The highest confidence density region and its usage for joint inferences about constrained parameters

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Joint inferences for constrained parameters often rely on normal approximations.
• Conventional confidence regions can be imprecise, especially with complex data structures.

Purpose of the Study:

• To develop optimal confidence regions for constrained parameters using confidence distributions.
• To apply this method for inferences on the survival function with censored data.

Main Methods:

• Utilized confidence distributions, a frequentist alternative to Bayesian posterior distributions.
• Employed Markov chain Monte Carlo (MCMC) algorithms for efficient region generation.
• Applied the technique to censored survival data, specifically from the Mayo primary biliary cirrhosis study.

Main Results:

• The proposed confidence distribution method provides optimal confidence regions.
• Demonstrated efficient generation of these regions using MCMC.
• Achieved a 0.95 confidence region with a volume 34 times smaller than conventional confidence bands in the Mayo PBC data.

Conclusions:

• Confidence distributions offer a powerful frequentist tool for constructing precise confidence regions.
• The new method significantly improves the efficiency and accuracy of inferences in survival analysis with censored data.