Abstract
Large studies of extended families usually collect valuable phenotypic data that may have scientific value for purposes other than testing genetic hypotheses if the families were not selected in a biased manner. These purposes include assessing population-based associations of diseases with risk factors/covariates and estimating population characteristics such as disease prevalence and incidence. Relatedness among participants however, violates the traditional assumption of independent observations in these classic analyses. The commonly used adjustment method for relatedness in population-based analyses is to use marginal models, in which clusters (families) are assumed to be independent (unrelated) with a simple and identical covariance (family) structure such as those called independent, exchangeable and unstructured covariance structures. However, using these simple covariance structures may not be optimally appropriate for outcomes collected from large extended families, and may under- or over-estimate the variances of estimators and thus lead to uncertainty in inferences. Moreover, the assumption that families are unrelated with an identical family structure in a marginal model may not be satisfied for family studies with large extended families. The aim of this paper is to propose models incorporating marginal models approaches with a covariance structure for assessing population-based associations of diseases with their risk factors/covariates and estimating population characteristics for epidemiological studies while adjusting for the complicated relatedness among outcomes (continuous/categorical, normally/non-normally distributed) collected from large extended families. We also discuss theoretical issues of the proposed models and show that the proposed models and covariance structure are appropriate for and capable of achieving the aim.