Ascertainment adjustment in complex diseases

Behavioral and Molecular Genetics of Reading-Related AM and FM Detection Thresholds

Auditory detection thresholds for certain frequencies of both amplitude modulated (AM) and frequency modulated (FM) dynamic auditory stimuli are associated with reading in typically developing and dyslexic readers. We present the first behavioral and molecular genetic characterization of these two auditory traits. Two extant extended family datasets were given reading tasks and psychoacoustic tasks to determine FM 2 Hz and AM 20 Hz sensitivity thresholds. Univariate heritabilities were significant for both AM (h 2  = 0.20) and FM (h 2  = 0.29). Bayesian posterior probability of linkage (PPL) analysis found loci for AM (12q, PPL = 81 %) and FM (10p, PPL = 32 %; 20q, PPL = 65 %). Bivariate heritability analyses revealed that FM is genetically correlated with reading, while AM was not. Bivariate PPL analysis indicates that FM loci (10p, 20q) are not also associated with reading.

Outcome vector dependent sampling with longitudinal continuous response data: stratified sampling based on summary statistics

The analysis of longitudinal trajectories usually focuses on evaluation of explanatory factors that are either associated with rates of change, or with overall mean levels of a continuous outcome variable. In this article, we introduce valid design and analysis methods that permit outcome dependent sampling of longitudinal data for scenarios where all outcome data currently exist, but a targeted substudy is being planned in order to collect additional key exposure information on a limited number of subjects. We propose a stratified sampling based on specific summaries of individual longitudinal trajectories, and we detail an ascertainment corrected maximum likelihood approach for estimation using the resulting biased sample of subjects. In addition, we demonstrate that the efficiency of an outcome-based sampling design relative to use of a simple random sample depends highly on the choice of outcome summary statistic used to direct sampling, and we show a natural link between the goals of the longitudinal regression model and corresponding desirable designs. Using data from the Childhood Asthma Management Program, where genetic information required retrospective ascertainment, we study a range of designs that examine lung function profiles over 4 years of follow-up for children classified according to their genotype for the IL 13 cytokine.

Modelling random effect variance with double hierarchical generalized linear models

Random-effect models are becoming increasingly popular in the analysis of data. Lee and Nelder (2006) introduced double hierarchical generalized linear models (DHGLMs) in which not only the mean but also the residual variance (overdispersion) can be further modelled as random-effect models. In this article, we introduce DHGLMs that allow random-effect models for both the variances of random effects and the residual variance. We show how to use this general model class for the analysis of data and discuss how to select the best fitting model using the likelihood and various model-checking plots.

Outcome-dependent sampling from existing cohorts with longitudinal binary response data: study planning and analysis

When novel scientific questions arise after longitudinal binary data have been collected, the subsequent selection of subjects from the cohort for whom further detailed assessment will be undertaken is often necessary to efficiently collect new information. Key examples of additional data collection include retrospective questionnaire data, novel data linkage, or evaluation of stored biological specimens. In such cases, all data required for the new analyses are available except for the new target predictor or exposure. We propose a class of longitudinal outcome-dependent sampling schemes and detail a design corrected conditional maximum likelihood analysis for highly efficient estimation of time-varying and time-invariant covariate coefficients when resource limitations prohibit exposure ascertainment on all participants. Additionally, we detail an important study planning phase that exploits available cohort data to proactively examine the feasibility of any proposed substudy as well as to inform decisions regarding the most desirable study design. The proposed designs and associated analyses are discussed in the context of a study that seeks to examine the modifying effect of an interleukin-10 cytokine single nucleotide polymorphism on asthma symptom regression in adolescents participating Childhood Asthma Management Program Continuation Study. Using this example we assume that all data necessary to conduct the study are available except subject-specific genotype data. We also assume that these data would be ascertained by analyzing stored blood samples, the cost of which limits the sample size.

The effect of misspecification of random effects distributions in clustered data settings with outcome-dependent sampling

Genetic epidemiologists often gather outcome-dependent samples of family data to measure within-family associations of genetic factors with disease outcomes. Generalized linear mixed models provide effective methods to estimate within-family associations but typically require parametric specification of the random effects distribution. Although misspecification of the random effects distribution often leads to little bias in estimated regression coefficients in standard, prospective clustered data settings, some recent studies suggest that such misspecification will impact parameter estimates from outcome-dependent cluster sampling designs. Using analytic results, simulation studies and fits to example data, this study examines the effect of misspecification of random effects distributions on parameter estimates in clustered data settings with outcome-dependent sampling. We show that the effects are consistent with results from prospective cluster sampling settings. In particular, ascertainment corrected mixed model methods that assume normally distributed random intercepts and conditional likelihood approaches provide accurate estimates of within-family covariate effects even under a misspecified random effects distribution.

