Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series B, Pt. 1, 31-47

LATENT WAITING TIME MODELS FOR BIVARIATE EVENT TIMES WITH CENSORING

By

SUJIT K. GHOSH Northy Carolina State University, Raleigh
and
ALAN E. GELFAND, University of Connecticut, Storrs

SUMMARY. Multivariate event time data arise frequently in both medical and industrial settings. In such data sets: event times may be associated with quite different occurrences, event times can not be considered as independent - the distribution of time to occurrence of one event may change after the occurrence of another, events can occur simultaneously, available covariate information may provide useful explanation. Censoring in some of the observations, both partial and complete, occurs. Focusing on the bivariate case, we formulate models rich enough to accommodate these features. In the spirit of fatal shock models our classes are built using latent waiting times which are assumed to follow general proportional hazards or accelerated life models. We adopt a Bayesian perspective for inference using simulation based fitting which routinely handles censoring. Since a wide range of model specifications can be introduced, we propose a generic model selection criterion for choosing among bivariate event time models. We conclude with the analysis of a sample of such event times for patients with a clinical diagnosis of AIDS.

AMS (1991) subject classification. 62C10.

Key words and phrases. Accelerated life models, fatal shock models, model choice, proportional hazards models.

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