Bayesian probability of agreement for comparing survival or reliability functions with parametric lifetime regression models

Abstract

In this article, we describe a quantitative approach for comparing the reliability or survival functions for two populations. The Bayesian probability of agreement (BPA) quantifies the similarity of the functions in regions of interest in the covariate space while accounting for a user-specified measure of what constitutes a practically important difference. The BPA method can be flexibly used for relationships with any number of covariates and for a variety of parametric models, including Weibull, lognormal and gamma regression. We provide an R Shiny app that allows practitioners to easily use the method without the need to implement the underlying computational details. Three examples from industrial and medical applications illustrate the implementation of the method as well as how to interpret the results from the analysis.

Keywords:

• equivalence testing
• gamma regression
• lifetime analysis
• lognormal regression
• Markov chain Monte Carlo
• treatment-control comparisons
• Weibull regression

Additional information

Notes on contributors

Nathaniel T. Stevens

Nathaniel T. Stevens is an Assistant Professor of Statistics in the Department of Statistics and Actuarial Science at the University of Waterloo. Prior to this, he was an Assistant Professor at the University of San Francisco, and prior to that he earned is PhD in Statistics from the University of Waterloo. His research interests lie at the intersection of data science and industrial statistics and his publications span topics including experimental design and A/B testing, process monitoring and social network surveillance, network modeling, survival and reliability analysis, and the assessment and comparison of measurement systems.

Lu Lu

Lu Lu is an Assistant Professor of Statistics in the Department of Mathematics and Statistics at the University of South Florida in Tampa. She was a postdoctoral research associate in the Statistics Sciences Group at Los Alamos National Laboratory. She earned a doctorate in Statistics from Iowa State University in Ames, Iowa. Her research interests include reliability analysis, design of experiments, response surface methodology, survey sampling, multiple objective/response optimization. She is a member of the American Statistical Association and the American Society for Quality.

Christine M. Anderson-Cook

Christine M. Anderson-Cook is a Research Scientist and Statistician in the Statistical Sciences Group at Los Alamos National Laboratory. Her research areas include design of experiments, response surface methodology, reliability, multiple criterion optimization, and statistical engineering. She is a Fellow of the American Statistical Association and the American Society for Quality.

Steven E. Rigdon

Steven E. Rigdon is Professor of Biostatistics in the Department of Epidemiology and Biostatistics at Saint Louis University. He is also distinguished research professor emeritus at Southern Illinois University Edwardsville where he served on the faculty from 1986 to 2012. Currently, he is the editor of the Journal of Quantitative Analysis in Sports. He is the author of Calculus, 8th and 9th editions, with D. Varberg and E. Purcell, Statistical Methods for the Reliability of Repairable Systems, with A. Basu, and Monitoring the Health of Populations by Tracking Disease Outbreaks with R. D. Fricker, Jr. He is a fellow of the American Statistical Association.