Statistical issues in survival analysis (bootstrap box-cox CIs)
August 27, 2025 The authors are motivated by small sample laboratory or animal studies with non-Gaussian biomarker values and came up with a bootstrap box-cox likelihood ratio confidence interval for the median. Normally due to non-normality of data, one might attempt a Box-Cox transformation of the data but then the interpretation is difficult. Also, it is not easy to convert back to the original data. For the transformed variable, Z, the mean, µ, serves as both the mean and the median and due to the invariant property of the median then it is straightforward to convert the confidence interval of µ back to the median of the original data. They used a nonparametric bootstrap since they assumed the Box-Cox transformation to be a “working model” for the likelihood ratio confidence interval. They essentially bootstrapped the likelihood ratio statistics and from those bootstrapped samples, they computed the 95%-th percentile of the distribution of the bootstrap samples. They also offered a pure nonparametric method of handling this. They found when encountering small samples that they had to make some adjustments by adding a normally distributed random variable with mean 0 and variance ε2 to each data point where this small perturbation would break the tiers. They ran simulations to test their methods and compare to existing methods and they found the likelihood ratio based confidence intervals generally had poor coverage but that their