Fitting ACE structural equation models to case-control family data

Investigators interested in whether a disease aggregates in families often collect case-control family data, which consist of disease status and covariate information for members of families selected via case or control probands. Here, we focus on the use of case-control family data to investigate the relative contributions to the disease of additive genetic effects (A), shared family environment (C), and unique environment (E). We describe an ACE model for binary family data; this structural equation model, which has been described previously, combines a general-family extension of the classic ACE twin model with a (possibly covariate-specific) liability-threshold model for binary outcomes. We then introduce our contribution, a likelihood-based approach to fitting the model to singly ascertained case-control family data. The approach, which involves conditioning on the proband's disease status and also setting prevalence equal to a prespecified value that can be estimated from the data, makes it possible to obtain valid estimates of the A, C, and E variance components from case-control (rather than only from population-based) family data. In fact, simulation experiments suggest that our approach to fitting yields approximately unbiased estimates of the A, C, and E variance components, provided that certain commonly made assumptions hold. Further, when our approach is used to fit the ACE model to Austrian case-control family data on depression, the resulting estimate of heritability is very similar to those from previous analyses of twin data.

Matched ascertainment of informative families for complex genetic modelling

Family data are used extensively in quantitative genetic studies to disentangle the genetic and environmental contributions to various diseases. Many family studies based their analysis on population-based registers containing a large number of individuals composed of small family units. For binary trait analyses, exact marginal likelihood is a common approach, but, due to the computational demand of the enormous data sets, it allows only a limited number of effects in the model. This makes it particularly difficult to perform joint estimation of variance components for a binary trait and the potential confounders. We have developed a data-reduction method of ascertaining informative families from population-based family registers. We propose a scheme where the ascertained families match the full cohort with respect to some relevant statistics, such as the risk to relatives of an affected individual. The ascertainment-adjusted analysis, which we implement using a pseudo-likelihood approach, is shown to be efficient relative to the analysis of the whole cohort and robust to mis-specification of the random effect distribution.

A Variance-Component Framework for Pedigree Analysis of Continuous and Categorical Outcomes

Variance-component methods are popular and flexible analytic tools for elucidating the genetic mechanisms of complex quantitative traits from pedigree data. However, variance-component methods typically assume that the trait of interest follows a multivariate normal distribution within a pedigree. Studies have shown that violation of this normality assumption can lead to biased parameter estimates and inflations in type-I error. This limits the application of variance-component methods to more general trait outcomes, whether continuous or categorical in nature. In this paper, we develop and apply a general variance-component framework for pedigree analysis of continuous and categorical outcomes. We develop appropriate models using generalized-linear mixed model theory and fit such models using approximate maximum-likelihood procedures. Using our proposed method, we demonstrate that one can perform variance-component pedigree analysis on outcomes that follow any exponential-family distribution. Additionally, we also show how one can modify the method to perform pedigree analysis of ordinal outcomes. We also discuss extensions of our variance-component framework to accommodate pedigrees ascertained based on trait outcome. We demonstrate the feasibility of our method using both simulated data and data from a genetic study of ovarian insufficiency.

A two-stage approach to the correction of ascertainment bias in complex genetic studies involving variance components

Correction for ascertainment bias is a vital part of the analysis of genetic epidemiology studies that needs to be undertaken whenever subjects are not recruited at random. Adjustment often requires extensive numerical integration, which can be very slow or even computationally infeasible, especially if the model includes many fixed and random effects. In this paper we propose a two-stage method for ascertainment bias correction. In the first stage we estimate parameters that pertain to the ascertained population, that is the population that would be selected into the sample if the ascertainment criterion were applied to everyone. In the second stage we convert the estimates for the ascertained population into general population parameter estimates. We illustrate the method with simulations based on a simple model and then describe how the method can be used with complex models. The two-stage approach avoids some of the integration required in direct adjustment, hence speeding up the process of model fitting.

