The Genetic Analysis Workshop 16 Problem 3: simulation of heritable longitudinal cardiovascular phenotypes based on actual genome-wide single-nucleotide polymorphisms in the Framingham Heart Study

The Framingham Heart Study (FHS) is a rich platform for the study of cardiovascular disease and the application of novel, imaginative analytic strategies. For Genetic Analysis Workshop (GAW) 16, we use a semi-simulated approach using actual genotypes from the 500 k Affymetrix platform and the 50 k candidate gene chip and building phenotypes on the observed genetic variation. Because blood lipid levels are a major risk factor in the development of cardiovascular disease [1], we modeled disease risk on the lipid pathway, including both genetic and environmental determinants. The FHS has reported that long-term averages of low-density lipoprotein (LDL), high-density lipoprotein (HDL), and triglyceride (TG) levels were highly heritable (0.66, 0.69, and 0.58, respectively) [2]. Several familial studies also have reported heritabilities for LDL of 0.50, HDL of 0.54, and TG of 0.39 [3]. Dyslipidemia, as a fundamental component of the atherosclerotic process, is a medically correctable risk factor with established efficacious treatments for reducing risk of coronary heart disease [4]. Thus, we included in our simulation the use and effects of dyslipidemic medications, which have an important role in shaping lipid profiles. This simulation builds in the long tradition of previous simulations for Genetic Analysis Workshops [5, 6].

The FHS pedigrees, distributed as GAW16 Problem 2, formed the basis of our simulation [7]. In total, there were 6,476 subjects who had genotypes and simulated phenotypes. After the simulations began, additional FHS subjects provided broad consent for data sharing; these additional subjects were not included in the simulations. To ensure comparable data to that which was simulated, we provided a file that defined precisely which subjects were included and their relationships within families. The ~550 k measured single-nucleotide polymorphism (SNP) genotypes, distributed for GAW16 Problem 2 from both the genome-wide scan and the additional candidate gene platform (GeneChip^® Human Mapping 500 k Array Set (Nsp and Sty), and the 50 k Human Gene Focused Panel) comprised the genotypes for GAW16 Problem 3. Novel fictitious phenotypes were simulated for subjects.

Although family members of the FHS attended various exams at different times, depending on the generation, we modeled our study as if all subjects were recruited at one time, calculated the family member's relative ages at one particular exam, and then assigned a simulated age for everyone at three time points, with 10-year intervals. The mean age in years (range) for the simulation, by generation and visit, is shown in Table 1.

The simulation model is depicted in Figure 1. There are up to six "major" genes for the lipid phenotypes HDL, LDL, and TG, and 1,000 polygenes for each trait. Several polygenes have pleiotropic effects (i.e., several of these polygenes affect two or three or trait combinations simultaneously). The identity and effects of the major genes are documented in Table 2. The locus-specific heritabilities of the major genes range from 0.1-1.0% under additive (AA:AB:BB, 0:0.5:1), dominant (AA:AB:BB, 1:1:0), or overdominant (AA:AB:BB, 0:1:0; heterozygotes show higher effect than the two homozygotes) modes of inheritance, with minor allele frequencies at least 5%, with one exception (β4), for which the minor allele frequency was 1%. We simulated an overdominant effect (γ1) because there appears to be evidence supporting this possibility and this mode of inheritance is rarely, if ever, modeled. The gene α4 is pleiotropic for HDL and TG and interacts with β5 in determining LDL (Figure 1). The interaction accounts for 0.7% of the trait variance, and β5 has no marginal effect on any phenotype. The locus-specific effects of the polygenes were on average an order of magnitude smaller, ranging from 0.002-0.15%, with effect sizes extracted from negative exponential distributions. All polygenes act independently and have additive effects. HDL, TG, and LDL share 40% of their polygenes in common, and HDL and TG share an additional 20%. The specific identities of the polygenes, their locations, and their generating effect sizes are provided in the Additional Files 1, 2, 3 corresponding to HDL, LDL, and TG. A group of 39 polygenes influencing HDL were clustered within 0.5 Mb on chromosome 11; otherwise, the polygenes for each trait are randomly distributed throughout the genome. The overall effect of each trait-specific polygenic component was scaled to achieve the target total trait heritabilities of 60%, 55%, and 40% for HDL, LDL, and TG, respectively. The remaining variance is uncorrelated among family members, with the exception of a simulated dietary effect (variable: diet) on TG levels that accounts for a correlation of 0.05 among family members, regardless of their coefficient of relationship. The phenotypes generated from this genetic model were scaled to the empirically derived means and variances for the actual HDL, LDL, and TG traits within 13 age strata (in 5-year intervals) and sex as follows:

