TY - JOUR

T1 - Change-point diagnostics in competing risks models

T2 - Two posterior predictive p-value approaches

AU - Wang, Chen Pin

AU - Ghosh, Malay

N1 - Funding Information:
Fig. 10 Trend plots of means of PPP and PPPP associated with C, where the data are generated from Model 2 (xν = 3↪ 5), but are fitted to an incorrect model that assumes xν = 4 Acknowledgements An earlier version of this paper was presented at the Seventh World Meeting of International Society for Bayesian Analysis. Work on this paper was supported by facilities within the Veterans Evidence-based Research, Dissemination, and Implementation Center, the National Institute of Diabetes & Digestive & Kidney Diseases under grands No. K25 DK075092-01. The authors also wish to acknowledge helpful comments from the referees and the Editor.

PY - 2007/5

Y1 - 2007/5

N2 - 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.

AB - 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.

KW - Change-point

KW - Competing risks

KW - Posterior predictive p-values

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U2 - 10.1007/s11749-006-0006-x

DO - 10.1007/s11749-006-0006-x

M3 - Article

C2 - 25392679

AN - SCOPUS:70349578777

SN - 1133-0686

VL - 16

SP - 145

EP - 171

JO - Test

JF - Test

IS - 1

ER -