Augmented convex hull plots: Rationale, implementation in R and biomedical applications

The paper addresses the possibility to replace cluttered multi-group scatter-plots with augmented convex hull plots. By replacing scatter-plot points with convex hulls, space is gained for visualization of descriptive statistics with error bars or confidence ellipses within the convex hulls. An informative addition to the plot is calculation of the area of convex hull divided by corresponding group size as a bivariate dispersion measure. Marginal distributions can be depicted on the sides of the main plot in established ways. Bivariate density plots might be used instead of convex hulls in the presence of outliers. Like any scatter-plot type visualization, the technique is not limited to raw data -- points can be derived from any dimension reduction technique, or simple functions can be used as axes instead of original dimensions. The limited possibilities for producing such plots in existing software are surveyed, and our general and flexible implementation in R -- the publicly available chplot function -- is presented. Examples based on our daily biostatistical consulting practice illustrate the technique with various options.