Methods for Contrasting Gap Time Hazard Functions: Application to Repeat Liver Transplantation

Area of Science:

• Biostatistics
• Survival Analysis
• Medical Statistics

Background:

• Comparing time intervals between sequential events is crucial in many fields, yet methods for analyzing these "gap times" are limited.
• Existing statistical methods inadequately address the comparison of first and second gap times in ordered event sequences.

Purpose of the Study:

• To develop and validate novel statistical methods for estimating the hazard ratio between first and second gap times.
• To provide an interpretable and practical approach for analyzing sequential event data.

Main Methods:

• A two-stage procedure using estimating equations is proposed.
• The first stage involves fitting a proportional hazards model for the first gap time.
• The second stage estimates the hazard ratio between first and second gap times using weighted estimating equations.

Main Results:

• The proposed estimator is shown to have a closed form and is easily interpretable, similar to a standardized mortality ratio.
• Large sample properties were derived, and simulation studies confirmed the finite sample characteristics.
• The method was extended to handle piecewise constant hazard ratios.

Conclusions:

• The developed methods provide a statistically sound and interpretable way to compare gap times between successive events.
• The approach is applicable to real-world data, such as comparing primary versus repeat liver transplants for graft failure.