Reproduce “Kernelized Stein Discrepancy Tests of Goodness-of-fit for Time-to-Event Data” on OpenResearch

About this paper

Tamara Fernandez, Nicolas Rivera, Wenkai Xu, Arthur Gretton

The authors propose three tests for right-censored survival data using times and censoring indicators, without imputing censored times. The martingale test transforms times through the model’s distribution function and applies a kernel Stein discrepancy. In a periodic-hazard simulation, it reached about 75% power at theta=4 with n=100, 30% censoring, and alpha=0.01, while most methods had little power. The result assumes independent censoring.

Key insights

• The formulation of distinct Stein operators for censored data allows for robust goodness-of-fit testing, with the Martingale operator demonstrating stronger statistical properties and milder integrability conditions.
• A uniform-transformed variant (mKSDu) of the Martingale operator substantially improves test power for detecting certain complex, non-parametric deviations, such as periodic hazard functions.
• The Proportional Stein Operator enables specific validation of composite hypotheses, like the proportional hazards assumption, by being insensitive to scaling factors of the hazard function.

Summary by alphaXiv.