Table 1

Statistical methods for assessing small-study effects

MethodDescription
Funnel plotPresenting the study-specific effect size against its standard error (or the inverse of SE). It is roughly symmetrical around the overall effect size if no small-study effects appear.
Regression testSND = α + Embedded Image precision + error. Under the fixed-effect setting, SND (standard normal deviate) = Embedded Image and precision =Embedded Image ; under the random-effects setting, SND = Embedded Image and precision =Embedded Image . Here, y  and s  are the study-specific effect size and its standard error within studies, respectively, and Embedded Image is between-study variance due to heterogeneity. It tests for whether α = 0.
Regression intercept (Embedded Image  or Embedded Image )An estimate of the intercept α  of the regression test under the fixed-effect (Embedded Image ) or random-effects (Embedded Image ) setting.
Skewness (Embedded Image  or Embedded Image )An estimate of the skewness of the study-specific errors of the regression test under the fixed-effect (Embedded Image ) or random-effects (Embedded Image ) setting.
Trim-and-fill methodEstimating the suppressed studies and thus correcting small-study effects based on funnel plot’s asymmetry.
Proportion of suppressed studies (Embedded Image ) Embedded Image , where n is the number of studies in the original meta-analysis, and Embedded Image is the estimated number of suppressed studies using the trim-and-fill method.
Relative change of overall result by incorporating imputed suppressed studies (Embedded Image ) Embedded Image , where Embedded Image is the estimated overall result in the original meta-analysis of published studies, and Embedded Image is that after incorporating imputed suppressed studies using the trim-and-fill method.