PD.     

Comparison among three approaches for evaluation of sexual precocity in Nellore cattle

Restricted breeding seasons used in beef cattle produce censored data for reproduction traits measured in regard to these seasons. To analyze these data, adequate methods must be used. The objective of this paper was to compare three approaches aiming to evaluate sexual precocity in Nellore cattle. The final data set contained 6699 records of age at first conception (AFC14) (in days) and of heifer pregnancy (HP14) (binary) obtained from females exposed to the bulls for the first time at about 14 months of age. Records of females that did not calve in the following year after being exposed to a sire were considered censored (77.5% of total). The models used to obtain genetic parameters and expected progeny differences (EPDs) were a Weibull mixed and a censored linear model for AFC14 and threshold model for HP14. The mean heritabilities obtained were 0.76 and 0.44, respectively, for survival and censored linear models (for AFC14), and 0.58 for HP14. Ranking and Pearson correlations varied (in absolute values) from 0.54 to 0.99 (considering different percentages of sires selected), indicating moderate changes in the classification. Considering survival analysis as the best selection criterion (that would result in the best response to selection), it was observed that selection for HP14 would lead to a more significant decrease in selection response if compared with selection for AFC14 analysed by censored linear model, from which results were very similar to the survival analysis.     

Model-free linkage analysis with covariates confirms linkage of prostate cancer to chromosomes 1 and 4

As with many complex genetic diseases, genome scans for prostate cancer have given conflicting results, often failing to provide replication of previous findings. One factor contributing to the lack of consistency across studies is locus heterogeneity, which can weaken or even eliminate evidence for linkage that is present only in a subset of families. Currently, most analyses either fail to account for locus heterogeneity or attempt to account for it only by partitioning data sets into smaller and smaller portions. In the present study, we model locus heterogeneity among affected sib pairs with prostate cancer by including covariates in the linkage analysis that serve as surrogate measures of between-family linkage differences. The model is a modification of the Olson conditional logistic model for affected relative pairs. By including Gleason score, age at onset, male-to-male transmission, and/or number of affected first-degree family members as covariates, we detected linkage near three locations that were previously identified by linkage (1q24-25 [HPC1; LOD score 3.25, P=.00012], 1q42.2-43 [PCAP; LOD score 2.84, P=.0030], and 4q [LOD score 2.80, P=.00038]), near the androgen-receptor locus on Xq12-13 (AR; LOD score 3.06, P=.00053), and at five new locations (LOD score > 2.5). Without covariates, only a few weak-to-moderate linkage signals were found, none of which replicate findings of previous genome scans. We conclude that covariate-based linkage analysis greatly improves the likelihood that linked regions will be found by incorporation of information about heterogeneity within the sample.     

Genetic linkage analysis in familial breast and ovarian cancer: results from 214 families. The Breast Cancer Linkage Consortium.

Breast cancer is known to have an inherited component, consistent in some families with autosomal dominant inheritance; in such families the disease often occurs in association with ovarian cancer. Previous genetic linkage studies have established that in some such families disease occurrence is linked to markers on chromosome 17q. This paper reports the results of a collaborative linkage study involving 214 breast cancer families, including 57 breast-ovarian cancer families; this represents almost all the known families with 17q linkage data. Six markers on 17q, spanning approximately 30 cM, were typed in the families. The aims of the study were to define more precisely the localization of the disease gene, the extent of genetic heterogeneity and the characteristics of linked families and to estimate the penetrance of the 17q gene. Under the assumption of no genetic heterogeneity, the strongest linkage evidence was obtained with D17S588 (maximum LOD score [Zmax] = 21.68 at female recombination fraction [theta f] = .13) and D17S579 (Zmax = 13.02 at theta f = .16). Multipoint linkage analysis allowing for genetic heterogeneity provided evidence that the predisposing gene lies between the markers D17S588 and D17S250, an interval whose genetic length is estimated to be 8.3 cM in males and 18.0 cM in females. This position was supported over other intervals by odds of 66:1. The location of the gene with respect to D17S579 could not be determined unequivocally. Under the genetic model used in the analysis, the best estimate of the proportion of linked breast-ovarian cancer families was 1.0 (lower LOD-1 limit 0.79). In contrast, there was significant evidence of genetic heterogeneity among the families without ovarian cancer, with an estimated 45% being linked. These results suggest that a gene(s) on chromosome 17q accounts for the majority of families in which both early-onset breast cancer and ovarian cancer occur but that other genes predisposing to breast cancer exist. By examining the fit of the linkage data to different penetrance functions, the cumulative risk associated with the 17q gene was estimated to be 59% by age 50 years and 82% by age 70 years. The corresponding estimates for the breast-ovary families were 67% and 76%, and those for the families without ovarian cancer were 49% and 90%; these penetrance functions did not differ significantly from one another.