A framework for structural equation models in general pedigrees

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.

Heritability and longitudinal outcomes of spelling skills in individuals with histories of early speech and language disorders

This study examined the spelling skills in middle childhood and adolescence in individuals with histories of early childhood speech sound disorders (SSD) with and without language impairment (LI). Youth without such histories were also included (No SSD/LI group). The heritability of spelling skills at each age level was estimated. Children with SSD were classified as SSD-only, SSD with LI but without childhood apraxia of speech (SSD + LI/ No CAS), and CAS and LI (CAS + LI). The SSD-only group did not differ in spelling from the No SSD/LI group, suggesting that SSD-only did not increase risk for poor spelling. The SSD + LI/No CAS and CAS + LI groups had poorer spelling skills than the SSD-only and No SSD/LI groups. Spelling was associated with phonological awareness in the middle childhood and adolescent samples and with rapid automatized naming in the adolescent sample. Heritability of spelling skills was stronger in adolescence than in middle childhood. Differences in the correlates of spelling and in heritability at the two ages suggest developmental changes in the factors contributing to spelling.

Model-Free Linkage Analysis of a Quantitative Trait

Model-free methods of linkage analysis for quantitative traits are a class of easily implemented, computationally efficient and statistically robust approaches to searching for linkage to a quantitative trait. By "model-free" we refer to methods of linkage analysis that do not fully specify a genetic model (i.e., the causal allele frequency, and penetrance functions). In this chapter we briefly survey the methods that are available, and then we discuss the necessary steps to implement an analysis using the programs GENIBD, SIBPAL and RELPAL in the S.A.G.E. (Statistical Analysis for Genetic Epidemiology) software suite.

Structural Equation Modeling

Structural equation modeling (SEM) is a multivariate statistical framework that is used to model complex relationships between directly observed and indirectly observed (latent) variables. SEM is a general framework that involves simultaneously solving systems of linear equations and encompasses other techniques such as regression, factor analysis, path analysis, and latent growth curve modeling. Recently, SEM has gained popularity in the analysis of complex genetic traits because it can be used to better analyze the relationships between correlated variables (traits), to model genes as latent variables as a function of multiple observed genetic variants, and to assess the association between multiple genetic variants and multiple correlated phenotypes of interest. Though the general SEM framework only allows for the analysis of independent observations, recent work has extended SEM for the analysis of data on general pedigrees. Here, we review the theory of SEM for both unrelated and family data, describe the available software for SEM, and provide examples of SEM analysis.

Structural equation modeling with latent variables for longitudinal blood pressure traits using general pedigrees

Structural equation modeling (SEM) has been used in a wide range of applied sciences including genetic analysis. The recently developed R package, strum, implements a framework for SEM for general pedigree data. We explored different SEM techniques using strum to analyze the multivariate longitudinal data and to ultimately test the association of genotypes on blood pressure traits. The quantitative blood pressure (BP) traits, systolic BP (SBP) and diastolic BP (DBP) were analyzed as the main traits of interest with age, sex, and smoking status as covariates. The single nucleotide polymorphism (SNP) genotype information from genome-wide association studies (GWAS) data was used for the test of association. The adjustment for hypertension treatment effect was done by the censored regression approach. Two different longitudinal data models, autoregressive model and latent growth curve model, were used to fit the longitudinal BP traits. The test of association for SNP was done using a novel score test within the SEM framework of strum. We found the 10 SNPs within the GWAS suggestive P value level, and among those 10, the most significant top 3 SNPs agreed in rank in both analysis models. The general SEM framework in strum is very useful to model and test for the association with massive genotype data and complex systems of multiple phenotypes with general pedigree data.

Joint analysis of multiple phenotypes: summary of results and discussions from the Genetic Analysis Workshop 19

For Genetic Analysis Workshop 19, 2 extensive data sets were provided, including whole genome and whole exome sequence data, gene expression data, and longitudinal blood pressure outcomes, together with nongenetic covariates. These data sets gave researchers the chance to investigate different aspects of more complex relationships within the data, and the contributions in our working group focused on statistical methods for the joint analysis of multiple phenotypes, which is part of the research field of data integration. The analysis of data from different sources poses challenges to researchers but provides the opportunity to model the real-life situation more realistically.Our 4 contributions all used the provided real data to identify genetic predictors for blood pressure. In the contributions, novel multivariate rare variant tests, copula models, structural equation models and a sparse matrix representation variable selection approach were applied. Each of these statistical models can be used to investigate specific hypothesized relationships, which are described together with their biological assumptions.The results showed that all methods are ready for application on a genome-wide scale and can be used or extended to include multiple omics data sets. The results provide potentially interesting genetic targets for future investigation and replication. Furthermore, all contributions demonstrated that the analysis of complex data sets could benefit from modeling correlated phenotypes jointly as well as by adding further bioinformatics information.

A tutorial on structural equation modeling for analysis of overlapping symptoms in co-occurring conditions using MPlus

Structural equation modeling (SEM) is a very general approach to analyzing data in the presence of measurement error and complex causal relationships. In this tutorial, we describe SEM, with special attention to exploratory factor analysis, confirmatory factor analysis, and multiple indicator multiple cause modeling. The tutorial is motivated by a problem of symptom overlap routinely faced by clinicians and researchers, in which symptoms or test results are common to two or more co-occurring conditions. As a result of such overlap, diagnoses, treatment decisions, and inferences about the effectiveness of treatments for these conditions can be biased. This problem is further complicated by increasing reliance on patient-reported outcomes, which introduces systematic error based on an individual's interpretation of a test questionnaire. SEM provides flexibility in handling this type of differential item functioning and disentangling the overlap. Scales and scoring approaches can be revised to be free of this overlap, leading to better care. This tutorial uses an example of depression screening in multiple sclerosis patients in which depressive symptoms overlap with other symptoms, such as fatigue, cognitive impairment, and functional impairment. Details of how MPlus (Muthén & Muthén, Los Angeles, CA, USA) software can be used to address the symptom overlap problem, including data requirements, code and output are described in this tutorial.

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.

The household contact study design for genetic epidemiological studies of infectious diseases

Most genetic epidemiological study designs fall into one of two categories: family based and population-based (case–control). However, recent advances in statistical genetics call for study designs that combine these two approaches. We describe the household contact study design as we have applied it in our several years of study of the epidemiology of tuberculosis. Though we highlight its applicability for genetic epidemiological studies of infectious diseases, there are many facets of this design that are appealing for modern genetic studies, including the simultaneous enrollment of related and unrelated individuals, closely and distantly related individuals, collection of extensive epidemiologic and phenotypic data, and evaluation of effects of shared environment and gene by environment interaction. These study design characteristics are particularly appealing for current sequencing studies.

Structural equation modeling

Structural equation modeling (SEM) is a multivariate statistical framework that is used to model complex relationships between directly and indirectly observed (latent) variables. SEM is a general framework that involves simultaneously solving systems of linear equations and encompasses other techniques such as regression, factor analysis, path analysis, and latent growth curve modeling. Recently, SEM has gained popularity in the analysis of complex genetic traits because it can be used to better analyze the relationships between correlated variables (traits), to model genes as latent variables as a function of multiple observed genetic variants, and assess the association between multiple genetic variants and multiple correlated phenotypes of interest. Though the general SEM framework only allows for the analysis of independent observations, recent work has extended SEM for the analysis of general pedigrees. Here, we review the theory of SEM for both unrelated and family data, the available software for SEM, and provide an example of SEM analysis.