Increasing the information provided by probabilistic sensitivity analysis: The relative density plot

Abstract

Background: Results of probabilistic sensitivity analyses (PSA) are frequently visualized as a scatterplot, which is limited through overdrawing and a lack of insight in relative density. To overcome these limitations, we have developed the Relative Density plot (PSA-ReD). Methods: The PSA-ReD combines a density plot and a contour plot to visualize and quantify PSA results. Relative density, depicted using a color gradient, is transformed to a cumulative probability. Contours are then plotted over regions with a specific cumulative probability. We use two real-world case studies to demonstrate the value of the PSA-ReD plot. Results: The PSA-ReD method demonstrates proof-of-concept and feasibility. In the real-world case-studies, PSA-ReD provided additional visual information that could not be understood from the traditional scatterplot. High density areas were identified by color-coding and the contour plot allowed for quantification of PSA iterations within areas of the cost-effectiveness plane, diminishing overdrawing and putting infrequent iterations in perspective. Critically, the PSA-ReD plot informs modellers about non-linearities within their model. Conclusions: The PSA-ReD plot is easy to implement, presents more of the information enclosed in PSA data, and prevents inappropriate interpretation of PSA results. It gives modelers additional insight in model functioning and the distribution of uncertainty around the cost-effectiveness estimate.