Inverszvariancia

Inverszvariancia, or inverse-variance weighting, is a statistical method used to combine multiple estimates by giving each estimate a weight equal to the reciprocal of its variance. The idea is that more precise estimates (those with smaller variance) should contribute more to the combined result than less precise ones.

In a typical meta-analysis with studies i providing an effect estimate θ_i and variance var_i, the weight is w_i = 1/var_i. The fixed-effect pooled estimate is θ̂ = (Σ w_i θ_i) / (Σ w_i), and its variance is Var(θ̂) = 1 / (Σ w_i). This approach is equivalent to performing a generalized least squares analysis with known, uncorrelated variances.

In random-effects meta-analysis, between-study heterogeneity is acknowledged by adding a term τ^2 to each study’s variance: w_i = 1/(var_i + τ^2). Here, τ^2 represents the between-study variance and is estimated from the data (common methods include DerSimonian-Laird or REML). The pooled estimate uses these adjusted weights, reflecting both within-study precision and between-study variability.

Interpretation: inverse-variance weighting emphasizes results with smaller uncertainty, producing a more precise combined effect estimate when model assumptions hold.

Assumptions and limitations: accurate variance estimates, independence of study results, and absence of substantial publication or small-study bias. Misestimated variances or biased data can distort weights. In the presence of substantial heterogeneity, random-effects weighting is more appropriate than fixed-effect weighting.

Related concepts include generalized least squares, meta-regression, and Bayesian precision-weighted approaches, all of which rely on the idea that precision (inverse variance) determines influence on the combined result.