Triglyceride phenotype transformations
The real data example for GAW20 is from the Genetics of Lipid Lowering Drugs and Diet Network (GOLDN) study data set . This study ascertained and recruited families from the Family Heart Study at 2 centers, Minneapolis, MN and Salt Lake City, UT, who self-reported to be white. TG levels in the GAW20 data set were measured at 4 exams: 2 pretreatment exams (visits 1 and 2) and 2 posttreatment exams (visits 3 and 4). At visit 1, subjects were measured after an overnight fast with a standard lipid profile. The next day, they returned to clinic, again fasting, for a second, repeat lipid profile. All subjects were then given the fenofibrate drug for a 3-week treatment period, after which they returned to the clinic for 2 consecutive days of lipid profiling (visits 3 and 4, both with overnight fasting), to assess the response to treatment. We performed association analyses of single-nucleotide polymorphisms (SNPs) with the average natural-log TG pretreatment (TG1–2), the average natural-log TG posttreatment (TG3–4), and the natural-log TG difference between pre- and posttreatment (∆TG1–4) using a linear mixed-effect model to account for familial correlations and adjusted for age, sex, center (0 = Minnesota, 1 = Utah), and smoking (coded as never, former, or current).
Association analysis of SNPs with TG level
GWAS genotyping was performed on DNA extracted from blood drawn at baseline, using the Affymetrix Genome-wide Human SNP Array 6.0. Association analyses were conducted using the QTDT software with and without accounting for POO effects. From the real data, we analyzed 823 genotyped individuals from 173 families (715,787 SNPs). We evaluated the association of principal components calculated in the GAW20 data set with the traits evaluated in this study. As population stratification was not expected to be a major concern, we used the QTDT -at option to perform a total association analysis . This model is not a transmission disequilibrium test and has a considerably higher power and greater efficiency to detect POO effects. The trait mean of child j in family i is modeled as: Yij = α + βGGij + eij where βG is the genetic effect of the minor allele (a) of the SNP and Gij is the number of minor alleles carried by child j in family i.
Then, our association analyses focused on POO effects on TG in the offspring. This approach involves modeling the phenotype as a function of covariates and genotypes, taking parental original of each allele into consideration . We use the QTDT with POO effect options (−of, −ot, −om, and −op) to get estimates of parental origin of the alleles . The model for the mean of the trait of child j in family i is: Yij = α + βmat G1ij + βpat G2ij + eij where βmat is the genetic effect of a maternally inherited minor allele, βpat is the genetic effect of a paternally minor allele, G1ij is the estimated number of minor allele inherited from the mother, and G2ij is the estimated number of minor alleles inherited from the father. The -at -ot tests for difference between paternal and maternal transmissions (βpat = βmat), the -at -of uses a saturated model where maternal and paternal inherited alleles are modeled separately (βpat = βmat = 0), whereas the -at -om and -at -op tests for maternal effect (βmat = 0) or paternal effect (βpat = 0) only. We modified the QTDT to test 1 parental effect while adjusting for the other parent contribution (om_op and op_om models).
Selection of suggestive POO effects was performed using 2 different approaches. We first used a candidate approach in regions known to be associated with TG levels using the GWAS catalog (http://www.ebi.ac.uk/gwas/search?query=triglycerides). We selected 14 European-ancestry GWAS after excluding GWAS performed on specific phenotypes (responses to treatment) or related phenotypes (obesity, Type 2 diabetes, lipids). A total of 129 variants in 59 regions were reported associated with TG levels at P < 10− 5 (threshold to include associations in the GWAS catalog). We used a ± 50-kb window around the reported SNPs to define candidate loci. We used an arbitrary threshold of 10− 5 to declare a SNP association suggestive under the POO effect model (in at least one of the following models: ot, of, om, op, om_op, op_om). We then used an agnostic approach over the full genome with the same arbitrary threshold of 10− 5 to declare a SNP association suggestive under the POO effect model (in at least 1 of the following models: ot, of, om, op, om_op, op_om).
Association analyses of DNA methylation probes with TGs
DNA was extracted from CD4+ T cells and the proportion of sample methylation at > 450,000 CpG sites was quantified by using the Illumina Infinium Human Methylation 450 K BeadChip from blood drawn in both visit 2 and visit 4 for each participant. We selected DNA methylation probes located within a ± 50-kb window around the suggestive SNPs under the POO effect model. We performed epigenetic association analyses of natural-log TG pretreatment (TG2), natural-log TG posttreatment (TG4), and natural-log pre- and posttreatment TG difference (∆TG2–4) using a linear mixed-effect model adjusted for age, sex, center, and smoking to account for familial correlations. From the real data, we analyzed 679 and 403 individuals from 163 and 136 families with genotypes and methylation available at exam 2 or 4, respectively. We selected all DNA methylation probes associated with at least 1 trait at the nominal level of P < 0.05.
Association analyses of SNPs with methylation probes
Association analysis between DNA methylation probes and SNPs was conducted using the same approach described for SNP-TG association, using the QTDT software to evaluate the association between suggestive SNPs under the POO effect model and significant DNA methylation probes, while including the phenotype in the model.
Causal inference test
We performed a causal inference test  to determine if the detected POO effects were mediated by DNA methylation at nearby probes associated with the phenotypes. The causal inference test comprises 4 conditions that have to be met to conclude that mediation is responsible for the observed association: the SNP and the phenotype are associated; the SNP is associated with methylation after adjusting for the phenotype; the methylation is associated with the phenotype after adjusting for the SNP; and the SNP is independent of the phenotype after adjusting for the methylation .