Ascertainment-adjusted parameter estimates revisited

Statistical approaches for meta-analysis of genetic mutation prevalence

Estimating the prevalence of rare germline genetic mutations in the general population is of interest as it can inform genetic counseling and risk management. Most studies that estimate the prevalence of mutations are performed in high-risk populations, and each study is designed with differing inclusion criteria, resulting in ascertained populations. Quantifying the effects of ascertainment is necessary to estimate the prevalence in the general population. This quantification is difficult as the inclusion criteria is often based on disease status and/or family history. Combining estimates from multiple studies through a meta-analysis is challenging due to the variety of study designs and ascertainment mechanisms as well as the complexity of quantifying the effect of these mechanisms. We provide guidelines on how to quantify the ascertainment mechanism for a wide range of settings and propose a general approach for conducting a meta-analysis in these complex settings by incorporating study-specific ascertainment mechanisms into a joint likelihood function. We implement the proposed likelihood-based approach using both frequentist and Bayesian methodologies. We evaluate these approaches in simulations and show that the methods are robust and produce unbiased estimates of the prevalence. An advantage of the Bayesian approach is that it can easily incorporate uncertainty in ascertainment probability values. We apply our methods to estimate the prevalence of PALB2 mutations in the United States by combining data from multiple studies and obtain a prevalence estimate of around 0.02%.

Familial recurrence risk with varying amount of family history

The familial recurrence risk is the probability a person will have disease, given a reported family history. When family histories are obtained as simple counts of disease among family members, as often obtained in cancer registries or surveys, we propose methods to estimate recurrence risks based on truncated binomial distributions. By this approach, we are able to obtain unbiased estimates of risk for a person with at least k-affected relatives, where k can be specified to determine how risk varies with k. We also derive robust variances of the recurrence risk estimate, to account for correlations within families, such as those induced by shared genes or shared environment, without explicitly modeling the factors that cause familial correlations. Furthermore, we illustrate how mixture models can be used to account for a sample composed of low- and high-risk families. Using simulations, we illustrate the properties of the proposed methods. Application of our methods to a family history survey of prostate cancer shows that the recurrence risk for prostate cancer increased from 16%, when there was at least one affected relative, to 52%, when there was at least five affected relatives.

Efficient generalized least squares method for mixed population and family-based samples in genome-wide association studies

Genome-wide association studies (GWAS) that draw samples from multiple studies with a mixture of relationship structures are becoming more common. Analytical methods exist for using mixed-sample data, but few methods have been proposed for the analysis of genotype-by-environment (G×E) interactions. Using GWAS data from a study of sarcoidosis susceptibility genes in related and unrelated African Americans, we explored the current analytic options for genotype association testing in studies using both unrelated and family-based designs. We propose a novel method-generalized least squares (GLX)-to estimate both SNP and G×E interaction effects for categorical environmental covariates and compared this method to generalized estimating equations (GEE), logistic regression, the Cochran-Armitage trend test, and the WQLS and MQLS methods. We used simulation to demonstrate that the GLX method reduces type I error under a variety of pedigree structures. We also demonstrate its superior power to detect SNP effects while offering computational advantages and comparable power to detect G×E interactions versus GEE. Using this method, we found two novel SNPs that demonstrate a significant genome-wide interaction with insecticide exposure-rs10499003 and rs7745248, located in the intronic and 3' UTR regions of the FUT9 gene on chromosome 6q16.1.

Multiple genetic variant association testing by collapsing and kernel methods with pedigree or population structured data

Searching for rare genetic variants associated with complex diseases can be facilitated by enriching for diseased carriers of rare variants by sampling cases from pedigrees enriched for disease, possibly with related or unrelated controls. This strategy, however, complicates analyses because of shared genetic ancestry, as well as linkage disequilibrium among genetic markers. To overcome these problems, we developed broad classes of "burden" statistics and kernel statistics, extending commonly used methods for unrelated case-control data to allow for known pedigree relationships, for autosomes and the X chromosome. Furthermore, by replacing pedigree-based genetic correlation matrices with estimates of genetic relationships based on large-scale genomic data, our methods can be used to account for population-structured data. By simulations, we show that the type I error rates of our developed methods are near the asymptotic nominal levels, allowing rapid computation of P-values. Our simulations also show that a linear weighted kernel statistic is generally more powerful than a weighted "burden" statistic. Because the proposed statistics are rapid to compute, they can be readily used for large-scale screening of the association of genomic sequence data with disease status.

