Change-point diagnostics in competing risks models: Two posterior predictive p-value approaches

Chen Pin Wang, Malay Ghosh

Research output: Contribution to journalArticlepeer-review

Abstract

This paper presents a Bayesian diagnostic procedure for examining change-point assumption in the competing risks model framework. It considers the family of distributions arising from the cause-specific model as reported by Chiang (Introduction to stochastic processes in biostatistics. Wiley, New York, 1968) upon which change-points are added to accommodate possible distributional heterogeneity. Model departure, due to misspecification of change-points associated with either the overall survival distribution or cause-specific probabilities, is quantified in terms of a sequence of cumulative-sum statistics between each pair of adjacent change-points assumed. When assessing the asymptotic behavior of each sequence of cumulative-sum statistics using its posterior predictive p-values, see Rubin (Ann Stat 12:1151-1172, 1984) and partial posterior predictive p-values as reported by Bayarri and Berger (J Am Stat Assoc 95:1127-1142, 2000), we show that both types of p-values attain their greatest departure from 0.5 at the change-point that is missed in the assumed model, from which a diagnostic procedure is formalized. Statistical power of these two types of p-values is discussed.

Original languageEnglish (US)
Pages (from-to)145-171
Number of pages27
JournalTest
Volume16
Issue number1
DOIs
StatePublished - May 2007

Keywords

  • Change-point
  • Competing risks
  • Posterior predictive p-values

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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