where, for example, _{(HDL|age 5 year interval, sex)} represents the mean of HDL in FHS, given a 5-year age interval and sex; _{(HDL|age 5 year interval, sex)} is standard deviation of HDL in FHS, given a 5-year age interval and sex; h_α1 is the square root of simulated heritability for the α₁ SNP (as described in Table 2); a_α1 is a simulated effect that reflects in part the penetrance of the α₁ SNP; sign is a random integer number that takes values (-1) or (+1) with the purpose of randomly changing the contribution direction of polygenes; apoly_κ represents an instance of each of the 1,000 SNPs effects (k = 1 to 1,000), selected as polygenes for HDL; hapoly_κ is an instance of the of square roots of heritabilities for 1,000 SNPs selected as polygenes for HDL; a _ε represents the environmental effect that contributes to HDL; and h _ε is the square root of HDL variance explained by environmental causes.

As individuals progressed to the next visit 10 years later, their phenotypes were scaled by the appropriate age-sex means and variance, but there are no genes governing longitudinal trends per se. Instead, we simulated the complicating effects of medication. The simulated value for LDL at each visit for each subject was checked, and individuals in the upper tail of the distribution were simulated as medicated. The proportion of subjects that are medicated increased across visits to comprise 2%, 5%, and 15% of the subjects in Visits 1, 2, and 3, respectively. These proportions were estimated from the FHS data, and reflected the secular increase in the proportion of individuals being treated for elevated cholesterol levels. The response to treatment is governed by two loci (δ1 and δ2) as pharmacogenetic processes. The δ1 variant has a marginal effect on both HDL and TG levels via additive effects but also, individuals that are homozygous for the minor allele are non-responders to the treatment. Responders (homozygotes and heterozygotes for the major allele) exhibit a 10% increase in their HDL levels and a 15% decrease in TG levels. Similarly, δ2 is a variant with an additive marginal effect on LDL, and homozygotes for the minor allele are non-responders to treatment. Responders exhibit a 30% decrease in LDL levels. Total cholesterol (CHOL) level is calculated as 0.8*(HDL + LDL + TG/5), and has no independent genetic effects except those influencing the component phenotypes.

Coronary artery calcification (CAC) was simulated as a quantitative phenotype that takes many years to develop. For this reason, CAC was modeled in two stages. First, age-independent CAC (CAC_AI) was modeled as a function of total CHOL, HDL, and five other genes (τ1-τ5) having direct effects on its development. CAC_AI was simulated under the model

where ME is a joint genetic effect from an epistatic interaction between τ1 and τ2, the effect of τ1 is purely epistatic (i.e., τ1 displays only a minimal main effect) while τ2 displays an additional measurable additive main effect; PE is the joint effect from τ3 and τ4, a pair of purely epistatic SNPs, each with no main effect; Het is an effect from τ5, a SNP that displays heterosis (over-dominance); and ε is the residual variation not explained by the factors mentioned above. The term ε, 300 times a random draw from a normal distribution with mean 0 and variance 1 (300 × N(0,1)), represents the sum of normal deviations from the mean of each of the modeled genetic effects and "noise" from unmeasured environmental and genetic effects. Because CAC cannot be negative, CAC_AI = 0 if the generated value was negative. The models for the effects on CAC_AI due to the ME and PE genotypes are illustrated in Tables 3 and 4. The minor allele frequency (MAF) for each of the four SNPs τ1-τ4 is ~0.5. SNP τ5, which determines the Het effect, has a MAF of 0.2. SNP τ5 genotype 1/1 (common homozygote) increases CAC_AI on average by 25, genotype 1/3 decreases CAC_AI by 100, and genotype 3/3 increases CAC_AI by 400. CAC is derived from CAC_AI by using a piecewise linear age adjustment: subjects under 20 years have not developed measurable levels of CAC, CAC buildup is linear from the ages of 20 to 60, and for subjects older than 60, CAC = CAC_AI. Table 5 lists estimates of the proportion of the variability of CAC attributable to each of the genetic factors averaged over the 200 replicate datasets.

