In risk prediction, it is common to collect information of predictors that have a clustered or longitudinal structure. NEXT Generation Health Study is interested in modelling peer influence in adolescent drinking, using partial peer network data. The study participants nominated a few close friends who self-reported their own drinking behavior. A unique feature is that, the number of peers each participant had was random; and conceivably, the number of nominated peers may be associated with the drinking outcome, posing an informative cluster size problem. Meanwhile, there were some participants who did not nominate any peers, which could potentially bias the sample. We develop a novel joint model to account for these unique data features, which has three components: a participant’s outcome model, a peer outcome model, and a cluster size model of the peer network. A random effect term is shared in these model components to introduce a dependence structure. We discuss the advantage of this new method over several simple alternatives that ignore the informative network size, and then compare their performance in simulation studies and analyses of NEXT data example.