Calculating asymptotic significance levels of the constrained likelihood ratio test with application to multivariate genetic linkage analysis

An Accidental Genetic Epidemiologist

I briefly describe my early life and how, through a series of serendipitous events, I became a genetic epidemiologist. I discuss how the Elston–Stewart algorithm was discovered and its contribution to segregation, linkage, and association analysis. New linkage findings and paternity testing resulted from having a genotyping lab. The different meanings of interaction—statistical and biological—are clarified. The computer package S.A.G.E. (Statistical Analysis for Genetic Epidemiology), based on extensive method development over two decades, was conceived in 1986, flourished for 20 years, and is now freely available for use and further development. Finally, I describe methods to estimate and test hypotheses about familial correlations, and point out that the liability model often used to estimate disease heritability estimates the heritability of that liability, rather than of the disease itself, and so can be highly dependent on the assumed distribution of that liability.

strum: an R package for structural modeling of latent variables for general pedigrees

BACKGROUND

Structural equation modeling (SEM) is an extremely general and powerful approach to account for measurement error and causal pathways when analyzing data, and it has been used in wide range of applied sciences. There are many commercial and freely available software packages for SEM. However, it is difficult to use any of the packages to analyze general pedigree data, and SEM packages for genetics are limited in their application.

RESULTS

We present the new R package strum to serve the need of a suitable SEM software tool for genetic analysis. It implements a general framework for SEM within the context of general pedigree data. This context requires specialized considerations such as familial correlations and ascertainment. Our package is an extraordinarily flexible tool capable of modeling genetic association, linkage analysis, polygenic effects, shared environment, and ascertainment combined with confirmatory factor analysis and general SEM. It also provides a convenient tool for model visualization, and integrates tools for simulating pedigree data. The various features of this package are tested through a simulation study to evaluate performance, and our results show that strum is very reliable and robust in terms of the accuracy and coverage of parameter estimates.

CONCLUSIONS

strum is a valuable new tool for genetic analysis. It can be easily used with general pedigree data, incorporating both measurement and structural models, giving it some significant advantages over other software packages. It also includes a built-in approach for handling ascertainment, a helpful integrated tool for genetic data simulation, and built-in tools for model visualization, providing a significant addition to biomedical research.

PLXNA4 is associated with Alzheimer disease and modulates tau phosphorylation

OBJECTIVE

Much of the genetic basis for Alzheimer disease (AD) is unexplained. We sought to identify novel AD loci using a unique family-based approach that can detect robust associations with infrequent variants (minor allele frequency < 0.10).

METHODS

We conducted a genome-wide association study in the Framingham Heart Study (discovery) and NIA-LOAD (National Institute on Aging-Late-Onset Alzheimer Disease) Study (replication) family-based cohorts using an approach that accounts for family structure and calculates a risk score for AD as the outcome. Links between the most promising gene candidate and AD pathogenesis were explored in silico as well as experimentally in cell-based models and in human brain.

RESULTS

Genome-wide significant association was identified with a PLXNA4 single nucleotide polymorphism (rs277470) located in a region encoding the semaphorin-3A (SEMA3A) binding domain (meta-analysis p value [meta-P] = 4.1 × 10(-8) ). A test for association with the entire region was also significant (meta-P = 3.2 × 10(-4) ). Transfection of SH-SY5Y cells or primary rat neurons with full-length PLXNA4 (TS1) increased tau phosphorylation with stimulated by SEMA3A. The opposite effect was observed when cells were transfected with shorter isoforms (TS2 and TS3). However, transfection of any isoform into HEK293 cells stably expressing amyloid β (Aβ) precursor protein (APP) did not result in differential effects on APP processing or Aβ production. Late stage AD cases (n = 9) compared to controls (n = 5) had 1.9-fold increased expression of TS1 in cortical brain tissue (p = 1.6 × 10(-4) ). Expression of TS1 was significantly correlated with the Clinical Dementia Rating score (ρ = 0.75, p = 2.2 × 10(-4) ), plaque density (ρ = 0.56, p = 0.01), and Braak stage (ρ = 0.54, p = 0.02).

INTERPRETATION

Our results indicate that PLXNA4 has a role in AD pathogenesis through isoform-specific effects on tau phosphorylation.

A framework for structural equation models in general pedigrees

BACKGROUND/AIMS

Structural Equation Modeling (SEM) is an analysis approach that accounts for both the causal relationships between variables and the errors associated with the measurement of these variables. In this paper, a framework for implementing structural equation models (SEMs) in family data is proposed.

METHODS

This framework includes both a latent measurement model and a structural model with covariates. It allows for a wide variety of models, including latent growth curve models. Environmental, polygenic and other genetic variance components can be included in the SEM. Kronecker notation makes it easy to separate the SEM process from a familial correlation model. A limited information method of model fitting is discussed. We show how missing data and ascertainment may be handled. We give several examples of how the framework may be used.

RESULTS

A simulation study shows that our method is computationally feasible, and has good statistical properties.

CONCLUSION

Our framework may be used to build and compare causal models using family data without any genetic marker data. It also allows for a nearly endless array of genetic association and/or linkage tests. A preliminary Matlab program is available, and we are currently implementing a more complete and user-friendly R package.

Comparison of univariate and multivariate linkage analysis of traits related to hypertension

Complex traits are often manifested by multiple correlated traits. One example of this is hypertension (HTN), which is measured on a continuous scale by systolic blood pressure (SBP). Predisposition to HTN is predicted by hyperlipidemia, characterized by elevated triglycerides (TG), low-density lipids (LDL), and high-density lipids (HDL). We hypothesized that the multivariate analysis of TG, LDL, and HDL would be more powerful for detecting HTN genes via linkage analysis compared with univariate analysis of SBP. We conducted linkage analysis of four chromosomal regions known to contain genes associated with HTN using SBP as a measure of HTN in univariate Haseman-Elston regression and using the correlated traits TG, LDL, and HDL in multivariate Haseman-Elston regression. All analyses were conducted using the Framingham Heart Study data. We found that multivariate linkage analysis was better able to detect chromosomal regions in which the angiotensinogen, angiotensin receptor, guanine nucleotide-binding protein 3, and prostaglandin I2 synthase genes reside. Univariate linkage analysis only detected the AGT gene. We conclude that multivariate analysis is appropriate for the analysis of multiple correlated phenotypes, and our findings suggest that it may yield new linkage signals undetected by univariate analysis.

Combining information from linkage and association methods

Group 12 evaluated approaches to incorporate outside information or otherwise optimize traditional linkage and association analyses. The abundance of available data allowed exploration of identity-by-descent (IBD) estimation, score statistics, formal combination of linkage and association testing, significance estimation, and replication. We observed that IBD estimation can be optimized with a subset of marker data while estimation of inheritance vectors can provide both IBD estimates and a measure of their uncertainty. Score statistics incorporating covariates or combining association and linkage information performed at least as well as standard approaches while requiring less computation time. The formal combination of linkage and association methods may be fruitful, although the nature of the simulated data limited our conclusions. Estimation of significance may be improved through simulation, correction for cryptic relatedness, and the inclusion of prior information. Replication using real data provided consistent results, though the same was not true of simulated data replicates. Overall, we found that increasing the amount of available data limits analyses due to computational constraints and motivates the need to improve methods for the identification of complex-trait genes.