  Small study effects occur when smaller studies show different, often larger,
treatment effects than large ones, which may threaten the validity of
systematic reviews and meta-analyses. The most well-known reasons for small
study effects include publication bias, outcome reporting bias and clinical
heterogeneity. Methods to account for small study effects in univariate
meta-analysis have been extensively studied. However, detecting small study
effects in a multivariate meta-analysis setting remains an untouched research
area. One of the complications is that different types of selection processes
can be involved in the reporting of multivariate outcomes. For example, some
studies may be completely unpublished while others may selectively report
multiple outcomes. In this paper, we propose a score test as an overall test of
small study effects in multivariate meta-analysis. Two detailed case studies
are given to demonstrate the advantage of the proposed test over various naive
applications of univariate tests in practice. Through simulation studies, the
proposed test is found to retain nominal Type I error with considerable power
in moderate sample size settings. Finally, we also evaluate the concordance
between the proposed test with the naive application of univariate tests by
evaluating 44 systematic reviews with multiple outcomes from the Cochrane
Database.
