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Abstract:
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We describe prediction methods for the number of future events from a population of units associated with an on-going time-to-event process. Important decisions such as whether a product recall should be mandated are often based on such predictions.
Data, generally right-censored (and sometimes left truncated and right-censored), are used to estimate the parameters of a time-to-event distribution. This distribution can then be used to predict the number of events over future periods of time. Such predictions are sometimes called within-sample predictions, and differ from other prediction problems considered in most of the prediction literature. We show that the plug-in (also known as estimative or naive) prediction method is not asymptotically correct (i.e., for large amounts of data, the coverage probability always fails to converge to the nominal confidence level). However, a commonly used prediction calibration method is shown to be asymptotically correct for within-sample predictions, and we present and justify two alternative methods, based on predictive distributions, that perform better.
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