  Network meta-analysis (NMA) is a useful tool to compare multiple
interventions simultaneously in a single meta-analysis, it can be very helpful
for medical decision making when the study aims to find the best therapy among
several active candidates. However, the validity of its results is threatened
by the publication bias issue. Existing methods to handle the publication bias
issue in the standard pairwise meta-analysis are hard to extend to this area
with the complicated data structure and the underlying assumptions for pooling
the data. In this paper, we aimed to provide a flexible inverse probability
weighting (IPW) framework along with several t-type selection functions to deal
with the publication bias problem in the NMA context. To solve these proposed
selection functions, we recommend making use of the additional information from
the unpublished studies from multiple clinical trial registries. A
comprehensive numerical study and a real example showed that our methodology
can help obtain more accurate estimates and higher coverage probabilities, and
improve other properties of an NMA (e.g., ranking the interventions).
