Estimating equations for association structures

TLDR

Generalized estimating equations for association parameters are frequently used in family studies, with a focus on covariance estimation. The study investigates generalized estimating equations for association parameters in family studies, emphasizing covariance estimation. The authors use separate link functions to connect mean, scale, and correlation to linear predictors with distinct covariate sets, propose estimating equations for each, and illustrate the approach with data from a genetics of alcoholism study. Simulations demonstrate that robust sandwich and jackknife variance estimators for correlation parameters closely match empirical variance in 50‑cluster samples, contradicting earlier software results, and a general jackknife formula is proposed that performs well.

Abstract

This paper investigates generalized estimating equations for association parameters, which are frequently of interest in family studies, with emphasis on covariance estimation. Separate link functions are used to connect the mean, the scale, and the correlation to linear predictors involving possibly different sets of covariates, and separate estimating equations are proposed for the three sets of parameters. Simulations show that the robust 'sandwich' variance estimator and the jackknife variance estimator for the correlation parameters are generally close to the empirical variance for the sample size of 50 clusters. The results contradict Ziegler et al. and Kastner and Ziegler, where the 'sandwich' estimator obtained from the software MAREG was shown to be unsuitable for practical usage. The problem appears to arise because the MAREG variance estimator does not account for variability in estimation of the scale parameters, but may be valid with fixed scale. We also find that the formula for the approximate jackknife variance estimator in Ziegler et al. is deficient, resulting in systematic deviations from the fully iterated jackknife variance estimator. A general jackknife formula is provided and performs well in numerical studies. Data from a study on the genetics of alcoholism is used to illustrate the importance of reliable variance estimation in biomedical applications.