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

PURPOSE: 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.

METHODS

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).

RESULTS

The Inf.P method demonstrated lower bias and MSE compared to the Youden Index, especially when specificity was prioritized. Both methods yielded similar accuracy in larger samples, but Inf.P provided more reliable cut-off points. In smaller samples, the difference between estimated cut-off points increased with the number of items but decreased in larger samples. These findings suggest that studies with small sample sizes should consider limiting the number of items to maintain optimal cut-off precision.

CONCLUSION

Inf.P offers a robust and reliable approach for defining optimal cut-off in scale-based assessments of complex latent traits, supported by real data, with an interactive web tool available for practical use ( https://spapp.shinyapps.io/InfPcutoff/ ). It promises to enhance diagnostic accuracy and clinical decision-making, particularly in the assessment of psychological and neurological disorders, as well as in determination of quality of life.