Threshold Limit Graphical Approach to Understanding Outcome Predictive Metrics: Data from the Osteoarthritis Initiative

Abstract

Scatter plots, bar charts, linear regressions, analysis of variance, and other graphics and tests are frequently used to document associations between an independent variable and an outcome. However, these methods are also frequently limited when understanding how to use an independent variable in subsequent research or patient management. A novel graphical approach to visualizing data-the threshold limit graph-was therefore developed. Publically available data from the Osteoarthritis Initiative was used to illustrate the graphical approach to understanding the association between the change in joint space width (DeltaJSW, independent variable) over four years, and knee symptoms at four years (using the Knee Injury and Osteoarthritis Outcome Score [KOOS], dependent variable). Using data for 4,202 knees, the traditional scatter plot and linear regression approach showed a significant but weak linear relationship between the symptom subscore of the KOOS and DeltaJSW. However, the threshold level of DeltaJSW that affects symptoms was not clear from the data. The same dataset was then plotted using the threshold limit graphical approach, which revealed a non-linear relationship between the variables. In contrast to the scatter plot, plotting the average KOOS symptom subscore for subgroups of the data, with each subgroup defined using sequentially increasing or decreasing DeltaJSW thresholds revealed that symptoms got worse with joint space loss, but only when there was a significant amount of DeltaJSW. A threshold limit analysis was repeated using small, randomly selected subsets of the data (N = ~100) to demonstrate the utility of the technique for identifying trends in smaller datasets. The threshold limit graph is a simple, graphical approach that may prove helpful in understanding how an independent variable might be used to predict outcomes. This approach provides an additional option for visualizing and quantifying associations between variables.