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.