  Collection of genotype data in case-control genetic association studies may
often be incomplete for reasons related to genes themselves. This non-ignorable
missingness structure, if not appropriately accounted for, can result in
participation bias in association analyses. To deal with this issue, Chen et
al. (2016) proposed to collect additional genetic information from family
members of individuals whose genotype data were not available, and developed a
maximum likelihood method for bias correction. In this study, we develop an
estimating equation approach to analyzing data collected from this design that
allows adjustment of covariates. It jointly estimates odds ratio parameters for
genetic association and missingness, where a logistic regression model is used
to relate missingness to genotype and other covariates. Our method allows
correlation between genotype and covariates while using genetic information
from family members to provide information on the missing genotype data. In the
estimating equation for genetic association parameters, we weight the
contribution of each genotyped subject to the empirical likelihood score
function by the inverse probability that the genotype data are available. We
evaluate large and finite sample performance of our method via simulation
studies and apply it to a family-based case-control study of breast cancer.
