  Missing data is a common issue in many biomedical studies. Under a paired
design, some subjects may have missing values in either one or both of the
conditions due to loss of follow-up, insufficient biological samples, etc. Such
partially paired data complicate statistical comparison of the distribution of
the variable of interest between the two conditions. In this paper, we propose
a general class of test statistics based on the difference in weighted sample
means without imposing any distributional or model assumption. An optimal
weight is derived for this class of tests. Simulation studies show that our
proposed test with the optimal weight performs well and outperforms existing
methods in practical situations. Two cancer biomarker studies are provided for
illustration.
