Online Appendix for:
Kent JW Jr., Comuzzie AG, Mahaney MC, Almasy L, Rainwater DL, VandeBerg JL, MacCluer JW, and Blangero J: Intercellular Adhesion Molecule-1 is Genetically Correlated with Insulin Resistance, Obesity, and High-density Lipoprotein Concentration in Mexican Americans
Details of statistical methods
Preparation of data. Distributional parameters (mean, standard deviation, skew, kurtosis, etc.) for all phenotypic measures were estimated using Microsoft Excel, and deviations from normal distribution were visualized using the “Normal Plot” routine in Dataplot (A1). Outlying measures that were more than 4 standard deviations from the mean were excluded from further analysis. For ICAM-1, this criterion excluded 2 very low values and 4 very high values, and reduced the study sample from 434 to 428 individuals. This exclusion had technical as well as statistical support: the excluded measures were also at the limits of the manufacturer’s stated sensitivity range for the ICAM-1 ELISA assay.
Exploratory analysis. The formal study was preceded by an extensive exploratory analysis. The genetic analysis software package SOLAR (Southwest Foundation for Biomedical Research, San Antonio, TX) was used to make preliminary estimates of heritability for each phenotype. SOLAR computes maximum likelihood estimates of all parameters of variance-component models simultaneously. Assuming a multivariate normal distribution for a phenotype y, the loge-likelihood for t individuals is
ln L(, 2G, 2E, | y, X) = (-t/2)ln(2) – (1/2)ln|| - (1/2) -1
where is the grand phenotypic mean and is a matrix of kinship coefficients between relative pairs. If covariate effects are included in the model, = y - - X, where X is a matrix of covariate measures and is a matrix of regression coefficients. SOLAR estimates the regression parameters simultaneously with the other parameters of the model.
Several ‘environmental’ covariates (including sex, age, menopause status, presence or absence of diabetes or CVD, medication, alcohol use, and smoking) were tested with the screening function built into SOLAR: the effect of each covariate was tested separately for significance by comparison to a model from which that covariate had been removed. Covariates were retained in the final (exploratory) models if their regression slopes were significantly different from zero at a permissive threshold of p < 0.10. None of the covariates examined ‘explained’ a significant portion of the variance of ICAM-1. Patterns varied for the other phenotypes, with sex, age, and menopause status having significant effects on several traits (data not shown).
SOLAR reports the kurtosis of the residuals in the final model. The raw data were loge transformed for subsequent analyses if the residual kurtosis deviated strongly from normality, and particularly if the kurtosis was ≥ 1. Leptokurtic distributions are known to increase the Type I error rate in variance-component genetic analyses (A2).
In a univariate model that included effects of current shared household on levels of ICAM-1, the portion of total variance due to household was 0.03 ± 0.06 (PE ± SE; p = 0.26). Household effects were not estimated in subsequent analyses.
Formal analyses. The formal analyses, including final estimation of phenotype heritabilities and genetic correlations, were informed by the preceding exploratory analyses. In particular, all measures except LDL cholesterol and LDL mean particle diameter were loge transformed prior to formal analysis, and sex, age, and menopause status were included as covariates (without screening for significance) in all analyses. A multivariate t distribution was assumed for all phenotypes in the formal analyses; this adjustment down-weights outlying observations but approximates the multivariate normal distribution when kurtosis approaches zero (A2).
The bivariate model for two phenotypes is described in the main text. In this case, SOLAR estimates parameters separately for both phenotypes in addition to the correlations between them. Thus, covariate effects could (and did) vary between phenotypes; for example, sex was not a significant covariate for ICAM-1, but was significant, as expected, for BMI. These data are not presented here for the sake of concision. The purpose of the present study was to identify those traits that, adjusted for a consistent set of covariates, exhibit significant genetic correlation and thus suggest future lines of inquiry. The differential effects of sex, age, and menopause status will, no doubt, be of interest in the subsequent studies.
References
A1.Filliben JJ, Heckert A. http://www.itl.nist.gov/div898/software/dataplot/ homepage.htm, 2002.
A2.Blangero J, Williams JT, Almasy L. Advances in Genetics 42: 151-181, 2001.