Bootstrap-type confidence intervals for quantiles of the survival distribution

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Methods

Background:

• Estimating survival quantiles with right-censored data is crucial in medical research.
• Existing methods for confidence intervals often rely on inverting test statistics or other survival quantities.
• Incorporating covariates into survival analysis requires robust confidence interval estimation.

Purpose of the Study:

• To develop an easy-to-program, direct analytical method for calculating bootstrap-type confidence intervals for survival quantiles.
• To enable the incorporation of covariates within parametric survival models.
• To compare the performance of the new method against existing approaches for median confidence intervals.

Main Methods:

• The proposed method utilizes fractional order statistics and a beta transformation of the estimated survival function.
• It allows for both parametric and non-parametric approaches to survival function estimation.
• The method provides a direct calculation of confidence intervals, unlike indirect methods.

Main Results:

• The new analytical method is straightforward to program and implement.
• It successfully incorporates covariates into parametric survival models.
• Favorable coverage probabilities were observed for median confidence intervals generated by this method compared to six other methods.

Conclusions:

• This novel method offers a direct and efficient way to compute confidence intervals for survival quantiles with censored data.
• The approach is versatile, accommodating both parametric and non-parametric models and covariate incorporation.
• The demonstrated superior performance in coverage probabilities highlights its utility in survival data analysis.