Association tests for traits with variable age at onset

This paper is concerned with testing association between marker genotypes and traits with variable age at onset. Two methods are proposed, one which makes use of both age-at-ascertainment and age-at-onset information, and one which may be applied when only age-at-ascertainment information is available. (Here, by age-at-ascertainment, is meant the subject's age when presence of onset and age at onset are determined; for subjects who have died or are otherwise censored before ascertainment, the censoring time should be used instead). Adjustment for confounding due to population stratification is carried out by conditioning on observed traits and parental genotypes, or, if complete parental genotypes are not available, by conditioning on observed traits and the minimal sufficient statistics under the null hypothesis for the parental genotypes. Proportional hazards regression models and logistic regression models are used to motivate the methods, but correct type I error rates result even if the models are not correct. An illustrative example is described.     

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.     

Case-control and case-only designs with genotype and family history data: estimating relative risk, residual familial aggregation, and cumulative risk

In case-control studies of inherited diseases, participating subjects (probands) are often interviewed to collect detailed data about disease history and age-at-onset information in their family members. Genotype data are typically collected from the probands, but not from their relatives. In this article, we introduce an approach that combines case-control analysis of data on the probands with kin-cohort analysis of disease history data on relatives. Assuming a marginally specified multivariate survival model for joint risk of disease among family members, we describe methods for estimating relative risk, cumulative risk, and residual familial aggregation. We also describe a variation of the methodology that can be used for kin-cohort analysis of the family history data from a sample of genotyped cases only. We perform simulation studies to assess performance of the proposed methodologies with correct and mis-specified models for familial aggregation. We illustrate the proposed methodologies by estimating the risk of breast cancer from BRCA1/2 mutations using data from the Washington Ashkenazi Study.     

Correlating Two Viral Load Assays with Known Detection Limits

A timely objective common to many HIV studies involves assessing the correlation between two different measures of viral load obtained from each of a sample of patients. This correlation has scientific utility in a number of contexts, including those aimed at a comparison of competing assays for quantifying virus and those aimed at determining the level of association between viral loads in two different reservoirs using the same assay. A complication for the analyst seeking valid point and interval estimates of such a correlation is the fact that both variables may be subject to left censoring due to values below assay detection limits. We address this problem using a bivariate normal likelihood that accounts for left censoring of two variables that may have different detection limits. We provide simulation results to evaluate sampling properties of the resulting correlation estimator and compare it with ad hoc estimators in the presence of nondetects. In an effort to obtain improved confidence interval properties relative to the Wald approach, we evaluate and compare profile likelihood-based intervals. We apply the methods to HIV viral load data on women and infants from a trial in Bangkok, Thailand, and we discuss an extension of the original model to accommodate interval censoring arising due to the study design.     

A frailty model for informative censoring

To account for the correlation between failure and censoring, we propose a new frailty model for clustered data. In this model, the risk to be censored is affected by the risk of failure. This model allows flexibility in the direction and degree of dependence between failure and censoring. It includes the traditional frailty model as a special case. It allows censoring by some causes to be analyzed as informative while treating censoring by other causes as noninformative. It can also analyze data for competing risks. To fit the model, the EM algorithm is used with Markov chain Monte Carlo simulations in the E-steps. Simulation studies and analysis of data for kidney disease patients are provided. Consequences of incorrectly assuming noninformative censoring are investigated.     

A note on a conditional-likelihood approach for family-based association studies of candidate genes

The family-based association study design is a variation of the case-control study design, where unaffected family members instead of unrelated subjects are sampled as controls. This variation is useful in assessing the effects of candidate genes on disease, because it avoids false associations caused by admixture of populations. A complication of this design is that because of an inherited genotypic correlation among family members, the genotypic distributions between cases and relative controls may be distorted by the ascertainment criteria of families, which could involve not only cases and relative controls, but also other relatives. Analyzing such data naively may lead to biased estimates of relative risk. In this note, we will discuss the consistency of a conditional-likelihood approach. We show analytically that maximum conditional-likelihood estimators are consistent for the true relative risks, if genotypes for family members are exchangeable under the sampling process, for example, sibling clusters. Besides being straightforward conceptually and computationally, this approach is robust to ascertainment bias and naturally accommodates genetic heterogeneity across families.     

