Incidence Proportions From Random-Effects Meta-Analyses of Rare Events With Large Cluster Heterogeneity, Including...

Area of Science:

• Biostatistics
• Epidemiology
• Health Services Research

Background:

• Estimating rare event incidence proportions (≤5%) with significant cluster heterogeneity presents statistical challenges.
• Existing methods may misrepresent data, particularly in administrative and quality improvement reports within healthcare settings like anesthesia.

Purpose of the Study:

• To review and compare statistical methods for estimating rare event incidence proportions in the presence of large cluster heterogeneity.
• To recommend appropriate statistical approaches for accurate estimation and inference, especially for administrative and quality improvement applications in anesthesia.

Main Methods:

• Narrative review of statistical methods, including weighted mean proportions (marginal estimates) and incidence proportions for the median cluster (conditional estimates).
• Evaluation of random-effects logistic regression, probit regression, two-step methods (arcsine transformations), and fixed-effects models.
• Application and assessment using example datasets from meta-analyses of neurological complications after regional anesthesia and faculty anesthesiologist ratings.

Main Results:

• Random-effects logistic regression provides accurate confidence interval coverage for both conditional and marginal estimates when incidence logits follow a normal distribution.
• Two-step methods (arcsine, double arcsine) offer reasonable confidence interval coverage for forest plots but are inferior for primary inference.
• Fixed-effects methods and generalized estimating equations can lead to significant errors and falsely precise estimates by neglecting cluster heterogeneity.

Conclusions:

• Random-effects logistic regression is recommended for estimating rare event incidence proportions with large cluster heterogeneity due to its superior performance and accurate confidence interval coverage.
• Distinguishing between marginal and conditional estimates is crucial, as marginal estimates are generally larger.
• Administrative and quality improvement reports in anesthesia should utilize random-effects models to avoid data misuse and ensure reliable inference.