Detecting small-study effects and funnel plot asymmetry in meta-analysis of survival data: A comparison of new and existing tests

Abstract

Small-study effects are a common threat in systematic reviews and may indicate publication bias. Their existence is often verified by visual inspection of the funnel plot. Formal tests to assess the presence of funnel plot asymmetry typically estimate the association between the reported effect size and their standard error, the total sample size, or the inverse of the total sample size. In this paper, we demonstrate that the application of these tests may be less appropriate in meta-analysis of survival data, where censoring influences statistical significance of the hazard ratio. We subsequently propose 2 new tests that are based on the total number of observed events and adopt a multiplicative variance component. We compare the performance of the various funnel plot asymmetry tests in an extensive simulation study where we varied the true hazard ratio (0.5 to 1), the number of published trials (N=10 to 100), the degree of censoring within trials (0% to 90%), and the mechanism leading to participant dropout (noninformative versus informative). Results demonstrate that previous well-known tests for detecting funnel plot asymmetry suffer from low power or excessive type-I error rates in meta-analysis of survival data, particularly when trials are affected by participant dropout. Because our novel test (adopting estimates of the asymptotic precision as study weights) yields reasonable power and maintains appropriate type-I error rates, we recommend its use to evaluate funnel plot asymmetry in meta-analysis of survival data. The use of funnel plot asymmetry tests should, however, be avoided when there are few trials available for any meta-analysis.

Keywords: RCT; funnel plot; meta-analysis; publication bias; small-study effects; survival.

Figure 1

Funnel plots for a meta‐analysis of the association between plasma fibrinogen concentration and the risk of coronary heath disease (π ^cens=0.96). The vertical line indicates the fixed effect estimate

Figure 2

Funnel plots for a meta‐analysis of the effect of erythropoiesis‐stimulating agents on overall survival (π ^cens=0.92). The vertical line indicates the fixed effect estimate

Figure 3

Funnel plots for a meta‐analysis of adjusted hazard ratios of total stroke for depressed subjects versus nondepressed subjects (π ^cens=0.94). The vertical line indicates the fixed effect estimate

Figure 4

Type‐I error (false positive) rates in the absence of small‐study effects. Results are presented for 3 variations of the true hazard ratio (0.5, 0.75, and 1) and for 3 variations of noninformative participant dropout within trials (values for π ^cens by row). Results for each scenario are based on 10 000 simulations

Figure 5

Power (true positive) rates in the presence of small‐study effects. Results are presented for 3 variations of the true hazard ratio (0.5, 0.75, and 1) and for 3 variations of noninformative participant dropout within trials (values for π ^cens by row). Results for each scenario are based on 10 000 simulations