Longitudinal variance components models for systolic blood pressure, fitted using Gibbs sampling

Software for generating liability distributions for pedigrees conditional on their observed disease states and covariates

For many multifactorial diseases, aetiology is poorly understood. A major research aim is the identification of disease predictors (environmental, biological, and genetic markers). In order to achieve this, a two-stage approach is proposed. The initial or synthesis stage combines observed pedigree data with previous genetic epidemiological research findings, to produce estimates of pedigree members' disease risk and predictions of their disease liability. A further analysis stage uses the latter as inputs to look for associations with potential disease markers. The incorporation of previous research findings into an analysis should lead to power gains. It also allows separate predictions for environmental and genetic liabilities to be generated. This should increase power for detecting disease predictors that are environmental or genetic in nature. Finally, the approach brings pragmatic benefits in terms of data reduction and synthesis, improving comprehensibility, and facilitating the use of existing statistical genetics tools. In this article we present a statistical model and Gibbs sampling approach to generate liability predictions for multifactorial disease for the synthesis stage. We have implemented the approach in a software program. We apply this program to a specimen disease pedigree, and discuss the results produced, comparing its results with those generated under a more naïve model. We also detail simulation studies that validate the software's operation.

Genetic random effects model for family data with long-term survivors: analysis of diabetic nephropathy in type 1 diabetes

A shared and additive genetic variance component-long-term survivor (LTS) model for familial aggregation studies of complex diseases with variable age-at-onset phenotype and non-susceptible subjects in the study cohort is proposed. LTS has been used from the early 1970s, especially in epidemiological studies of cancer. The LTS model utilizes information on the age at onset (survival) distribution to make inference on partially latent susceptibility. Bayesian modeling with uninformative priors is used and estimates of the posterior distribution of age at onset and susceptibility parameters of interest have been obtained using Bayesian Markov chain Monte Carlo (MCMC) methods with OpenBugs program. A simulation study confirms that we obtain posterior estimates of the model parameters on shared and genetic variance components of age at onset and susceptibility with good coverage rates. Further, we analyze familial aggregation of diabetic nephropathy (DN) in large Finnish cohort of 528 sibships with type 1 diabetes (T1D). According to the variance components estimated a substantial familial variation in the susceptibility to DN exist among families, while time to DN is less influenced by shared familial factors.

Longitudinal data analysis in pedigree studies

Longitudinal family studies provide a valuable resource for investigating genetic and environmental factors that influence long-term averages and changes over time in a complex trait. This paper summarizes 13 contributions to Genetic Analysis Workshop 13, which include a wide range of methods for genetic analysis of longitudinal data in families. The methods can be grouped into two basic approaches: 1) two-step modeling, in which repeated observations are first reduced to one summary statistic per subject (e.g., a mean or slope), after which this statistic is used in a standard genetic analysis, or 2) joint modeling, in which genetic and longitudinal model parameters are estimated simultaneously in a single analysis. In applications to Framingham Heart Study data, contributors collectively reported evidence for genes that affected trait mean on chromosomes 1, 2, 3, 5, 8, 9, 10, 13, and 17, but most did not find genes affecting slope. Applications to simulated data suggested that even for a gene that only affected slope, use of a mean-type statistic could provide greater power than a slope-type statistic for detecting that gene. We report on the results of a small experiment that sheds some light on this apparently paradoxical finding, and indicate how one might form a more powerful test for finding a slope-affecting gene. Several areas for future research are discussed.

Genome-wide linkage analysis of longitudinal phenotypes using sigma2A random effects (SSARs) fitted by Gibbs sampling

The study of change in intermediate phenotypes over time is important in genetics. In this paper we explore a new approach to phenotype definition in the genetic analysis of longitudinal phenotypes. We utilized data from the longitudinal Framingham Heart Study Family Cohort to investigate the familial aggregation and evidence for linkage to change in systolic blood pressure (SBP) over time. We used Gibbs sampling to derive sigma-squared-A-random-effects (SSARs) for the longitudinal phenotype, and then used these as a new phenotype in subsequent genome-wide linkage analyses.

Additive genetic effects (σ²_A.time) were estimated to account for ~9.2% of the variance in the rate of change of SBP with age, while additive genetic effects (σ²_A) were estimated to account for ~43.9% of the variance in SBP at the mean age. The linkage results suggested that one or more major loci regulating change in SBP over time may localize to chromosomes 2, 3, 4, 6, 10, 11, 17, and 19. The results also suggested that one or more major loci regulating level of SBP may localize to chromosomes 3, 8, and 14.

Our results support a genetic component to both SBP and change in SBP with age, and are consistent with a complex, multifactorial susceptibility to the development of hypertension. The use of SSARs derived from quantitative traits as input to a conventional linkage analysis appears to be valuable in the linkage analysis of genetically complex traits. We have now demonstrated in this paper the use of SSARs in the context of longitudinal family data.

Multilevel modeling for the analysis of longitudinal blood pressure data in the Framingham Heart Study pedigrees

Background

The data arising from a longitudinal familial study have a complex correlation structure that cannot be modeled using classical methods for the analysis of familial data at a single time point.

Methods

To fit the longitudinal systolic blood pressure (SBP) pedigree data arising from the Framingham Heart Study, we proposed to use multilevel modeling. That approach was used to distinguish multiple levels of information with individual repeated measurements (Level 1) being made within individuals (Level 2), and individuals clustered within pedigrees (Level 3). Residuals from the subject-specific and pedigree-specific regression models were summed both for the mean SBP and slope of SBP change over time, in order to define two new outcomes that were then used in a genome-wide linkage analysis.

Results

Evidence for linkage for the two outcomes (mean SBP and slope) was found in several chromosomal regions with a maximum LOD score of 3.6 on chromosome 8 and 3.5 on chromosome 17 for the mean SBP, and 2.5 on chromosome 1 for SBP slope. However, the linkage on chromosome 8 was only detected when the sample was restricted to subjects between age 25 and 75 and with at least four exams (Cohort 1) or 3 exams (Cohort 2).

Discussion

Multilevel modeling is a powerful approach to detect genes involved in complex traits when longitudinal data are available. It allows for complex hierarchical data structure to be taken into account and therefore, a better partitioning of random within-individual variation from other sources of variability (genetic or nongenetic).

Segregation and linkage analysis for longitudinal measurements of a quantitative trait

We present a method for using slopes and intercepts from a linear regression of a quantitative trait as outcomes in segregation and linkage analyses. We apply the method to the analysis of longitudinal systolic blood pressure (SBP) data from the Framingham Heart Study. A first-stage linear model was fit to each subject's SBP measurements to estimate both their slope over time and an intercept, the latter scaled to represent the mean SBP at the average observed age (53.7 years). The subject-specific intercepts and slopes were then analyzed using segregation and linkage analysis. We describe a method for using the standard errors of the first-stage intercepts and slopes as weights in the genetic analyses. For the intercepts, we found significant evidence of a Mendelian gene in segregation analysis and suggestive linkage results (with LOD scores ≥ 1.5) for specific markers on chromosomes 1, 3, 5, 9, 10, and 17. For the slopes, however, the data did not support a Mendelian model, and thus no formal linkage analyses were conducted.