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The probability of agreement (PoA) has been used as an effective strategy for quantifying the similarity between the reliability of two populations. In contrast to the p-value approach associated with hypothesis testing, the PoA provides a more realistic assessment of similarity by accounting for a practically important difference. This talk discusses the adaptation of the PoA to the comparison of population reliabilities as estimated by Kaplan-Meier curves, when lifetime data is right censored. Three methods for quantifying uncertainty in the PoA estimate are explored: the first approach provides a convenient assessment based on large sample approximations, and the second two approaches offer nonparametric bootstrap-based alternatives. One of these relies on the traditional bootstrap while the other is based on the fractional random-weight bootstrap, which is necessitated by high censoring rates. All methods are illustrated with examples for which comparing the reliability curves of related populations is of interest.
Nathaniel Stevens is an Assistant Professor of Statistics in the Department of Statistics and Actuarial Science at the University of Waterloo. Prior to this Nathaniel held a faculty position at the University of San Francisco in the Department of Mathematics and Statistics where he served as Program Director for the undergraduate data science program. Having overseen 30+ data science internships at 20+ companies, Nathaniel is interested in using statistics to solve practical problems, and he has a passion for inspiring and training students to do the same. His research interests lie at the intersection of data science and industrial statistics; his publications span topics including experimental design and A/B testing, social network modeling and monitoring, survival and reliability analysis, measurement system analysis, and the development of estimation-based alternatives to traditional hypothesis testing.