Volume 3 Supplement 7
A genome-wide association analysis of Framingham Heart Study longitudinal data using multivariate adaptive splines
© Zhu et al; licensee BioMed Central Ltd. 2009
Published: 15 December 2009
The Framingham Heart Study is a well known longitudinal cohort study. In recent years, the community-based Framingham Heart Study has embarked on genome-wide association studies. In this paper, we present a Framingham Heart Study genome-wide analysis for fasting triglycerides trait in the Genetic Analysis Workshop16 Problem 2 using multivariate adaptive splines for the analysis of longitudinal data (MASAL). With MASAL, we are able to perform analysis of genome-wide data with longitudinal phenotypes and covariates, making it possible to identify genes, gene-gene, and gene-environment (including time) interactions associated with the trait of interest. We conducted a permutation test to assess the associations between MASAL selected markers and triglycerides trait and report significant gene-gene and gene-environment interaction effects on the trait of interest.
Current advances in genotyping technologies, such as the Affymetrix 500 k GeneChip, make genome-wide association studies (GWAS) feasible for identifying common variants that underlie complex traits. Some of the recent genetic variants discovered by GWAS include age-related macular degeneration (AMD) [1, 2], inflammatory bowel disease , and electrocardio-graphic QT interval . Data from the 500 k genome-wide scan of the Framingham Heart Study (FHS) is available for use in the Genetic Analysis Workshop (GAW) 16. The FHS, a community-based cohort study initiated in 1948, aims to identify cardiovascular disease risk factors. FHS provides a collection of data from three generation families who had been followed up every 2 or 4 years over time. This longitudinal feature poses methodological challenges. Applying an efficient approach to analyzing the FHS longitudinal data may help in discovering new genetic variants in GWAS.
Previously, several approaches [5, 6] were proposed to analyze the FHS 100 k data set; however, most of these did not directly deal with longitudinal data. These methods require the longitudinal measures to be summarized into one time-point trait by taking the average of several measures or by using the family-based association test (FBAT) principal-components method . It is inevitable that there may be some loss of information by using the summary trait values . Furthermore, when applying the adjustment of FBAT-principal-components method in GWAS, it is difficult to include environment factors such as sex and age.
In our study, we use the multivariate adaptive splines for analysis of longitudinal data (MASAL) presented by Zhang  to analyze the FHS longitudinal data. MASAL is a nonparametric regression approach that was developed specifically to handle longitudinal data. MASAL not only accommodates time-varying covariates, but also allows interactions between gene and environmental factors and between time and covariates . Here we demonstrate and apply MASAL to identify genes, gene-gene, and gene-environment interactions in relation to the trait triglyceride (TG) level in GWAS using FHS data in GAW16 Problem 2.
where f is an unknown smooth function and ε ij is the error term.
where β m is the regression coefficient and B m (x) is a special basis function of the p + 1 covariates x = (x1, ..., xp+1) (m = 1, ..., M), and M is the number of terms. Specifically, B m (x) is either one of (x k - τ)+ and x k or their product (k = 1, ..., p + 1), and a+ = max(a,0) for any number a and τ is called a knot.
In the forward step, terms are added to minimize the (weighted) sum of squared residuals: , where and is the predicted value of y i , and W i is the within-subject covariance matrix for , i = 1, ..., n. After the forward step, all knots are found and each corresponding basis function will be treated as if it is a given predictor. In the backward step, based on generalized cross-validation (GCV), we delete one least significant term from the large model at a time. The final model we select is the one that yields the smallest , where WLS l is the WLS of a reduced model with l terms and λ (usually λ = 4 [10, 11]) is the penalizing parameter for model complexity.
GWA analyses with MASAL
where represents terms containing any genetic component (i.e., single-nucleotide polymorphism (SNP), SNP-SNP interaction, or SNP-covariate interaction), refers to non-genetic covariate terms, and , is the estimate of the corresponding regression coefficients.
where , and is the estimated covariance matrix of . We use a permutation procedure to establish the null distribution of W The permutation test is done by randomly assigning the phenotype while keeping the set of genotypes intact for each individual and then performing the GWA analysis using MASAL. It is noteworthy that non-genetic covariates go together with the phenotype.
