The Log-Burr XII Regression Model for Grouped Survival Data

Abstract

The log-Burr XII regression model for grouped survival data is evaluated in the presence of many ties. The methodology for grouped survival data is based on life tables, where the times are grouped in k intervals, and we fit discrete lifetime regression models to the data. The model parameters are estimated by maximum likelihood and jackknife methods. To detect influential observations in the proposed model, diagnostic measures based on case deletion, so-called global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to these measures, the total local influence and influential estimates are also used. We conduct Monte Carlo simulation studies to assess the finite sample behavior of the maximum likelihood estimators of the proposed model for grouped survival. A real data set is analyzed using a regression model for grouped data.

Key Words:

• Burr XII distribution
• Censored data
• Grouped survival data
• Regression model
• Sensitivity analysis

ACKNOWLEDGMENT

This work was supported by FAPESP grant 2010/04496-2 and CNPq. The authors are grateful to two anonymous referees and the editor for very useful comments and suggestions.