Defining an optimal cut-off for subscales without a gold standard: a novel method using inflection points of latent attribute probabilities and raw scores

This study introduces Inf.P, a novel method for determining optimal cut-off points using the inflection point approach in the absence of a gold standard. It models the nonlinear relationship between raw scores and latent class probabilities with a cubic polynomial function, offering a data-driven boundary that reflects the underlying latent structure. Inf.P enhances diagnostic precision of scale-based assessments by providing more accurate thresholds for distinguishing different levels of latent attributes.

To evaluate the Inf.P, high- and low-attribute groups were created for benchmarking. The method was compared to the traditional Youden Index through a comprehensive simulation study, exploring variations in sample sizes and item numbers. Real-world data were also employed to assess its applicability. Performance was assessed using accuracy, bias, and mean squared error (MSE).