We perform GWA analyses of TG trait with MASAL. We consider the genotype at every SNP as a covariate in the model in addition to sex and age variables. MASAL has the option of setting the maximum order of interactions in the model. We set it to three in our analyses because it is difficult to interpret interactions higher than the third order. We first use MASAL to perform GWA analyses in the Offspring Cohort, in which the repeated TG values and the familial correlations are properly accounted for in the analysis. Next, we perform GWA analyses with MASAL in the Original Cohort in which the subjects are considered to be independent, whereas the longitudinal trait values are considered to be correlated. Then, we examine significant SNPs, SNP-SNP, and SNP-covariate interactions in the two generation data sets analyzed and compare the level of concordance of significant associations in the two samples.
In the Offspring Cohort, some pedigrees have more than 100 subjects, which cannot be treated as independent individuals. These families with repeated traits induce a large covariance matrix in MASAL and thus markedly limit its efficiency. Therefore, in the analyses of Offspring Cohort, we split all pedigrees into sibship units according to the information from the Original Cohort. We obtained 1,767 sibship units, for which each sibship unit consists of one set of siblings and their spouses from each nuclear family. All subjects included in our study have all TG trait values (Exams 1, 3, 5, and 7) and genotypes. In the Original Cohort, we used 146 individuals who have all TG trait values (Exams 7 and 11) and genotypes. All of these subjects were genotyped for 488,146 SNPs.
Results and discussion
We applied MASAL to analyze the FHS 500 k SNP data set (GAW 16 Problem 2). Before the analysis, TG level values were log-transformed to approximate a normal distribution, although there is no such limitation when using MASAL. Furthermore, in order to minimize false-positive associations due to rarer SNPs and genotyping artifact, we limited our analyses to SNPs with minor allele frequency ≥ 10% and the p-value for testing Hardy-Weinberg equilibrium <0.001. Thus, there were a total of 294,434 SNPs remaining in our analysis.
and the value of the corresponding Wald statistic is 359.575.
Significant SNPs selected by MASAL
In this report, we proposed a testing procedure to perform GWAS for longitudinal data, using a nonparametric regression method (MASAL) presented by Zhang . In contrast to other GWA methods, our testing procedure has two novel features. First, it can handle longitudinal data without combining longitudinal measures into a one-time-point measure in GWAS. Second, it can accommodate gene-gene, gene-environment, and time-covariate interactions in GWAS. Using MASAL, we analyzed the FHS 500 k genotype data (GAW 16 Problem 2) using TG as the trait of interest and found some significant gene-gene and gene-environment interaction effects on TG trait. These results indicated that MASAL is useful for exploring gene-gene and gene-environment interactions in the GWAS of longitudinal data.
We used a permutation procedure to establish the null distribution of the Wald statistic and then estimated the significance level. However, the computation time was lengthy, especially for the large pedigree and large number of exams of each subject. Theoretical studies exploring the asymptotic distribution of the involved statistic would be useful.
List of abbreviations used
Age-related macular degeneration
Family-based association test
Framingham Heart Study
Genetic Analysis Workshop
Genome-wide association studies
Multivariate adaptive splines for the analysis of longitudinal data
This research is supported in part by grants K02DA017713, R01DA016750, and T32 MH014235 from the National Institutes of Health. The Framingham Heart Study project is conducted and supported by the National Heart, Lung, and Blood Institute (NHLBI) in collaboration with Boston University (N01 HC25195). The Genetic Analysis Workshop is supported by NIH grant R01 GM031575 from the National Institute of General Medical Sciences. The simulated data was supported by the Washington University Institute of Clinical and Translational Sciences, NIH grant 1U54RR023496. The GAW16 Framingham and simulated data used for the analyses described in this manuscript were obtained through dbGaP (accession numbers). The authors acknowledge the investigators that contributed the phenotype, genotype, and simulated data for this study. This manuscript was not prepared in collaboration with investigators of the Framingham Heart Study and does not necessarily reflect the opinions or views of the Framingham Heart Study, Boston University, or the NHLBI.
This article has been published as part of BMC Proceedings Volume 3 Supplement 7, 2009: Genetic Analysis Workshop 16. The full contents of the supplement are available online at http://www.biomedcentral.com/1753-6561/3?issue=S7.
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