  A/B testing refers to the statistical procedure of conducting an experiment
to compare two treatments, A and B, applied to different testing subjects. It
is widely used by technology companies such as Facebook, LinkedIn, and Netflix,
to compare different algorithms, web-designs, and other online products and
services. The subjects participating these online A/B testing experiments are
users who are connected in different scales of social networks. Two connected
subjects are similar in terms of their social behaviors, education and
financial background, and other demographic aspects. Hence, it is only natural
to assume that their reactions to the online products and services are related
to their network adjacency. In this paper, we propose to use the conditional
auto-regressive model to present the network structure and include the network
effects in the estimation and inference of the treatment effect. A D-optimal
design criterion is developed based on the proposed model. Mixed integer
programming formulations are developed to obtain the D-optimal designs. The
effectiveness of the proposed method is shown through numerical results with
synthetic networks and real social networks.
