Background: Meta-analyses of outcomes with three or more mutually exclusive categorical responses (e.g., cause-specific death, other death and no death) typically employ binomial models by collapsing or ignoring categories (e.g., death vs. no death or cause-specific death vs. no death). Besides requiring multiple analyses, such methods may introduce bias and inefficiency by only analyzing part of the data and ignoring correlation among the dependent responses. Objectives: Develop a model to compare multiple treatments that form a network with a categorical outcome. The model is applied to analyze the effect of statins on cardiovascular outcomes. The trials form a network with four types of treatments (high and low dose statins, fibrates and controls) and report on an outcome with six categories (fatal and non-fatal stroke, fatal and non-fatal myocardial infarction, other causes of mortality and no event). Methods: We apply a multinomial Bayesian model estimated using Markov chain Monte Carlo that can incorporate missing outcomes or treatments. Such missing data may arise when some studies report only some outcome categories or treatments and not others. Results: We analyze data from 23 randomized trials in which each trial compares two of the four treatments. Nine of the trials report all six outcome categories; the others report some subset, usually because they do not split the stroke or myocardial infarction outcomes into fatal and non-fatal groups. Using a non-informative prior distribution for the treatment effects, high dose statins reduce fatal and non-fatal myocardial infarctions compared with control treatments. Posterior probabilities of events in each study indicate that statins reduce the chance of poor outcomes and increase the probability of no event. Conclusions: We demonstrate how to estimate the relative effect of multiple treatments on multiple categorical outcomes and produce valid simultaneous uncertainty estimates. This model should have many applications in the clinical literature.