gms | German Medical Science

Background: Calculation of the area under the curve (AUC) is a widely used practice in longitudinal study settings. The AUC values should reflect study participants’ particular trajectories by means of a continuous measure which can be further analyzed with ordinary statistical methods. Since longitudinal data are often collected in the course of randomized as well as observational studies in health services research, usage of AUC has a practical relevance for the field.

Research question: AUCs calculated by means of the common formulas do not necessarily mirror exactly the piece of information one is seeking for, since they always refer to the full area which is enclosed by the trajectory and both plotting axes. The available formulas need to be adapted in some cases in order to prevent misleading conclusions.

Methods: Common formulas for the calculation of the AUC as well as their specific advantages and limitations are presented. Furthermore, different approaches are discussed for developing AUC-derived measures for the application in particular analysis situations, e.g. capturing the extent of undercutting or exceeding a given threshold. All analyses are conducted in the statistical software R (version 3.2.1).

Results: The presented approaches are applied to various data sets from practice. First, a clinical data set capturing the follow-up of blood pressure measurements in intensive care patients are used. Second, longitudinal measurements of cerebral oxygenation in preterm infants are considered. Third, the time course of rehabilitation treatments in a large secondary data set is analyzed. All analyses base on sensible research questions which may be addressed in the course of a longitudinal data analysis.

Discussion: The results will demonstrate the inappropriateness of common AUC formulas when interpreting specific research questions related to longitudinal data. The standard calculation approaches only reveal the entire area enclosed by the trajectory and both axes, but the full AUC value is often not of primary interest. Therefore, the available formulas were adapted to more flexible algorithms. By means of the applied data examples it will be obvious that more situational approaches are required.

Practical implications: Since the analysis of longitudinal data is frequently used in health services research, this contribution may be of significant interest for data analysts in the field. A comprehensive description of study participants’ time course is required in order to assess treatments effects, risk factors, etc. in routine care to the full extent.