Change-point diagnostics in competing risks models: Two posterior predictivep-value approaches.
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 predictivep-values, see Rubin (Ann Stat 12:1151-1172, 1984) and partial posterior predictivep-values as reported by Bayarri and Berger (J Am Stat Assoc 95:1127-1142, 2000), we show that both types ofp-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 ofp-values is discussed.
Department of Epidemiology and Biostatistics, University of Texas Health Science Center at San Antonio, San Antonio, USA.
Chen-Pin
CP
Wang
Department of Statistics, University of Florida, Gainesville, USA.
Malay
M
Ghosh
Change-point; Competing risks; Posterior predictive p-values