Estimation of genetic and environmental factors for melanoma onset using population-based family data

Estimation of genetic and environmental contributions to cancers falls in the framework of generalized linear mixed modelling with several random effect components. Computational challenges remain, however, in dealing with binary or survival phenotypes. In this paper, we consider the analysis of melanoma onset in a population of 2.6 million nuclear families in Sweden, for which none of the current survival-based methodologies is feasible. We treat the disease outcome as a binary phenotype, so that the standard proportional hazard model leads to a generalized linear model with the complementary-log link function. For rare diseases this link is very close to the probit link, and thus allows the use of marginal likelihood for the estimation of the variance components. We correct for the survival length bias by censoring the parent generation within each family at the time they attain the same cumulative hazard as the child generation, thus improving the validity of the estimates. Our finding that childhood shared environment in addition to genetic factors had a considerable effect on the development of melanoma is consistent with epidemiological studies.

Multicomponent variance estimation for binary traits in family-based studies

In biometrical genetic analyses of binary traits, the use of family data overcomes some limitations of twin studies, particularly in terms of sample size and types of genetic or environmental factors that can be estimated. However, because of computational problems, recent methods in the application of generalized linear mixed models for family data structure have limited the ability to handle large data sets with general covariates. In this paper, we investigate the use of the hierarchical likelihood approach to the analysis of binary traits from family data. In a simulation study, the method is shown to be highly accurate for the estimation of both the variance components and fixed regression parameters, even for small family sizes. For illustration, we analyze a real data set of familial aggregation of preeclampsia, a pregnancy-induced hypertension. When possible, the analysis is compared with the exact maximum likelihood approach.

Genomewide scan for real-word reading subphenotypes of dyslexia: novel chromosome 13 locus and genetic complexity

Dyslexia is a common learning disability exhibited as a delay in acquiring reading skills despite adequate intelligence and instruction. Reading single real words (real-word reading, RWR) is especially impaired in many dyslexics. We performed a genome scan, using variance components (VC) linkage analysis and Bayesian Markov chain Monte Carlo (MCMC) joint segregation and linkage analysis, for three quantitative measures of RWR in 108 multigenerational families, with follow up of the strongest signals with parametric LOD score analyses. We used single-word reading efficiency (SWE) to assess speed and accuracy of RWR, and word identification (WID) to assess accuracy alone. Adjusting SWE for WID provided a third measure of RWR efficiency. All three methods of analysis identified a strong linkage signal for SWE on chromosome 13q. Based on multipoint analysis with 13 markers we obtained a MCMC intensity ratio (IR) of 53.2 (chromosome-wide P < 0.004), a VC LOD score of 2.29, and a parametric LOD score of 2.94, based on a quantitative-trait model from MCMC segregation analysis (SA). A weaker signal for SWE on chromosome 2q occurred in the same location as a significant linkage peak seen previously in a scan for phonological decoding. MCMC oligogenic SA identified three models of transmission for WID, which could be assigned to two distinct linkage peaks on chromosomes 12 and 15. Taken together, these results indicate a locus for efficiency and accuracy of RWR on chromosome 13, and a complex model for inheritance of RWR accuracy with loci on chromosomes 12 and 15.

A genome scan in multigenerational families with dyslexia: Identification of a novel locus on chromosome 2q that contributes to phonological decoding efficiency

Dyslexia is a common and complex developmental disorder manifested by unexpected difficulty in learning to read. Multiple different measures are used for diagnosis, and may reflect different biological pathways related to the disorder. Impaired phonological decoding (translation of written words without meaning cues into spoken words) is thought to be a core deficit. We present a genome scan of two continuous measures of phonological decoding ability: phonemic decoding efficiency (PDE) and word attack (WA). PDE measures both accuracy and speed of phonological decoding, whereas WA measures accuracy alone. Multipoint variance component linkage analyses (VC) and Markov chain Monte-Carlo (MCMC) multipoint joint linkage and segregation analyses were performed on 108 families. A strong signal was observed on chromosome 2 for PDE using both VC (LOD=2.65) and MCMC methods (intensity ratio (IR)=32.1). The IR is an estimate of the ratio of the posterior to prior probability of linkage in MCMC analysis. The chromosome 2 signal was not seen for WA. More detailed mapping with additional markers provided statistically significant evidence for linkage of PDE to chromosome 2, with VC-LOD=3.0 and IR=59.6 at D2S1399. Parametric analyses of PDE, using a model obtained by complex segregation analysis, provided a multipoint maximum LOD=2.89. The consistency of results from three analytic approaches provides strong evidence for a locus on chromosome 2 that influences speed but not accuracy of phonological decoding.

