Meta-analysis

Generic inverse-variance (effect size + SE)

Generic inverse-variance meta-analysis pools any per-study effect size yᵢ with its standard error seᵢ — the right tool when Hedges' g, log RR, log OR or Fisher z was computed elsewhere.

What is Generic inverse-variance (effect size + SE)?

Inverse-variance pooling weights each study by 1/seᵢ², giving more weight to precise studies. The fixed-effect estimator assumes all studies estimate the same true effect; the random-effects estimator (DerSimonian-Laird τ²) accommodates between-study heterogeneity by treating each study's true effect as a draw from a distribution.

Three heterogeneity statistics report together: Q (Cochran's chi-square test against homogeneity), I² (percentage of total variance attributable to between-study heterogeneity, with rough anchors 25%/50%/75% = low/moderate/high), and τ² (the estimated between-study variance).

When the effect-size is on a log scale (log RR, log OR), the forest plot back-transforms for display while pooling on the log scale — the right approach because the log-scale effects are approximately normal while the raw OR / RR aren't.

When should I use Generic inverse-variance (effect size + SE)?

  • When study effect sizes + SEs are pre-computed in your software or spreadsheet.
  • Pooling effect sizes that don't fit the binary / continuous / proportion specialised tools.
  • Switch to meta_continuous / meta_binary / meta_proportion when the input is per-study summary stats — those handle the escalc step for you.

What data does it need?

Two numeric columns: yᵢ and seᵢ + optional study-label column.

What does it report?

Fixed-effect + random-effect pooled estimates with CIs and z/p; Q + I² + τ² heterogeneity; Egger's test for funnel asymmetry; forest + funnel plots.

What does it assume?

  • Studies estimate effects on the same scale (transform first if needed).
  • SEs are correctly computed.
  • Studies are independent.

How do I interpret the result?

I² > 50% ⇒ substantial heterogeneity ⇒ prefer random-effects pooling and report τ² alongside.

Egger's test p < 0.05 ⇒ funnel asymmetry, possibly small-study bias / publication bias. Look at the funnel plot before deciding what to make of it.

See also

References

  • Borenstein, Hedges, Higgins & Rothstein (2009). Introduction to Meta-Analysis.