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When are observed failures more informative than observed survivals?

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  • Nader Ebrahimi
  • Ehsan S. Soofi
  • Refik Soyer

Abstract

A framework involving independent competing risks permits observing failures due to a specific cause and failures due to a competing cause, which constitute survival times from the cause of primary interest. Is observing more failures more informative than observing survivals? Intuitively, due to the definitiveness of failures, the answer seems to be the former. However, it has been shown before that this intuition holds when estimating the mean but not the failure rate of the exponential model with a gamma prior distribution for the failure rate. In this article, we address this question at a more general level. We show that for a certain class of distributions failures can be more informative than survivals for prediction of life length and vice versa for some others. We also show that for a large class of lifetime models, failure is less informative than survival for estimating the proportional hazards parameter with gamma, Jeffreys, and uniform priors. We further show that, for this class of lifetime models, on average, failure is more informative than survival for parameter estimation and for prediction. These results imply that the inferential purpose and properties of the lifetime distribution are germane for conducting life tests. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013

Suggested Citation

  • Nader Ebrahimi & Ehsan S. Soofi & Refik Soyer, 2013. "When are observed failures more informative than observed survivals?," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(2), pages 102-110, March.
  • Handle: RePEc:wly:navres:v:60:y:2013:i:2:p:102-110
    DOI: 10.1002/nav.21522
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    1. Arnold Zellner, 1997. "Bayesian Analysis in Econometrics and Statistics," Books, Edward Elgar Publishing, number 825.
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    1. Majid Asadi & Nader Ebrahimi & Ehsan S. Soofi & Somayeh Zarezadeh, 2014. "New maximum entropy methods for modeling lifetime distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(6), pages 427-434, September.

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