  Publication bias occurs when the publication of research results depends not
only on the quality of the research but also on its nature and direction. The
consequence is that published studies may not be truly representative of all
valid studies undertaken, and this bias may threaten the validity of systematic
reviews and meta-analyses - on which evidence-based medicine increasingly
relies. Multivariate meta-analysis has recently received increasing attention
for its ability reducing potential bias and improving statistical efficiency by
borrowing information across outcomes. However, detecting and accounting for
publication bias are more challenging in multivariate meta-analysis setting
because some studies may be completely unpublished whereas some studies may
selectively report part of multiple outcomes. In this paper, we propose a score
test for jointly testing publication bias for multiple outcomes, which is novel
to the multivariate setting. The proposed test is a natural multivariate
extension of the univariate Egger's test, and can handle the above mentioned
scenarios simultaneously, It accounts for correlations among multivariate
outcomes, while allowing different types of outcomes, and can borrow
information across outcomes. The proposed test is shown to be more powerful
than the Egger's test, Begg's test and Trim and Fill method through simulation
studies. Two data analyses are given to illustrate the performance of the
proposed test in practice.
