Shift-Invariant Semiparametric Time-to-Event Modeling for Longitudinal Biomarkers

Thomas M. Menino Convention & Exhibition Center 

Longitudinal time-to-event studies often index covariates to an imprecise subject-specific origin (e.g., estimated disease onset or conception), creating an unknown additive shift in individual time scales. Standard landmark and joint models that use the observed clock as correct can yield biased dynamic risk estimates. We introduce SILK (Shift-Invariant Landmark Kernels), a methodology for dynamic prediction under subject-specific time-shift error. SILK reformulates landmark analysis on shift-invariant primitives-residual time-to-event and visit increments-so that estimation and prediction do not require specifying a parametric measurement-error model. At each landmark, SILK combines (i) a survival model for the residual-time outcome with (ii) nonparametric learning of the conditional distribution of longitudinal biomarkers given history via RKHS conditional mean embeddings that capture evolving biology. We establish identifiability of the latent time shift when biomarkers encode stage information and provide finite sample guarantees. Simulations show gains under realistic misalignment. Application to pregnancy ultrasound biomarkers shows improved dynamic PTB risk prediction.

Survival Analysis

Measurement Error

Reproducing Kernel Hilbert Space

Non-parametric

Longitudinal data 

Biometrics Section