Inference for cumulative incidence functions with informatively coarsened discrete event-time data

Area of Science:

• Biostatistics
• Epidemiology
• Survival Analysis

Background:

• Comparing cumulative incidence functions (CIFs) is crucial for understanding disease progression and risk factors.
• Informative coarsening (censoring) and competing risks (like death) complicate standard survival analysis.
• Existing frequentist methods for non-informative coarsening require extension.

Purpose of the Study:

• To develop and compare statistical methods for analyzing CIFs in the presence of informative coarsening and competing risks.
• To extend existing frequentist hypothesis tests for non-informative coarsening.
• To propose a novel Bayesian approach for comparing CIFs under informative coarsening.

Main Methods:

• Extended frequentist hypothesis tests for non-informative coarsening.
• Developed a novel Bayesian method comparing posterior distributions to null hypothesis expectations.
• Utilized extended estimation procedures to handle censoring by death.
• Conducted a sensitivity analysis using expert-elicited information on informative censoring.

Main Results:

• The study presents robust statistical frameworks for handling complex censoring scenarios in survival data.
• Both extended frequentist and novel Bayesian methods provide valid comparisons of cumulative incidence functions.
• Sensitivity analysis demonstrates the impact of informative censoring on results.

Conclusions:

• The proposed methods offer improved accuracy for comparing event rates in the presence of informative coarsening and competing risks.
• The Bayesian approach provides a flexible framework for incorporating expert knowledge.
• These methods are applicable to real-world epidemiological studies, such as analyzing HIV incidence in the ALIVE study.