Why does the Bonn Risk Index discriminate between calcium oxalate stone formers and healthy controls?

The BRI has been shown to discriminate between calcium oxalate stone formers and controls. BRI is the ratio of the concentration of ionized calcium and the amount of oxalate that must be added to 200 ml urine to initiate crystallization. Higher BRI values are predictive of being a stone former and a value of 1.0 has been found to be the cutoff value to distinguish stone formers and controls. It is not easy to present a consistent argument based on the thermodynamics of calcium oxalate crystallization to account for the success of this index. For instance, why should 2 samples sharing the same BRI but with different ionized calcium and oxalate values have the same likelihood of being obtained from a stone former?

Using data on 195 samples the distribution and interrelationships of measured variables were examined. They were used to calculate illustrative data with which it was possible to examine the effects of varying the parameters and their relationships.

Data simulations identified 3 necessary and sufficient conditions that must be met for BRI to be an effective discriminator between stone former and nonstone former urine samples.

The success of BRI can be explained as the natural outcome of there being significantly different distributions (stone formers vs nonstone formers) of the concentration of ionized calcium and the formation product minus activity product difference as well as the correlation between these 2 variables.