Approximate Tolerance and Prediction in Non-normal Models with Application to Clinical Trial Recruitment and End-of-study Success

by   Geoffrey S Johnson, et al.

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. Outside of normality it can sometimes be challenging to identify an ancillary pivotal quantity without assuming some of the model parameters are known. A common solution is to identify an appropriate transformation of the data that yields normally distributed observations, or to treat model parameters as random variables and construct a Bayesian predictive distribution. Analogously, a tolerance interval covers a population percentile in repeated sampling and poses similar challenges outside of normality. The approach we consider leverages a link function that results in a pivotal quantity that is approximately normally distributed and produces tolerance and prediction intervals that work well for non-normal models where identifying an exact pivotal quantity may be intractable. This is the approach we explore when modeling recruitment interarrival time in clinical trials, and ultimately, time to complete recruitment.



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