A Hybrid Scale Intensity Model for Recurrent Event Data

Abstract

We propose an extended parametric class of models for analysing multiple failure data where the study subjects can experience repeated events. The general framework allows a broad class of hazard or intensity models including the Poisson and renewal process models as very special cases. A proportional intensity baseline function is assumed for the model with covariates. Maximum likelihood estimation is discussed. A particular flexible parametrization is considered in details. Theoretical calculation of the information matrix is used to assess when discrimination between different kinds of dependency is likely to be feasible.

Key Words:

• Intensity models
• Maximum likelihood estimation
• Poisson process
• Recurrent events
• Renewal process

Acknowledgments

The author is very grateful to D. R. Cox, A. C. Davison, D. Firth and V. Isham for helpful comments and suggestions. The work was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico, Brazil.