Estimating the reference range from a meta-analysis.

Often clinicians are interested in determining whether a subject's measurement falls within a normal range, defined as a range of values of a continuous outcome which contains some proportion (eg, 95%) of measurements from a healthy population. Several studies in the biomedical field have estimated reference ranges based on a meta-analysis of multiple studies with healthy individuals. However, the literature currently gives no guidance about how to estimate the reference range of a new subject in such settings. Instead, meta-analyses of such normative range studies typically report the pooled mean as a reference value, which does not incorporate natural variation across healthy individuals in different studies. We present three approaches to calculating the normal reference range of a subject from a meta-analysis of normally or lognormally distributed outcomes: a frequentist random effects model, a Bayesian random effects model, and an empirical approach. We present the results of a simulation study demonstrating that the methods perform well under a variety of scenarios, though users should be cautious when the number of studies is small and between-study heterogeneity is large. Finally, we apply these methods to two examples: pediatric time spent awake after sleep onset and frontal subjective postural vertical measurements.