An epidemiological reappraisal of the familial aggregation of prostate cancer: a meta-analysis

Studies on familial aggregation of cancer may suggest an overall contribution of inherited genes or a shared environment in the development of malignant disease. We performed a meta-analysis on familial clustering of prostate cancer. Out of 74 studies reporting data on familial aggregation of prostate cancer in unselected populations retrieved by a Pubmed search and browsing references, 33 independent studies meeting the inclusion criteria were used in the analysis performed with the random effects model. The pooled rate ratio (RR) for first-degree family history, i.e. affected father or brother, is 2.48 (95% confidence interval: 2.25–2.74). The incidence rate for men who have a brother who got prostate cancer increases 3.14 times (CI:2.37–4.15), and for those with affected father 2.35 times (CI:2.02–2.72). The pooled estimate of RR for two or more affected first-degree family members relative to no history in father and in brother is 4.39 (CI:2.61–7.39). First-degree family history appears to increase the incidence rate of prostate cancer more in men under 65 (RR:2.87, CI:2.21–3.74), than in men aged 65 and older (RR:1.92, CI:1.49–2.47), p for interaction = 0.002. The attributable fraction among those having an affected first-degree relative equals to 59.7% (CI:55.6–63.5%) for men at all ages, 65.2% (CI:57.7–71.4%) for men younger than 65 and 47.9% (CI:37.1–56.8%) for men aged 65 or older. For those with a family history in 2 or more first-degree family members 77.2% (CI:65.4–85.0%) of prostate cancer incidence can be attributed to the familial clustering. Our combined estimates show strong familial clustering and a significant effect-modification by age meaning that familial aggregation was associated with earlier disease onset (before age 65).     

A genetic model for age at onset in Huntington disease.

Although numerous investigators have confirmed excess paternal transmission among juvenile-onset cases of Huntington disease (HD), there are conflicting reports that the late-onset form is inherited more often from the mother than from the father. Results from a survey of age at onset and age at death in 569 patients corroborate earlier findings of delayed onset of HD among offspring of affected mothers at both ends of the onset-age spectrum: 23 of 28 juvenile-onset offspring had affected fathers, and there were 1.6 times more late-onset offspring born to affected mothers than to affected fathers. These patterns, together with data that link age-at-onset variability to familial longevity trends, suggest a model where age at onset is governed, generally, by a set of independently inherited aging genes, but expression of the HD gene may be significantly delayed in individuals who possess a particular maternally transmitted factor.     

Estimation of morbid risk and age at onset with missing information.

Investigators of genetic illnesses are currently employing life-table techniques to estimate the lifetime risk of disease and the age-at-onset distribution. This methodology assumes that onset ages are known for affected individuals and that censoring ages are known for unaffected individuals. We extend these methods to incorporate affected individuals with unknown onset ages and unaffected persons with unknown censoring ages and illustrate how conventional life-table methods can produce seriously biased estimates, particularly of lifetime risk. The methodology is not restricted to genetic illnesses and can be applied to more complex illnesses with unknown etiology. We present an example for Huntington disease, which is generally assumed to be a Mendelian autosomal dominant disease, yielding estimates of lifetime risk of .503 +/- .70 and mean onset age of 47.7 +/- 3.1 years for offspring with a single affected parent. When conventional life-table techniques are employed, these estimates are .238 +/- .032 and 43.2 +/- 2.2.     

G-estimation and artificial censoring: problems, challenges, and applications

In principle, G-estimation is an attractive approach for dealing with confounding by variables affected by treatment. It has rarely been applied for estimation of the effects of treatment on failure-time outcomes. Part of this is due to artificial censoring, an analytic device which considers some subjects who actually were observed to fail as if they were censored. Artificial censoring leads to a lack of smoothness in the estimating function, which can pose problems in variance estimation and in optimization. It also can lead to failure to have solutions to the usual estimating functions, which then raises questions about the appropriate criteria for optimization. To improve performance of the optimization procedures, we consider approaches for reducing the amount of artificial censoring, propose the substitution of smooth for indicator functions, and propose the use of estimating functions scaled to a measure of the information in the data; we evaluate performance of these approaches using simulation. We also consider appropriate optimization criteria in the presence of information loss due to artificial censoring. We motivate and illustrate our approaches using observational data on the effect of erythropoietin on mortality among subjects on hemodialysis.     

