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Meta-Analysis
. 2022 Mar 24;191(5):948-956.
doi: 10.1093/aje/kwac013.

A Guide to Estimating the Reference Range From a Meta-Analysis Using Aggregate or Individual Participant Data

Lianne Siegel, M Hassan Murad, Richard D Riley, Fateh Bazerbachi, Zhen Wang, Haitao Chu
Meta-Analysis

A Guide to Estimating the Reference Range From a Meta-Analysis Using Aggregate or Individual Participant Data

Lianne Siegel et al. Am J Epidemiol. .

Abstract

Clinicians frequently must decide whether a patient's measurement reflects that of a healthy "normal" individual. Thus, the reference range is defined as the interval in which some proportion (frequently 95%) of measurements from a healthy population is expected to fall. One can estimate it from a single study or preferably from a meta-analysis of multiple studies to increase generalizability. This range differs from the confidence interval for the pooled mean and the prediction interval for a new study mean in a meta-analysis, which do not capture natural variation across healthy individuals. Methods for estimating the reference range from a meta-analysis of aggregate data that incorporates both within- and between-study variations were recently proposed. In this guide, we present 3 approaches for estimating the reference range: one frequentist, one Bayesian, and one empirical. Each method can be applied to either aggregate or individual-participant data meta-analysis, with the latter being the gold standard when available. We illustrate the application of these approaches to data from a previously published individual-participant data meta-analysis of studies measuring liver stiffness by transient elastography in healthy individuals between 2006 and 2016.

Keywords: meta-analysis; normative data; prediction interval; random effects; reference range.

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Figures

Figure 1
Figure 1
Marginal (overall) distribution and a selection of hypothetical study distributions according to a random-effects model where formula image. The distributions of study means and individuals within each study are all normal. The vertical lines represent the 2.5th and 97.5th quantiles of the marginal distribution. Each of the meta-analysis methods presented allows for true differences between subpopulations, and the target population is the overall distribution that captures each of these.
Figure 2
Figure 2
Estimated mean and 95% confidence interval (CI) for each transient elastography liver-stiffness measurement study and estimated pooled mean (95% CI) based on aggregate data from a previously published meta-analysis of liver stiffness measurements collected between 2006–2016 (1). kPa, kilopascal.
Figure 3
Figure 3
Estimated mean, 95% confidence interval (CI), and 95% frequentist prediction interval (PI) for a new individual’s transient elastography liver stiffness measurement by study, 95% CI for the pooled mean, 95% PI for a new study mean, and estimated 95% reference ranges (RRs) using the 3 methods presented, based on aggregate data (AD) from a previously published meta-analysis of liver stiffness measurements collected between 2006–2016 (1). Each reference range was estimated on the log-scale and the resulting bounds were exponentiated. kPa, kilopascal.
Figure 4
Figure 4
95% confidence interval for the pooled mean, 95% prediction interval for the mean of a new study, and estimated 95% reference range for hypothetical data where formula image and for different within-study sample size (n) and number of studies (N).
See this image and copyright information in PMC

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