  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.
