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Bootstrapped confidence intervals for the Cox model using a linear relative risk form.

W E Barlow¹, W H Sun

¹Center for Health Studies, Group Health Cooperative, Seattle, WA 98121.

Statistics in Medicine

|August 1, 1989

Summary

For Cox models with linear relative risk, bootstrapped confidence intervals may not provide accurate coverage. These resampling methods often underestimated the true coverage, indicating potential issues with their application in this context.

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Area of Science:

Biostatistics
Survival Analysis
Statistical Modeling

Background:

The Cox proportional hazards model is a standard tool in survival analysis.
An exponential relative risk form is commonly used, but a linear form can be more appropriate in certain scenarios.
Standard asymptotic confidence intervals may lack adequate coverage due to likelihood flatness near the parameter estimate (beta).

Purpose of the Study:

To derive and evaluate bootstrapped confidence intervals for Cox models with a linear relative risk form.
To compare the performance of different bootstrapping methods against traditional intervals.

Main Methods:

Two resampling methods were developed for bootstrapping confidence intervals.
Method 1: Resampling original data to obtain one-step and fully iterated estimates of beta.

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Method 2: Resampling score and information quantities at each failure time for a one-step estimate.

Main Results:

Bootstrapped confidence intervals were computed using three distinct methods.
These intervals were compared to intervals based on asymptotic standard error and likelihood.
The evaluated bootstrapped intervals generally performed poorly, underestimating true coverage in most instances.

Conclusions:

Bootstrapped confidence intervals derived via the presented methods may not be reliable for Cox models with linear relative risk.
Further research is needed to develop more accurate confidence interval methods for this model specification.