Area under the curve-derived measures characterizing longitudinal patient responses for given thresholds

Abstract

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 analysed with ordinary statistical methods. However, its sheer calculation does not necessarily mirror exactly the piece of information one is seeking for. 

Methods: Available formulas for the calculation of the AUC as well as their specific advantages and limitations are presented. Furthermore, some approaches are discussed to develop AUC-derived measures for the application in particular analysis situations, especially capturing the extent of undercutting or exceeding a given threshold. 

Results: The presented formulas provide an extension of the well-established AUC formulas for respective situations where threshold-dependent subareas of the entire AUC are of interest. To our knowledge, the proposed formulas have been introduced for the first time. Their application to real-world data sets demonstrated the ability to flexibly calculate AUCs of specific interest. 

Conclusions: The extended AUC formulas presented in this paper may help to answer research questions more properly in situations where particular thresholds have to be considered in the course of the analysis. Future developments may address the problem of missing values as well as the current limitation of a fixed threshold.