Evidence for a novel late-onset Alzheimer disease locus on chromosome 19p13.2

Late-onset familial Alzheimer disease (LOFAD) is a genetically heterogeneous and complex disease for which only one locus, APOE, has been definitively identified. Difficulties in identifying additional loci are likely to stem from inadequate linkage analysis methods. Nonparametric methods suffer from low power because of limited use of the data, and traditional parametric methods suffer from limitations in the complexity of the genetic model that can be feasibly used in analysis. Alternative methods that have recently been developed include Bayesian Markov chain-Monte Carlo methods. These methods allow multipoint linkage analysis under oligogenic trait models in pedigrees of arbitrary size; at the same time, they allow for inclusion of covariates in the analysis. We applied this approach to an analysis of LOFAD on five chromosomes with previous reports of linkage. We identified strong evidence of a second LOFAD gene on chromosome 19p13.2, which is distinct from APOE on 19q. We also obtained weak evidence of linkage to chromosome 10 at the same location as a previous report of linkage but found no evidence for linkage of LOFAD age-at-onset loci to chromosomes 9, 12, or 21.     

Statistical evaluation of age-at-onset anticipation: a new test and evaluation of its behavior in realistic applications.

The discovery that microsatellite repeat expansions can cause clinical disease has fostered renewed interest in testing for age-at-onset anticipation (AOA). A commonly used procedure is to sample affected parent-child pairs (APCPs) from available data sets and to test for a difference in mean age at onset between the parents and the children. However, standard statistical methods fail to take into account the right truncation of both the parent and child age-at-onset distributions under this design, with the result that type I error rates can be inflated substantially. Previously, we had introduced a new test, based on the correct, bivariate right-truncated, age-at-onset distribution. We showed that this test has the correct type I error rate for random APCPs, even for quite small samples. However, in that paper, we did not consider two key statistical complications that arise when the test is applied to realistic data. First, affected pairs usually are sampled from pedigrees preferentially selected for the presence of multiple affected individuals. In this paper, we show that this will tend to inflate the type I error rate of the test. Second, we consider the appropriate probability model under the alternative hypothesis of true AOA due to an expanding microsatellite mechanism, and we show that there is good reason to believe that the power to detect AOA may be quite small, even for substantial effect sizes. When the type I error rate of the test is high relative to the power, interpretation of test results becomes problematic. We conclude that, in many applications, AOA tests based on APCPs may not yield meaningful results.     

A Model for the Censoring Process in Incomplete Repeated Measurement Experiments

Premature terminations or dropouts occur often in repeated measurement experiments. A number of methods have been proposed to analyze such data but most of them assume that the censoring mechanism is, within each group, unaffected by the mechanism generating the response variables. In this paper, we propose a model for the censoring mechanism that generates dropouts. We then show how this model can be used to check whether the censoring mechanism is affected by the response variables and other covariates. Finally, the methods of the paper are applied to the “Halothane” data set.     

Regression survival analysis with an assumed copula for dependent censoring: a sensitivity analysis approach

SUMMARY: In clinical studies, when censoring is caused by competing risks or patient withdrawal, there is always a concern about the validity of treatment effect estimates that are obtained under the assumption of independent censoring. Because dependent censoring is nonidentifiable without additional information, the best we can do is a sensitivity analysis to assess the changes of parameter estimates under different assumptions about the association between failure and censoring. This analysis is especially useful when knowledge about such association is available through literature review or expert opinions. In a regression analysis setting, the consequences of falsely assuming independent censoring on parameter estimates are not clear. Neither the direction nor the magnitude of the potential bias can be easily predicted. We provide an approach to do sensitivity analysis for the widely used Cox proportional hazards models. The joint distribution of the failure and censoring times is assumed to be a function of their marginal distributions. This function is called a copula. Under this assumption, we propose an iteration algorithm to estimate the regression parameters and marginal survival functions. Simulation studies show that this algorithm works well. We apply the proposed sensitivity analysis approach to the data from an AIDS clinical trial in which 27% of the patients withdrew due to toxicity or at the request of the patient or investigator.     

Estimating the product‐moment correlation in samples with censoring on both variables

Bivariate samples may be subject to censoring of both random variables. For example, for two toxins measured in batches of wheat grain, there may be specific detection limits. Alternatively, censoring may be incomplete over a certain domain, with the probability of detection depending on the toxin level. In either case, data are not missing at random, and the missing data pattern bears some information on the parameters of the underlying model (informative missingness), which can be exploited for a fully efficient analysis. Estimation (after suitable data transformation) of the correlation in such samples is the subject of the present paper. We consider several estimators. The first is based on the tetrachoric correlation. It is simple to compute, but does not exploit the full information. The other two estimators exploit all information and use full maximum likelihood, but involve heavier computations. The one assumes fixed detection limits, while the other involves a logistic model for the probability of detection. For a real data set, a logistic model for the probability of detection fitted markedly better than a model with fixed detection limits, suggesting that censoring is not complete.     

