OptBand: optimization-based confidence bands for functions to characterize time-to-event distributions

Area of Science:

• Biostatistics
• Survival Analysis
• Clinical Trials

Background:

• Classical confidence bands for survival functions rely on Brownian motion properties, limiting closed-form derivations for highest confidence density regions.
• Existing methods like Hall-Wellner, equal precision, and empirical likelihood bands have theoretical constraints.
• Accurate estimation of survival functions and cumulative hazards is crucial in medical research and clinical practice.

Purpose of the Study:

• To develop novel confidence bands for survival and cumulative hazard functions using local time processes.
• To address the limitations of traditional methods in deriving highest confidence density regions.
• To provide a statistically sound approach for one-sample and two-sample survival data analysis.

Main Methods:

• Derivation of confidence bands from an optimization problem involving local time processes.
• Application to one-sample problems for cumulative hazard and survival functions.
• Development of a solution for the two-sample problem to test differences in cumulative hazard functions.

Main Results:

• The proposed method provides confidence bands applicable to both cumulative hazard and survival functions.
• A novel solution is presented for testing differences between cumulative hazard functions in two-sample scenarios.
• Monte Carlo simulations demonstrate the finite sample performance of the new bands.

Conclusions:

• The developed confidence bands offer a viable alternative to classical methods, overcoming theoretical limitations.
• The approach is applicable to both one-sample and two-sample survival data analysis.
• The method shows promise for analyzing clinical trial data, exemplified by its application to primary biliary cirrhosis patient survival.