Estimating Viral Genetic Linkage Rates in the Presence of Missing Data

Although the interest in the the use of social and information networks has grown, most inferences on networks assume the data collected represents the complete. However, when ignoring missing data, even when missing completely at random, this results in bias for estimators regarding inference network related parameters. In this paper, we focus on constructing estimators for the probability that a randomly selected node has node has at least one edge under the assumption that nodes are missing completely at random along with their corresponding edges. In addition, issues also arise in obtaining asymptotic properties for such estimators, because linkage indicators across nodes are correlated preventing the direct application of the Central Limit Theorem and Law of Large Numbers. Using a subsampling approach, we present an improved estimator for our parameter of interest that accommodates for missing data. Utilizing the theory U-statistics, we derive consistency and asymptotic normality of the proposed estimator. This approach decreases the bias in estimating our parameter of interest. We illustrate our approach using the HIV viral strains from a large cluster-randomized trial of a combination HIV prevention intervention -- the Botswana Combination Prevention Project (BCPP).