Predicting the Number of Future Events

TL;DR

This paper evaluates methods for predicting the number of future events in time-to-event data, highlighting the limitations of plug-in predictions and proposing improved calibration and predictive-distribution methods.

Contribution

It demonstrates the asymptotic failure of plug-in predictions and introduces two alternative methods that outperform calibration in within-sample event predictions.

Findings

Plug-in prediction methods are asymptotically incorrect.

Calibration methods are asymptotically correct for within-sample predictions.

Two new predictive-distribution methods outperform calibration.

Abstract

This paper describes prediction methods for the number of future events from a population of units associated with an on-going time-to-event process. Examples include the prediction of warranty returns and the prediction of the number of future product failures that could cause serious threats to property or life. 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. This paper shows 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 two alternative predictive-distributionbased methods that perform better than the calibration method are presented and justified.