In a clinical setting, biomarkers are typically measured and evaluated as biological indicators of a physiological state. Population based reference ranges, known as `static` or `normal` reference ranges, are often used as a tool to classify a biomarker value for an individual as typical or atypical. However, these ranges may not be informative to a particular individual when considering changes in a biomarker over time since each observation is assessed in isolation and against the same reference limits. To allow early detection of unusual physiological changes, adaptation of static reference ranges is required that incorporates within-individual variability of biomarkers arising from longitudinal monitoring in addition to between-individual variability. To overcome this issue, methods for generating individualised reference ranges are proposed within a Bayesian framework which adapts successively whenever a new measurement is recorded for the individual. This new Bayesian approach also allows the within-individual variability to differ for each individual, compared to other less flexible approaches. However, the Bayesian approach usually comes with a high computational cost, especially for individuals with a large number of observations, that diminishes its applicability. This difficulty suggests that a computational approximation may be required. Thus, methods for generating individualised adaptive ranges by the use of a time-efficient approximate Expectation-Maximisation (EM) algorithm will be presented which relies only on a few sufficient statistics at the individual level.
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