Discretization of Prostate Cancer Indicators: A Latent-Threshold Framework for Quantifying Information Loss and Correlational Distortion

Prostate cancer research relies heavily on continuous indicators such as prostate-specific antigen(PSA), PSA density, PSA velocity, PSA doubling time, and tumor volume. In practice, these indicators are frequently discretized into binary or ordinal categories to support interpretability, clinical decision thresholds, or harmonization across cohorts. Discretization, however, induces systematic changes in association measures and can distort effect size summaries. We present a latent-threshold framework that connects pre- and post-discretization correlations for prostate cancer indicators. We unify Pearson, biserial, tetrachoric, polyserial, polychoric, phi, and ordinal-phi correlations and describe computational strategies for mapping between them under flexible distributional assumptions. We also propose a simulation-oriented workflow that preserves clinically meaningful marginal distributions and target post-discretization associations. Discretization generally attenuates observed correlations relative to latent continuous associations, with the magnitude of attenuation depending on cutoffs, marginal proportions, and distributional shape. The proposed framework enables investigators to (i) recover implied latent associations from observed discretized correlations, (ii) design simulation studies with calibrated association structures, and (iii) conduct sensitivity analyses over discretization cutoffs. Discretization is often unavoidable in prostate cancer research because clinical decision-making is threshold-based. Explicitly modeling correlation transitions improves interpretability, reproducibility, and simulation fidelity when PSA and related indicators are discretized.