  In this article, we derive and compare methods to derive \textit{p}-values
and sets of confidence intervals with strong control of the family-wise error
rates and coverage for estimates of treatment effects in cluster randomised
trials with multiple outcomes. There are few methods for \textit{p}-value
corrections and deriving confidence intervals, limiting their application in
this setting. We discuss the methods of Bonferroni, Holm, and Romano \& Wolf
(2005) and adapt them to cluster randomised trial inference using
permutation-based methods with different test statistics. We develop a novel
search procedure for confidence set limits using permutation tests to produce a
set of confidence intervals under each method of correction. We conduct a
simulation-based study to compare family-wise error rates, coverage of
confidence sets, and the efficiency of each procedure in comparison to no
correction using both model-based standard errors and permutation tests. We
show that the Romano-Wolf type procedure has nominal error rates and coverage
under non-independent correlation structures and is more efficient than the
other methods in a simulation-based study. We also compare results from the
analysis of a real-world trial.