A unified framework for detecting rare variant quantitative trait associations in pedigree and unrelated individuals via sequence data

OBJECTIVES

There is great interest to sequence unrelated or pedigree samples for detecting rare variant quantitative trait associations. In order to reduce the cost of sequencing and improve power, many studies sequence selected samples with extreme traits. Existing methods for detecting rare variant associations were developed for unrelated samples. Methods are needed to analyze (selected or randomly ascertained) pedigree samples.

METHODS

We propose a unified framework of modeling extreme trait genetic associations (MEGA) with rare variants. Using MEGA and appropriate permutation algorithms, many rare variant tests can be extended to family data. As an application, we compared study designs using both sib-pairs and unrelated individuals. Extensive simulations were carried out using realistic population genetic and complex trait models.

RESULTS

It is demonstrated that when extreme sampling is implemented within equal-sized cohorts of unrelated individuals or sib-pairs, analyzing unrelated individuals is consistently more powerful than studying sib-pairs. A higher portion of rare variants can be identified through sequencing unrelated samples compared to sibs. Alternatively, if samples are ascertained using fixed thresholds from an infinite-sized population, sequencing one sib with the most extreme trait from each extreme concordant sib-pair is consistently the most powerful design.

CONCLUSIONS

MEGA will play an important role in the analysis of sequence-based genetic association studies.

A Frailty-Model-Based Method for Estimating Age-Dependent Penetrance from Family Data

Accurate estimates of disease risk (penetrance) associated with inherited gene mutations are critical for the clinical management of individuals at risk, but this estimation raises many statistical challenges especially when performed in a family-based design. In this paper, we propose a general frailty model-based approach to accommodate this design, where the frailty random effect accounts for shared risk among family members not due to the observed risk factors. It is of major interest when the goal is to discover other genetic variations besides the major gene and to get accurate estimates of penetrance (i.e. unbiased by unknown confounding factors). This approach is further extended to accommodate missing genotypes in family members and the non-random ascertainment of the families. Simulation results show that the proposed method performs well in realistic settings. Finally, a family-based breast cancer study of the BRCA1 and BRCA2 genes is used to illustrate the method.

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.

Score test for age at onset genetic linkage analysis in selected sibling pairs

A new score statistic is derived, which uses information from registries (age-specific incidences) and family studies (sib-sib marginal correlation) to weight affected sibling pairs according to their age at onset. Age at onset of sibling pairs is modelled by a gamma frailty model. From this model we derive a bivariate survival function, which depends on the marginal survival and on the marginal correlation. The score statistic for linkage is a classical nonparametric linkage (NPL) statistic where the identical by descent sharing is weighted by a particular function of the age at onset data. Since the statistic is based on survival models, it can also be applied to discordant and healthy sibling pairs. Simulation studies show that the proposed method is robust and more powerful than standard NPL methods. As illustration we apply the new score statistic to data from a breast cancer study.

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.

Efficient study designs for test of genetic association using sibship data and unrelated cases and controls

Linkage mapping of complex diseases is often followed by association studies between phenotypes and marker genotypes through use of case-control or family-based designs. Given fixed genotyping resources, it is important to know which study designs are the most efficient. To address this problem, we extended the likelihood-based method of Li et al., which assesses whether there is linkage disequilibrium between a disease locus and a SNP, to accommodate sibships of arbitrary size and disease-phenotype configuration. A key advantage of our method is the ability to combine data from different family structures. We consider scenarios for which genotypes are available for unrelated cases, affected sib pairs (ASPs), or only one sibling per ASP. We construct designs that use cases only and others that use unaffected siblings or unrelated unaffected individuals as controls. Different combinations of cases and controls result in seven study designs. We compare the efficiency of these designs when the number of individuals to be genotyped is fixed. Our results suggest that (1) when the disease is influenced by a single gene, the one sibling per ASP-control design is the most efficient, followed by the ASP-control design, and familial cases contribute more association information than singleton cases; (2) when the disease is influenced by multiple genes, familial cases provide more association information than singleton cases, unless the effect of the locus being tested is much smaller than at least one other untested disease locus; and (3) the case-control design can be useful for detecting genes with small effect in the presence of genes with much larger effect. Our findings will be helpful for researchers designing and analyzing complex disease-association studies and will facilitate genotyping resource allocation.

