  Parental origin effects play an important role in mammal development and
disorder. Case-control mother-child pair genotype data can be used to detect
parental origin effects and is often convenient to collect in practice. Most
existing methods for assessing parental origin effects do not incorporate any
covariates, which may be required to control for confounding factors. We
propose to model the parental origin effects through a logistic regression
model, with predictors including maternal and child genotypes, parental
origins, and covariates. The parental origins may not be fully inferred from
genotypes of a target genetic marker, so we propose to use genotypes of markers
tightly linked to the target marker to increase inference efficiency. A
computationally robust statistical inference procedure is developed based on a
modified profile likelihood in a retrospective way. A computationally feasible
expectation-maximization algorithm is devised to estimate all unknown
parameters involved in the modified profile likelihood. This algorithm differs
from the conventional expectation-maximization algorithm in the sense that it
is based on a modified instead of the original profile likelihood function. The
convergence of the algorithm is established under some mild regularity
conditions. This expectation-maximization algorithm also allows convenient
handling of missing child genotypes. Large sample properties, including weak
consistency, asymptotic normality, and asymptotic efficiency, are established
for the proposed estimator under some mild regularity conditions. Finite sample
properties are evaluated through extensive simulation studies and the
application to a real dataset.
