Graphical Examples Show Why Caution Is Required When Using the Coefficient of Determination (R²) to Interpret Data for Medical Case Reports

A patient with a medical condition can have medical tests or symptoms scored that generate numerical results before, during, or after a treatment, usually over several days, to determine if any benefits have occurred. The changes in the numerical measurements or scores over time can be readily plotted using computer software to show an equation for the line of best fit for either linear or log equations, together with the coefficient of determination (R2). Despite the ease of generating this type of graphical representation, caution is required in interpreting the R2 value with reference to medical case reports. To understand why this is so, at a basic level, four scenarios using hypothetical patient scores were used to generate scatter plots showing the equation for the line of best fit and R2 values with comparison to the average and standard deviation (SD) values. The graphical examples are used to supplement the more complex mathematical and statistical explanations and choices for effect measures that are available. It was found that R2 values for log equations for the line of best fit did not follow a trend with increasing treatment days. For linear equations, a higher R2 value may not necessarily correspond to a lower standard deviation (SD) value for the averaged scores. The R2 value can be influenced by the day on which the scores were recorded, despite the equivalence of the average scores and SD values. R2 values may not indicate the strength of a treatment benefit or the magnitude of scatter between data sets. Score averaging can increase R2 values, while average values remain the same but with the SD value decreasing. The graphical examples shown provide an explanation of why line graphs may be the simplest and best option for reporting, particularly non-linear numerical data, in case reports.