Discretizing multiple continuous predictors with U-shaped relationships with lnOR: introducing the recursive gradient...

Area of Science:

• Statistics
• Biostatistics
• Machine Learning

Background:

• Linearity assumptions in clinical prediction models are often inappropriate, leading to biased estimates.
• Multiple U-shaped predictors can enhance accuracy but increase model complexity and overfitting risks.

Purpose of the Study:

• To introduce and evaluate the Recursive Gradient Scanning (RGS) method for discretizing multiple continuous variables with U-shaped relationships.
• To extend previous research on single U-shaped variables to more common, complex scenarios.

Main Methods:

• Proposed the Recursive Gradient Scanning (RGS) method involving fine screening and iterative AIC comparison for optimal discretization.
• Conducted Monte Carlo simulations varying correlation, sample size, missing rates, and U-shape symmetry.
• Compared RGS against median, Q1-Q3, and minimum P-value methods using AUC and AIC on a real dataset.

Main Results:

• RGS demonstrated superior discrimination and overall performance in simulations across diverse U-shaped scenarios.
• Empirical analysis confirmed RGS identified optimal cut-points with better clinical predictive power (AUC) than traditional methods.

Conclusions:

• The RGS method significantly outperforms common discretization techniques in goodness of fit and predictive ability.
• Future work will address separation/missing data issues and require further validation.