Abstract
Analysis of time-to-event (TTE) data is central to clinical research, yet conventional summary measures like the hazard ratio (HR) and restricted mean survival time (RMST) present significant challenges. The HR is often misinterpreted, and its validity depends on the frequently violated proportional hazards assumption, while the RMST is highly sensitive to the choice of time horizon. This paper introduces two novel, assumption-free estimands to address these limitations: the Highest Risk Density Region (HRDR) and the Highest Net Risk Difference Region (HNRDR).
The HRDR identifies the narrowest time interval containing a pre-specified probability mass of events, directly answering the clinical question: "When is the risk of an event highest?". The HNRDR identifies the narrowest time window in which a pre-specified net absolute risk difference is achieved, pinpointing the period of maximal therapeutic impact by answering: "When is the treatment working the most?". Grounded in a formal causal inference framework, these measures allow for principled estimation of confounder-adjusted treatment effects on the temporal redistribution of risk.
Through comprehensive Monte Carlo simulations across four distinct causal scenarios, we evaluated the performance of two flexible parametric modeling approaches—a spline-based Piecewise Exponential (PWE) model and a transformation model using pseudo-observations—for estimating these regions. Results show the PWE model is superior for estimating the probability density function (PDF), making it ideal for the "up-down" HRDR construction algorithm, while the pseudo-observation model excels at estimating the cumulative distribution function (CDF), pairing naturally with the "right-left" algorithm. The framework's clinical utility is demonstrated through an application to the Milan I trial, revealing distinct prognostic risk profiles for node-positive and node-negative patients. The HRDR/HNRDR framework offers a robust, intuitive, and highly communicable complement to existing TTE measures, providing richer insights into the temporal dynamics of risk and treatment effects
Disciplines
Biostatistics
Suggested Citation
Biganzoli, Giacomo; Marano, Giuseppe PhD; and Boracchi, Patrizia PhD, "Highest Risk Density Region for the communication of the impact of a treatment covariate on the time-to-event distribution" (January 2025). COBRA Preprint Series. Working Paper 126.
https://biostats.bepress.com/cobra/art126