Testing small study effects in multivariate meta-analysis

Abstract

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 For example, some studies may be completely unpublished while others may selectively report multiple outcomes.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 rates with considerable power in moderate sample size settings. Finally, we also evaluate the concordance between the proposed tests with the naive application of univariate tests by evaluating 44 systematic reviews with multiple outcomes from the Cochrane Database.

Keywords: comparative effectiveness research; composite likelihood; outcome reporting bias; publication bias; small study effect; systematic review.

Figure 1.

Funnel plots for Case study 1 in Section 4.1 (upper panels) and Case study 2 in Section 4.2 (lower panels).

Figure 2.

Probability of being published under Scenarios C1, C2, C3, and P. In Scenarios C1–C3, the probabilities are shaded from dark to light (i.e., the largest probability refers to the darkest shade). This figure appears in color in the electronic version of this article, and any mention of color refers to that version.

Figure 3.

Power plots of the proposed MSSET test, Egger’s regression test on one outcome (Egger₁), and Egger’s regression test on two outcomes with Bonferroni correction (Egger_BON) and Benjamini & Hochberg correction (Egger_BH) at the 10% nominal level for sample sizes varying from 25 to 100 and between-study variances varying from 0.1 to 0.6. This figure appears in color in the electronic version of this article, and any mention of color refers to that version.