The problem of ascertainment for linkage analysis.

It is generally believed that ascertainment corrections are unnecessary in linkage analysis, provided individuals are selected for study solely on the basis of trait phenotype and not on the basis of marker genotype. The theoretical rationale for this is that standard linkage analytic methods involve conditioning likelihoods on all the trait data, which may be viewed as an application of the ascertainment assumption-free (AAF) method of Ewens and Shute. In this paper, we show that when the observed pedigree structure depends on which relatives within a pedigree happen to have been the probands (proband-dependent, or PD, sampling) conditioning on all the trait data is not a valid application of the AAF method and will result in asymptotically biased estimates of genetic parameters (except under single ascertainment). Furthermore, this result holds even if the recombination fraction R is the only parameter of interest. Since the lod score is proportional to the likelihood of the marker data conditional on all the trait data, this means that when data are obtained under PD sampling the lod score will yield asymptotically biased estimates of R, and that so-called mod scores (i.e., lod scores maximized over both R and parameters theta of the trait distribution) will yield asymptotically biased estimates of R and theta. Furthermore, the problem appears to be intractable, in the sense that it is not possible to formulate the correct likelihood conditional on observed pedigree structure. In this paper we do not investigate the numerical magnitude of the bias, which may be small in many situations. On the other hand, virtually all linkage data sets are collected under PD sampling. Thus, the existence of this bias will be the rule rather than the exception in the usual applications.     

HLODs, trait models, and ascertainment: implications of admixture for parameter estimation and linkage detection

Maximizing the homogeneity lod is known to be an appropriate procedure for estimating parameters of the trait model in an approximately 'ascertainment assumption free' (AAF) manner. We have investigated whether this same property also holds for the heterogeneity lod (HLOD). We show that, when the genetic models at linked and unlinked loci differ, HLODs are not AAF, and maximizing the HLOD yields parameter estimates that are for all practical purposes meaningless; indeed, the admixture parameter alpha does not even measure the proportion of linked families within the sample, as is commonly supposed. In spite of this, our results confirm a large body of evidence supporting the use of HLODs as robust tools for linkage detection, and suggest further that maximizing the HLOD over both alpha and parameters of the trait model can improve accuracy in estimation of the recombination fraction theta;. These findings have important implications for the optimal handling of nuisance parameters in linkage analysis, particularly when evaluating the evidence for or against linkage based on multiple independent heterogeneous sets of data.     

A major susceptibility locus for specific language impairment is located on 13q21

Children who fail to develop language normally-in the absence of explanatory factors such as neurological disorders, hearing impairment, or lack of adequate opportunity-are clinically described as having specific language impairment (SLI). SLI has a prevalence of approximately 7% in children entering school and is associated with later difficulties in learning to read. Research indicates that genetic factors are important in the etiology of SLI. Studies have consistently demonstrated that SLI aggregates in families. Increased monozygotic versus dizygotic twin concordance rates indicate that heredity, not just shared environment, is the cause of the familial clustering. We have collected five pedigrees of Celtic ancestry that segregate SLI, and we have conducted genomewide categorical linkage analysis, using model-based LOD score techniques. Analysis was conducted under both dominant and recessive models by use of three phenotypic classifications: clinical diagnosis, language impairment (spoken language quotient <85) and reading discrepancy (nonverbal IQ minus non-word reading >15). Chromosome 13 yielded a maximum multipoint LOD score of 3.92 under the recessive reading discrepancy model. Simulation to correct for multiple models and multiple phenotypes indicated that the genomewide empirical P value is <.01. As an alternative measure, we also computed the posterior probability of linkage (PPL), obtaining a PPL of 53% in the same region. One other genomic region yielded suggestive results on chromosome 2 (multipoint LOD score 2.86, genomic P value <.06 under the recessive language impairment model). Our findings underscore the utility of traditional LOD-score-based methods in finding genes for complex diseases, specifically, SLI.     

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.     

Performance comparison of two-point linkage methods using microsatellite markers flanking known disease locations

The Genetic Analysis Workshop 14 simulated data presents an interesting, challenging, and plausible example of a complex disease interaction in a dataset. This paper summarizes the ease of detection for each of the simulated Kofendrerd Personality Disorder (KPD) genes across all of the replicates for five standard linkage statistics. Using the KPD affection status, we have analyzed the microsatellite markers flanking each of the disease genes, plus an additional 2 markers that were not linked to any of the disease loci. All markers were analyzed using the following two-point linkage methods: 1) a MMLS, which is a standard admixture LOD score maximized over theta, alpha, and mode of inheritance, 2) a MLS calculated by GENEHUNTER, 3) the Kong and Cox LOD score as computed by MERLIN, 4) a MOD score (standard heterogeneity LOD maximized over theta, alpha, and a grid of genetic model parameters), and 5) the PPL, a Bayesian statistic that directly measures the strength of evidence for linkage to a marker. All of the major loci (D1-D4) were detectable with varying probabilities in the different populations. However, the modifier genes (D5 and D6) were difficult to detect, with similar distributions under the null and alternative across populations and statistics. The pooling of the four datasets in each replicate (n = 350 pedigrees) greatly improved the chance of detecting the major genes using all five methods, but failed to increase the chance to detect D5 and D6.     

Examination of potential overlap in autism and language loci on chromosomes 2, 7, and 13 in two independent samples ascertained for specific language impairment

Specific language impairment is a neurodevelopmental disorder characterized by impairments essentially restricted to the domain of language and language learning skills. This contrasts with autism, which is a pervasive developmental disorder defined by multiple impairments in language, social reciprocity, narrow interests and/or repetitive behaviors. Genetic linkage studies and family data suggest that the two disorders may have genetic components in common. Two samples, from Canada and the US, selected for specific language impairment were genotyped at loci where such common genes are likely to reside. Significant evidence for linkage was previously observed at chromosome 13q21 in our Canadian sample (HLOD 3.56) and was confirmed in our US sample (HLOD 2.61). Using the posterior probability of linkage (PPL) to combine evidence for linkage across the two samples yielded a PPL over 92%. Two additional loci on chromosome 2 and 7 showed weak evidence for linkage. However, a marker in the cystic fibrosis transmembrane conductance regulator (7q31) showed evidence for association to SLI, confirming results from another group (O'Brien et al. 2003). Our results indicate that using samples selected for components of the autism phenotype may be a useful adjunct to autism genetics.     

KELVIN: a software package for rigorous measurement of statistical evidence in human genetics

This paper describes the software package KELVIN, which supports the PPL (posterior probability of linkage) framework for the measurement of statistical evidence in human (or more generally, diploid) genetic studies. In terms of scope, KELVIN supports two-point (trait-marker or marker-marker) and multipoint linkage analysis, based on either sex-averaged or sex-specific genetic maps, with an option to allow for imprinting; trait-marker linkage disequilibrium (LD), or association analysis, in case-control data, trio data, and/or multiplex family data, with options for joint linkage and trait-marker LD or conditional LD given linkage; dichotomous trait, quantitative trait and quantitative trait threshold models; and certain types of gene-gene interactions and covariate effects. Features and data (pedigree) structures can be freely mixed and matched within analyses. The statistical framework is specifically tailored to accumulate evidence in a mathematically rigorous way across multiple data sets or data subsets while allowing for multiple sources of heterogeneity, and KELVIN itself utilizes sophisticated software engineering to provide a powerful and robust platform for studying the genetics of complex disorders.