Semiparametric estimation of marginal hazard function from case-control family studies

Estimating marginal hazard function from the correlated failure time data arising from case-control family studies is complicated by noncohort study design and risk heterogeneity due to unmeasured, shared risk factors among the family members. Accounting for both factors in this article, we propose a two-stage estimation procedure. At the first stage, we estimate the dependence parameter in the distribution for the risk heterogeneity without obtaining the marginal distribution first or simultaneously. Assuming that the dependence parameter is known, at the second stage we estimate the marginal hazard function by iterating between estimation of the risk heterogeneity (frailty) for each family and maximization of the partial likelihood function with an offset to account for the risk heterogeneity. We also propose an iterative procedure to improve the efficiency of the dependence parameter estimate. The simulation study shows that both methods perform well under finite sample sizes. We illustrate the method with a case-control family study of early onset breast cancer.

Population-Calibrated Gene Characterization: Estimating Age at Onset Distributions Associated With Cancer Genes

Phenotypic characterization of rare disease genes poses a significant statistical challenge, but the need to do so is clear. Clinical management of patients carrying a disease gene depends crucially on an accurate characterization of the genetically predisposed disease, including its likelihood of occurrence among mutation carriers, natural history, and response to treatment. We propose a formal yet practical method for controlling for bias due to ignoring ascertainment, defined as the sampling mechanism, when quantifying the association between genotype and disease using data on high-risk families. The approach is more statistically efficient than conditioning on the variables used in sampling. In it, the likelihood is adjusted by a factor that is a function of sampling weights in strata defined by those variables. It requires that these variables and the sampling probabilities in the strata they define either are known or can be estimated. The latter requires a second, population-based dataset. As an example, we derive ascertainment-corrected estimates of penetrance for the breast cancer susceptibility genes BRCA1 and BRCA2. The Bayesian analysis that we use incorporates a modified segregation model and prior data on penetrance derived from the literature. Markov chain Monte Carlo methods are used for inference.

Robust ascertainment-adjusted parameter estimation

Nonrandom ascertainment is commonly used in genetic studies of rare diseases, since this design is often more convenient than the random-sampling design. When there is an underlying latent heterogeneity, Epstein et al. ([2002] Am. J. Hum. Genet. 70:886-895) showed that it is possible to get unbiased or consistent estimation of population parameters under ascertainment adjustment, but Glidden and Liang ([2002] Genet. Epidemiol. 23:201-208) showed in a simulation study that the resulting estimates are highly sensitive to misspecification of the latent components. To overcome this difficulty, we consider a heavy-tailed model for latent variables that allows a robust estimation of the parameters. We describe a hierarchical-likelihood approach that avoids the integration used in the standard marginal likelihood approach. We revisit and extend the previous simulation, and show that the resulting estimator is efficient and robust against misspecification of the distribution of latent variables.

Correcting for nonrandom ascertainment in generalized linear mixed models (GLMMs), fitted using Gibbs sampling

Gibbs sampling-based generalized linear mixed models (GLMMs) provide a convenient and flexible way to extend variance components models for multivariate normally distributed continuous traits to other classes of phenotype. This includes binary traits and right-censored failure times such as age-at-onset data. The approach has applications in many areas of genetic epidemiology. However, the required GLMMs are sensitive to nonrandom ascertainment. In the absence of an appropriate correction for ascertainment, they can exhibit marked positive bias in the estimated grand mean and serious shrinkage in the estimated magnitude of variance components. To compound practical difficulties, it is currently difficult to implement a conventional adjustment for ascertainment because of the need to undertake repeated integration across the distribution of random effects. This is prohibitively slow when it must be repeated at every iteration of the Markov chain Monte Carlo (MCMC) procedure. This paper motivates a correction for ascertainment that is based on sampling random effects rather than integrating across them and can therefore be implemented in a general-purpose Gibbs sampling environment such as WinBUGS. The approach has the characteristic that it returns ascertainment-adjusted parameter estimates that pertain to the true distribution of determinants in the ascertained sample rather than in the general population. The implications of this characteristic are investigated and discussed. This paper extends the utility of Gibbs sampling-based GLMMs to a variety of settings in which family data are ascertained nonrandomly.