Ascertainment adjustment in genetic studies of ordinal traits

Most genetic studies recruit high risk families and the discoveries are based on non-random selected groups. We must consider the consequences of this ascertainment process in order to apply the results of genetic research to the general population. In previous reports, we developed a latent variable model to assess the familial aggregation and inheritability of ordinal-scaled diseases, and found a major gene component of alcoholism after applying the model to the data from the Yale family study of comorbidity of alcoholism and anxiety (YFSCAA). In this report, we examine the ascertainment effects on parameter estimates and correct potential bias in the latent variable model. The simulation studies for various ascertainment schemes suggest that our ascertainment adjustment is necessary and effective. We also find that the estimated effects are relatively unbiased for the particular ascertainment scheme used in the YFSCAA, which assures the validity of our earlier conclusion.

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.

The molecular-genetic basis of functional hyperandrogenism and the polycystic ovary syndrome

The genetic mechanisms underlying functional hyperandrogenism and the polycystic ovary syndrome (PCOS) remain largely unknown. Given the large number of genetic variants found in association with these disorders, the emerging picture is that of a complex multigenic trait in which environmental influences play an important role in the expression of the hyperandrogenic phenotype. Among others, genomic variants in genes related to the regulation of androgen biosynthesis and function, insulin resistance, and the metabolic syndrome, and proinflammatory genotypes may be involved in the genetic predisposition to functional hyperandrogenism and PCOS. The elucidation of the molecular genetic basis of these disorders has been burdened by the heterogeneity in the diagnostic criteria used to define PCOS, the limited sample size of the studies conducted to date, and the lack of precision in the identification of ethnic and environmental factors that trigger the development of hyperandrogenic disorders. Progress in this area requires adequately sized multicenter collaborative studies after standardization of the diagnostic criteria used to classify hyperandrogenic patients, in whom modifying environmental factors such as ethnicity, diet, and lifestyle are identified with precision. In addition to classic molecular genetic techniques such as linkage analysis in the form of a whole-genome scan and large case-control studies, promising genomic and proteomic approaches will be paramount to our understanding of the pathogenesis of functional hyperandrogenism and PCOS, allowing a more precise prevention, diagnosis, and treatment of these prevalent disorders.

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.

The estimation of sibling genetic risk parameters revisited

This report points out that some sibling genetic risk parameters can be regarded as the ratios of the characteristic values in the ascertainment subpopulation. Based on this observation, we reconsider Olson and Cordell's ([2000] Genet. Epidemiol. 18:217-235) and Cordell and Olson's ([2000] Genet. Epidemiol. 18:307-321) estimators, and re-derive these estimators. Furthermore, we provide the closed-form variance estimators. Simulation results suggest that our proposed estimators perform very well, and single ascertainment may be better than complete ascertainment for estimating these genetic parameters.

Ascertainment-adjusted maximum likelihood estimation for the additive genetic gamma frailty model

The additive genetic gamma frailty model has been proposed for genetic linkage analysis for complex diseases to account for variable age of onset and possible covariates effects. To avoid ascertainment biases in parameter estimates, retrospective likelihood ratio tests are often used, which may result in loss of efficiency due to conditioning. This paper considers when the sibships are ascertained by having at least two affected sibs with the disease before a given age and provides two approaches for estimating the parameters in the additive gamma frailty model. One approach is based on the likelihood function conditioning on the ascertainment event, the other is based on maximizing a full ascertainment-adjusted likelihood. Explicit forms for these likelihood functions are derived. Simulation studies indicate that when the baseline hazard function can be correctly pre-specified, both approaches give accurate estimates of the model parameters. However, when the baseline hazard function has to be estimated simultaneously, only the ascertainment-adjusted likelihood method gives an unbiased estimate of the parameters. These results imply that the ascertainment-adjusted likelihood ratio test in the context of the additive genetic gamma frailty may be used for genetic linkage analysis.

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.

Ascertainment adjustment in complex diseases

Genetic studies of complex diseases must confront two statistically difficult issues simultaneously. First, in many settings, to minimize the number of individuals to be genotyped, families enriched for disease must be oversampled. Also, statistical models in family studies should allow for residual association. This association will represent unmeasured genetic and environmental factors influencing disease risk. Dealing with these features simultaneously is both compelling and challenging. Burton et al. [2000] (Am. J. Hum. Gen. 69: 1505-14) recently discussed this issue and suggested that ascertainment corrections may lead to problematic parameter estimation. We revisit the issues and examples of Burton et al. [2000] (Am. J. Hum. Genet. 69: 1505-14) and present a more optimistic assessment. Estimation in this context is conceptually straightforward, but may be more problematic in practice. Specifically, we find that even slight misspecification of the random effects distribution in ascertainment-adjusted likelihood can yield severely biased parameter estimates. This result should make scientists wary when interpreting results from ascertainment-adjusted variance-component models. .