Table 1

Statistical methods for assessing small-study effects

 Method Description Funnel plot Presenting 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 test SND = α + precision + error. Under the fixed-effect setting, SND (standard normal deviate) = and precision = ; under the random-effects setting, SND = and precision = . Here, y  and s  are the study-specific effect size and its standard error within studies, respectively, and is between-study variance due to heterogeneity. It tests for whether α = 0. Regression intercept (  or  ) An estimate of the intercept α  of the regression test under the fixed-effect ( ) or random-effects ( ) setting. Skewness (  or  ) An estimate of the skewness of the study-specific errors of the regression test under the fixed-effect ( ) or random-effects ( ) setting. Trim-and-fill method Estimating the suppressed studies and thus correcting small-study effects based on funnel plot’s asymmetry. Proportion of suppressed studies ( ) , where n is the number of studies in the original meta-analysis, and is the estimated number of suppressed studies using the trim-and-fill method. Relative change of overall result by incorporating imputed suppressed studies ( ) , where is the estimated overall result in the original meta-analysis of published studies, and is that after incorporating imputed suppressed studies using the trim-and-fill method.