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Small-study-effect tests

Small-study tests include Egger (unweighted regression, multiplicative dispersion, t test with k-2 degrees of freedom), Begg-Mazumdar rank correlation, Peters and Harbord for binary outcomes, and the Thompson-Sharp random-effects (REML) meta-regression test. Trim-and-fill uses L0 and REML. Numerical agreement depends on inputs and convergence; these methods do not establish publication bias on their own.

Input

Results

TestStatisticp-valueApplicable toVerdict

Funnel + regression overlay

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PET–PEESE and leave-one-out sensitivity

PET and PEESE are weighted regressions of the effects on their standard errors (PET) or variances (PEESE), weights 1/variance, with t inference on k−2 degrees of freedom; the intercept is the limit estimate for a study with zero standard error. PET is the same weighted model as the Egger test above. Conditional rule: use PEESE when PET’s intercept test rejects at two-sided 5% (p < 0.05), otherwise PET. Leave-one-out repeats every validated test with each study omitted in turn and flags omissions that move a p-value across 0.05, change the trim-and-fill k0 or change the PET–PEESE branch. These are sensitivity analyses; they do not establish publication bias.

Uses the studies and format entered above. Needs at least 3 studies for PET–PEESE and 4 to 100 studies for leave-one-out.

Full data: limit estimates (intercepts) with 95% t confidence intervals
ModelEstimateSE95% CIIntercept tIntercept pSlope tSlope p

Leave-one-out

Each row omits one study (numbered in input order); the first row uses all studies and equals the main results table