Speaker
Description
Selecting clinically meaningful cutoff values for continuous prognostic variables is challenging when the association with risk is U-shaped and competing risks are present. We propose a C index-based method to estimate an optimal pair of cutoff values (c_1,c_2) by directly targeting discriminative accuracy. Our approach first fits a smoothing spline to the log relative hazard from the Fine and Gray (FG) and cause specific hazard (CSH) model to confirm the U-shape relationship. This model then generates candidate cut-off pairs at equal heights on either side of the nadir, partitioning patients into the central low-risk group and the high-risk tail groups. From these candidates, we select the optimal pair that maximizes the inverse probability of censoring weighted (IPCW) C-index. For comparison, we also evaluated Gönen–Heller’s concordance probability estimate (CPE), the minimum p-value (Min-P), and the percentile (Q1, Q3) methods. Monte Carlo simulations spanning symmetric, moderately asymmetric, and severely asymmetric U-shapes with 20% and 50% censoring rate show that IPCW C-index using FG model consistently achieves the best Bayesian information criterion (BIC) and small standard errors (SE), and IPCW C-index using CSH model is the second best. The percentile method is highly stable but modestly inferior by BIC. Min-P tends to select more variable, wider cutoff values, and CPE often yields extreme or unstable cutoff values. Overall, IPCW C-index based cutoff value selection (particularly with the FG model) offers a stable, discriminative, and well-fitting strategy for risk stratification when the continuous prognostic variable exhibits U-shaped relationships under survival data with competing risks. The proposed method is also illustrated with a real kidney-transplant data.
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