Whether a subject smoked during the period before a visit influenced the risk of a myocardial infarction (MI). At first visit, men had a 27% chance to be smokers and women had a 23% chance. Each smoker had an 8% chance of permanently quitting smoking before each subsequent visit. The resulting smoking rates are commensurate with rates reported by the Centers for Disease Control for 1998. The risk of an MI before each visit is determined by CAC and its interactions with smoking and two genetic loci, φ1 and φ2. No MIs were fatal in our data. Smoking and φ1 have an interactive effect on risk of MI. The effect of smoking is to constrict blood vessels, thus increasing the risk that CAC will lead to an MI. The risk of MI for a smoker with the most common φ1 genotype (3/3) is the same as that of an equivalent non-smoker whose CAC is 10% higher. The risk of MI for a smoker with either of the other φ1 genotypes is the same as that of a non-smoker whose CAC is 40% higher. The φ1 genotype has no effect on risk of MI in non-smokers. Carrying the most common φ2 genotype (3/3) has the same effect on risk of MI as reducing CAC by 5%. The effect of any other genotype is the same as increasing CAC by 5%. The final model for MI risk is

where ∂ _smoke is the joint effect of smoking and φ1 (0 if a non-smoker, 0.1 if a smoker with genotype 3/3 at φ1, 0.4 if a smoker with another genotype); and the value of the event variable is -0.05 if the φ2 genotype is 3/3 and 0.05 otherwise. The MAFs for φ1 and φ2 are ~0.3. MI_risk was calculated for each visit and a draw from a uniform distribution determined whether the risk resulted in an MI. The SNPs for CAC and MI event were chosen from the 50 k SNPs in the Gene Focused Panel based on desired MAF, completeness of genotyping, and lack of linkage disequilibrium between the SNPs. The specific identities of the SNPs τ1-τ5, φ1 and φ2, and their chromosomes are listed in Table 6.

The phenotypic simulated files are named simphen#.txt, where # stands for a number from 1-200, representing the replication number. The simulated data are archived in the dbGAP of the National Center for Biotechnology Information under the name "GAW16 Framingham and Simulated Data" [8]. The 200 replications of the data include the indexing variable "shareid" that matches exactly with the same shareid of the Framingham Heart Study and can be used to merge the simulated phenotypic data with the FHS genotypic data. The phenotypic variables provided are sex, simage (simulation age), diet, rx (antihyperlipidemic medication use), LDL, HDL, TG, CHOL, CAC, SMOKE, and MIevent, each associated with a number (1, 2, or 3) to identify respectively variables that were simulated for Visit 1, Visit 2, or Visit 3.

We tested all the simulated traits and causative SNP heritabilities as well as the respective association models. Analyzing and interpreting data obtained as part of a genome-wide association study presents numerous challenges, as well as the promise of improved understanding of the genetic factors influencing complex traits. For validation and a detailed analysis of the simulated model see the Online Supplemental Materials for GAW16 [9]. Many genome-wide association studies have been published recently, and many more are being carried out on virtually every conceivable phenotype of biomedical or public health importance. While the rate of development of genetic technologies has propelled us to this point, development and evaluation of statistical and analytic techniques is still underway, with many issues not yet satisfactorily resolved. Nonetheless, important discoveries have been reported. We hope that the simulated GAW16 Problem 3 provides data with which investigators can test the strengths and limitations of their statistical analytic approaches and software.