Nonlinear modeling was applied thoughtfully for risk prediction: the Prostate Biopsy Collaborative Group

Area of Science:

• Biostatistics
• Medical Informatics
• Epidemiology

Background:

• Accurate prediction models for prostate cancer are crucial for clinical decision-making.
• Continuous predictors like prostate-specific antigen and prostate volume require appropriate handling in statistical models.
• Assessing model reproducibility and transportability across different settings is essential for reliable clinical use.

Purpose of the Study:

• To compare the performance of various nonlinear modeling techniques for continuous predictors in prostate cancer prediction models.
• To evaluate the impact of different nonlinear functions on model reproducibility and transportability.
• To identify optimal modeling strategies for internal validation versus external application.

Main Methods:

• Analysis of four independent cohorts of men undergoing prostate biopsy for prostate cancer diagnosis.
• Development of logistic regression models incorporating linear, logarithmic, fractional polynomial (FP1, FP2), and restricted cubic spline (RCS3, RCS5) terms for continuous predictors.
• Internal validation using bootstrap resampling and external validation in independent cohorts.
• Performance assessment using Area Under the Curve (AUC) and Brier Score calibration (CAL).

Main Results:

• Internally, models with fractional polynomials of degree two (FP2) or restricted cubic splines with five knots (RCS5) demonstrated slightly superior performance (AUC, CAL).
• Externally, models utilizing logarithmic terms, fractional polynomials of degree one (FP1), or restricted cubic splines with three knots (RCS3) exhibited better performance.
• The performance differences at external validation were modest but indicated a trend towards simpler nonlinear functions.

Conclusions:

• Highly flexible nonlinear modeling approaches (FP2, RCS5) enhance internal model performance.
• For models intended for broad application across diverse settings, less flexible nonlinear functions (logarithms, FP1, RCS3) may improve external validity and transportability.
• The choice of nonlinear modeling technique should consider the intended use and validation setting of the prediction model.