Methodologies

Generic inverse-variance, hazard ratios, and adjusted estimates

How reported estimates and standard errors are entered, transformed, pooled, and checked when arm-level data are insufficient or inappropriate.

18 min readUpdated June 15, 2026

When generic estimates are needed

Generic inverse-variance input is appropriate when the source study reports a defensible effect estimate and uncertainty, especially for adjusted analyses, time-to-event outcomes, cluster-aware analyses, crossover analyses, or non-randomized studies.

The extracted TE and seTE become the analysis input. The app does not know whether the source model was appropriate; reviewers must record adjustment covariates and model details.

Formulas and scale rules

For a 95 percent CI around a difference measure, SE = (upper - lower) / (2 * 1.96). For a ratio measure, SE(log effect) = (log(upper) - log(lower)) / (2 * 1.96).

Hazard ratios should usually be synthesized as log(HR) with SE(log HR). If a log-rank O-E statistic and variance V are available, log(HR) can be approximated as (O - E) / V with SE = 1 / sqrt(V).

Generic inverse-variance weights are w_i = 1 / seTE_i^2 for common-effect synthesis and w_i = 1 / (seTE_i^2 + tau^2) for random-effects synthesis.

App defaults and changeability

  • Generic synthesis requires the intended effect measure; missing effect measures should fail validation rather than silently falling back to MD.
  • HR is the default project effect measure for time-to-event outcomes.
  • Tau estimator defaults to REML and is user-changeable.
  • HKSJ/HK interval behavior is user-changeable where supported.
  • Generic/time-to-event extraction fields are opt-in so basic extraction stays compact.

Reporting checklist

  1. Report whether estimates were adjusted or unadjusted.
  2. Report model covariates for adjusted estimates.
  3. Do not mix adjusted and unadjusted estimates without a deliberate, reported decision.
  4. Confirm all estimates use the same direction and compatible scale.
  5. For HRs, report whether proportional hazards was assumed and how HR/SE were obtained.