An improved Bayesian approach to estimating the reference interval from a meta-analysis: Directly monitoring the marginal quantiles and characterizing their uncertainty

Reference intervals, or reference ranges, aid medical decision-making by containing a pre-specified proportion (e.g., 95%) of the measurements in a representative healthy population. We recently proposed three approaches for estimating a reference interval from a meta-analysis based on a random effects model: a frequentist approach, a Bayesian posterior predictive interval, and an empirical approach. Because the Bayesian posterior predictive interval becomes wider to incorporate estimation uncertainty, it may systematically contain greater than 95% of measurements when the number of studies is small or the between study heterogeneity is large. The frequentist and empirical approaches also captured a median of less than 95% of measurements in this setting, and 95% confidence or credible intervals for the reference interval limits were not developed. In this update, we describe how one can instead use Bayesian methods to summarize the appropriate quantiles (e.g., 2.5th and 97.5th) of the marginal distribution of individuals across studies and construct a credible interval describing the estimation uncertainty in the lower and upper limits of the reference interval. We demonstrate through simulations that this method performs well in capturing 95% of values from the marginal distribution and maintains a median coverage of near 95% of the marginal distribution even when the number of studies is small, or the between-study heterogeneity is large. We also compare the results of this method to those obtained from the three previously proposed methods in the original case study of the meta-analysis of frontal subjective postural vertical measurements.