Finite sample pointwise confidence intervals for a survival distribution with right-censored data

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Inference

Background:

• Pointwise confidence intervals are crucial for survival analysis with right-censored data.
• Existing methods may lack exactness for small samples under independent censoring.
• The beta product confidence procedure (BPCP) offers exact intervals for binomial parameters and certain censoring schemes.

Purpose of the Study:

• To develop and evaluate pointwise confidence intervals for survival distributions with right-censored data in small samples.
• To modify the BPCP for improved performance, particularly for small sample sizes and varying censoring levels.
• To compare the performance of the standard BPCP, a 'mid-p' version, and asymptotically-based approximations.

Main Methods:

• Review and development of pointwise confidence intervals for survival distributions.
• Modification of the BPCP to create a 'mid-p' version.
• Extensive simulations using a method of moments implementation enforcing monotonicity over time.

Main Results:

• The standard BPCP demonstrated exact coverage across simulated scenarios.
• The 'mid-p' BPCP showed coverage closer to nominal levels but may not be exact in all situations, especially with low censoring.
• Asymptotically-based approximations exhibited lower than nominal coverage due to inflated lower error rates.

Conclusions:

• The standard BPCP is recommended for its exactness in survival analysis with right-censored data.
• The 'mid-p' BPCP offers an alternative with potentially better simulated coverage but requires careful consideration of censoring levels.
• Both BPCP methods are available in the bpcp R package for practical application.