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 standard error). It is roughly symmetrical around the overall effect size if no small-study effects appear.
Regression test	SND = $\alpha$ + $\beta \times$ precision + error. Under the fixed-effect setting, SND (standard normal deviate) = $y/s$ and precision =$1/s$; under the random-effects setting, SND = $y/\sqrt{s^2+{\tau }^2}$ and precision =$1/\sqrt{s^2+{\tau }^2}$. Here, y and s are the study-specific effect size and its standard error within studies, respectively, and ${\tau }^2$ is between-study variance due to heterogeneity. It tests for whether $\alpha$ = 0.
Regression intercept ($T_I^{\text{FE}}$ or $T_I^{\text{RE}}$)	An estimate of the intercept $\alpha$ of the regression test under the fixed-effect ($T_I^{\text{FE}}$) or random-effects ($T_I^{\text{RE}}$) setting.
Skewness ($T_S^{\text{FE}}$ or $T_S^{\text{RE}}$)	An estimate of the skewness of the study-specific errors of the regression test under the fixed-effect ($T_S^{\text{FE}}$) or random-effects ($T_S^{\text{RE}}$) 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 ($P_{\text{TF}}$)	$P_{\text{TF}}={\widehat{k}}_0/\left(n+{\widehat{k}}_0\right)\times 100\%$, where n is the number of studies in the original meta-analysis, and ${\widehat{k}}_0$ is the estimated number of suppressed studies using the trim-and-fill method.
Relative change of overall result by incorporating imputed suppressed studies ($R_{\text{TF}}$)	$R_{\text{TF}}=\left({\widehat{\theta }}_{\text{published data}}/{\widehat{\theta }}_{\text{total data}}-1\right)\times 100\%$, where ${\widehat{\theta }}_{\text{published data}}$ is the estimated overall result in the original meta-analysis of published studies, and ${\widehat{\theta }}_{\text{total data}}$ is that after incorporating imputed suppressed studies using the trim-and-fill method.