Tolerance and Prediction Intervals for Non-normal Models
This work provides intuitive and computationally efficient methods for constructing prediction and tolerance intervals, which are crucial for researchers and practitioners working with non-normal data, particularly in fields like clinical trials.
This paper addresses the construction of prediction and tolerance intervals for non-normal models, proposing two main approaches: one leveraging a link function for approximate normality and another based on a confidence interval for the mean when the normal approximation fails. The methods are demonstrated in clinical trial settings, showing computational efficiency compared to alternative approaches.
A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a population percentile in repeated sampling and is often based on a pivotal quantity. One approach we consider in non-normal models leverages a link function resulting in a pivotal quantity that is approximately normally distributed. In settings where this normal approximation does not hold we consider a second approach for tolerance and prediction based on a confidence interval for the mean. These methods are intuitive, simple to implement, have proper operating characteristics, and are computationally efficient compared to Bayesian, re-sampling, and machine learning methods. This is demonstrated in the context of multi-site clinical trial recruitment with staggered site initiation, real-world time on treatment, and end-of-study success for a clinical endpoint.