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

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Abstract
A linear relative risk form for the Cox model is sometimes more appropriate than the usual exponential form. The usual asymptotic confidence interval may not have the appropriate coverage, however, due to flatness of the likelihood in the neighbourhood of β. For a single continuous covariate, we derive bootstrapped confidence intervals with use of two resampling methods. The first resamples the original data and yields both one‐step and fully iterated estimates of β. The second resamples the score and information quantities at each failure time to yield a one‐step estimate. We computed the bootstrapped confidence intervals by three different methods and compared these intervals to one based on the asymptotic standard error and to a likelihood‐based interval. The bootstrapped intervals did not perform well and underestimated the true coverage in most cases.