**Sankhya:
The Indian Journal of Statistics**

2007, Volume 69, Pt. 3, 548--580

**On Correlation Models for Longitudinal
Failure Time Data**

M. Tariqul Hasan,
University of New Brunswick, Canada

Brajendra C. Sutradhar and Gary Sneddon,
Memorial University of Newfoundland, Canada

SUMMARY. When repeated failure times are collected from a large number of independent individuals, interest is focused primarily on the efficient estimation of the effects of the associated covariates on the failure times. The construction of the efficient estimating equations requires the modelling of the true correlation structure of the repeated failure times. There exists several bivariate correlation structures, such as the Clayton model, Kendall’s rank and the so-called grade models, for the repeated failure times. These existing correlation structures are, however, limited to the equi-correlation case only. In this paper, as an alternative to the existing bivariate correlation structures, we introduce a class of observation-driven multivariate correlation structures appropriate for non-stationary failure times, which also accommodate the equi-correlation model as a special case. The proposed correlation structure for failure times is exploited to obtain the correlation structure of the cumulative hazard variates in order to construct the true correlation based estimating equations for the hazard ratio parameters. The efficiency loss due to any model mis-specification is examined through a simulation study. A numerical example is considered to illustrate the estimation methodology.

*AMS (2000) subject classification. *Primary 62N02, 62N01.

*Key words and phrases. *Censoring, marginal hazard rate, non-stationary
exponential correlation processes, repeated failure times, survival function,
weighted likelihood estimating equations.