ADR 0004: Hartung-Knapp prediction intervals

  • Status: Accepted
  • Date: 2026-07-24

Context

ADR 0002 applied the classic pooled-mean variance to every k - 2 random-effects prediction interval. That kept the interval independent of ci_method, but it diverged from metafor Riley predictions and the Hartung-Knapp Partlett-Riley option in R meta. Both use the covariance selected for mean inference inside the prediction variance.

This difference was material when the unmodified Hartung-Knapp variance was below or above the classic variance. The result metadata still identified the interval as HTS, so callers could not discover the difference from method configuration alone.

Decision

Random-effects inverse-variance prediction intervals retain the k - 2 critical value and three-study minimum:

mu_hat +/- t_(k - 2, 1 - alpha/2)
          * sqrt(tau^2 + Var_selected(mu_hat))
  • normal inference uses the classic pooled-mean variance and records HTS;
  • hartung_knapp uses its unmodified adjusted variance and records HK-PR;
  • hartung_knapp_adhoc uses its lower-bounded adjusted variance and records HK-PR.

Committed values are generated directly from metafor::predict(fit, predtype="Riley") for all three inference choices. Prediction intervals remain unavailable below three included studies and retain the explicit warning with three or four studies.

Consequences

  • prediction intervals and mean intervals use a coherent selected covariance;
  • HK and safeguarded HK prediction intervals can differ from the normal HTS interval even when tau-squared and the pooled estimate are unchanged;
  • result.method.prediction_interval_method distinguishes HTS from HK-PR;
  • this decision supersedes only the prediction-variance paragraph of ADR 0002.