Power comparisons between the TDT and two likelihood-based methods

The effect of ascertainment on penetrance estimates for rare variants: Implications for establishing pathogenicity and for genetic counselling

Next-generation sequencing has led to an explosion of genetic findings for many rare diseases. However, most of the variants identified are very rare and were also identified in small pedigrees, which creates challenges in terms of penetrance estimation and translation into genetic counselling in the setting of cascade testing. We use simulations to show that for a rare (dominant) disorder where a variant is identified in a small number of small pedigrees, the penetrance estimate can both have large uncertainty and be drastically inflated, due to underlying ascertainment bias. We have developed PenEst, an app that allows users to investigate the phenomenon across ranges of parameter settings. We also illustrate robust ascertainment corrections via the LOD (logarithm of the odds) score, and recommend a LOD-based approach to assessing pathogenicity of rare variants in the presence of reduced penetrance.

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.

Detecting linkage disequilibrium in the presence of locus heterogeneity

Locus heterogeneity is a common phenomenon in complex diseases and is one of the most important factors that affect the power of either linkage or linkage disequilibrium (LD) analysis. In linkage analysis, the heterogeneity LOD score (HLOD) rather than LOD itself is often used. However, the existing methods for detecting linkage disequilibrium, such as the TDT and many of its variants, do not take into account locus heterogeneity. We propose two novel likelihood-based methods, an LD-Het likelihood and an LD-multinomial likelihood, to test linkage disequilibrium (LD) that explicitly incorporate locus heterogeneity in the analysis. The LD-Het is applicable to general nuclear family data but requires a working penetrance model. The LD-multinomial is only applicable to affected sib-pair data but does not require specification of a trait model. For affected sib-pair data, both methods have similar power to detect LD under the recessive model, but the LD-multinomial model has greater power when the underlying model is dominant or additive.

The Posterior Probability of Linkage Allowing for Linkage Disequilibrium and a New Estimate of Disequilibrium between a Trait and a Marker

The posterior probability of linkage (PPL) statistic has been developed as a method for the rigorous accumulation of evidence for or against linkage allowing for both intra- and inter-sample heterogeneity. To date, the method has assumed linkage equilibrium between alleles at the trait locus and the marker locus. We now generalize the PPL to allow for linkage disequilibrium (LD), by incorporating variable phase probabilities into the underlying linkage likelihood. This enables us to recover the marginal posterior density of the recombination fraction, integrating out nuisance parameters of the trait model, including the locus heterogeneity (admixture) parameter, as well as a vector of LD parameters. The marginal posterior density can then be updated across data subsets or new data as they become available, while allowing parameters of the trait model to vary between data sets. The method applies immediately to general pedigree structures and to markers with multiple alleles. In the case of SNPs, the likelihood is parameterized in terms of the standard single LD parameter D'; and it therefore affords a mechanism for estimation of D' between the marker and the trait, again, without fixing the parameters of the trait model and allowing for updating across data sets. It is even possible to allow for a different associated allele in different populations, while accumulating information regarding the strength of LD. While a computationally efficient implementation for multi-allelic markers is still in progress, we have implemented a version of this new LD-PPL for SNPs and evaluated its performance in nuclear families. Our simulations show that LD-PPLs tend to be larger than PPLs (stronger evidence in favor of linkage/LD) with increased LD level, under a variety of generating models; while in the absence of linkage and LD, LD-PPLs tend to be smaller than PPLs (stronger evidence against linkage). The estimate of D' also behaves well even in relatively small, heterogeneous samples.