Prion protein gene analysis in three kindreds with fatal familial insomnia (FFI): codon 178 mutation and codon 129 polymorphism.

Fatal familial insomnia (FFI) is a disease linked to a GAC(Asp)-->AAC(Asn) mutation in codon 178 of the prion protein (PrP) gene. FFI is characterized clinically by untreatable progressive insomnia, dysautonomia, and motor dysfunctions and is characterized pathologically by selective thalamic atrophy. We confirmed the 178Asn mutation in the PrP gene of a third FFI family of French ancestry. Three family members who are under 40 years of age and who inherited the mutation showed only reduced perfusion in the basal ganglia on single photon emission computerized tomography. Some FFI features differ from the clinical and neuropathologic findings associated with 178Asn reported elsewhere. However, additional intragenic mutations accounting for the phenotypic differences were not observed in two affected individuals. In other sporadic and familial forms of Creutzfeldt-Jakob disease and Gerstmann-Sträussler syndrome, Met or Val homozygosity at polymorphic codon 129 is associated with a more severe phenotype, younger age at onset, and faster progression. In FFI, young and old individuals at disease onset had 129Met/Val. Moreover, of five 178Asn individuals who are above age-at-onset range and who are well, two have 129Met and three have 129Met/Val, suggesting that polymorphic site 129 does not modulate FFI phenotypic expression. Genetic heterogeneity and environment may play an important role in inter- and intrafamilial variability of the 178Asn mutation.     

Joint analysis of longitudinal data with informative right censoring

Longitudinal data arise when subjects are followed over a period of time. A commonly encountered complication in the analysis of such data is the variable length of follow-up due to right censorship. This can be further exacerbated by the possible dependency between the censoring time and the longitudinal measurements. This article proposes a combination of a semiparametric transformation model for the censoring time and a linear mixed effects model for the longitudinal measurements. The dependency is handled via latent variables which are naturally incorporated. We show that the likelihood function has an explicit form and develops a two-stage estimation procedure to avoid direct maximization over a high-dimensional parameter space. The resulting estimators are shown to be consistent and asymptotically normal, with a closed form for the variance-covariance matrix that can be used to obtain a plug-in estimator. Finite sample performance of the proposed approach is assessed through extensive simulations. The method is applied to renal disease data.     

Analysis of multivariate recurrent event data with time‐dependent covariates and informative censoring

Multivariate recurrent event data are usually encountered in many clinical and longitudinal studies in which each study subject may experience multiple recurrent events. For the analysis of such data, most existing approaches have been proposed under the assumption that the censoring times are noninformative, which may not be true especially when the observation of recurrent events is terminated by a failure event. In this article, we consider regression analysis of multivariate recurrent event data with both time‐dependent and time‐independent covariates where the censoring times and the recurrent event process are allowed to be correlated via a frailty. The proposed joint model is flexible where both the distributions of censoring and frailty variables are left unspecified. We propose a pairwise pseudolikelihood approach and an estimating equation‐based approach for estimating coefficients of time‐dependent and time‐independent covariates, respectively. The large sample properties of the proposed estimates are established, while the finite‐sample properties are demonstrated by simulation studies. The proposed methods are applied to the analysis of a set of bivariate recurrent event data from a study of platelet transfusion reactions.     

Inverse relationship between age at onset of Huntington disease and paternal age suggests involvement of genetic imprinting.

It is well recognized that age at onset of Huntington disease (HD) is strongly influenced by the sex of the affected parent, and this has lead to suggestions that genetic imprinting or maternal specific factors may play a role in the expression of the disease. This study evaluated maternal and paternal ages, birth order, parental age at onset, and sex of the affected parent and grandparent in 1,764 patients in the National HD Roster by using linear-regression techniques which incorporated a weighted least-squares approach to accommodate the correlation among siblings. It was found that paternal age is negatively associated with age at onset of HD, particularly among subjects who inherit the mutant gene from grandfathers. Apparent associations between age at onset and birth order and between age at onset and maternal age were not significant after adjustment for paternal age. The paternal age effect is strongest among juvenile-onset cases and individuals with anticipation of greater than or equal to 10 years, although it is detectable across the entire age-at-onset distribution. The tendency for older fathers, including those not transmitting the HD gene, to have affected offspring with early-onset disease may be consistent with a gene imprinting mechanism involving DNA methylation. Because paternal age in unaffected fathers is also a significant determinant of age at onset, methylation in this context might involve HD modifier genes or the normal HD allele.