Consistent and robust inference in hazard probability and odds models with discrete-time survival data.

Area of Science:

• Biostatistics
• Survival Analysis

Background:

• Conditional likelihood inference in Cox's hazard odds model is computationally challenging for discrete-time survival data with many tied events.
• Unconditional maximum likelihood estimation faces issues with numerous time intervals.

Purpose of the Study:

• To develop novel, computationally tractable methods for survival data analysis using discrete-time hazard probability and odds models.
• To provide robust variance estimation techniques for these models.

Main Methods:

• Development of numerically simple estimating functions for hazard probability and odds models.
• Derivation of the Breslow-Peto estimator as a consistent estimator for the probability hazard model.
• Proposal of a weighted Mantel-Haenszel estimator for the hazard odds model, ensuring conditional unbiasedness.

Main Results:

• The proposed methods are consistent and perform well across various settings, including those with numerous tied events or time intervals.
• The Breslow-Peto estimator is shown to be a consistent estimator.
• The weighted Mantel-Haenszel estimator achieves conditional unbiasedness.

Conclusions:

• The new methods offer practical and reliable solutions for analyzing discrete-time survival data, overcoming limitations of existing techniques.
• These advancements are implemented in the R package dSurvival for broader accessibility.