Multivariate Failure Time Analysis when only the Time to First Failure is Observed

Abstract

We propose a log-linear mixed model to assess covariate effects on the unobservable, catheter-related time-until-infection (TUI), utilizing the observable time-until-first-infection (TUFI). The model assumes that both log (TUI) and the common (random) patient effect follow an extreme value distribution, and TUIs of the same patient are conditionally independent. This model enables the assessment of covariate effects on TUI, accounting for both patient-level (age) and catheter-level (e.g., difficulty of insertion) covariates and the within-patient correlation. The efficient likelihood estimators of fixed-effects and scale parameters of random effects are shown to be consistent and asymptotically normal and appear to perform well in simulations. The methods are illustrated using an example.

Keywords:

• Asymptotic normality
• Consistent
• Efficient likelihood estimate
• Log-linear mixed model
• Simulation
• Time until first event

Mathematics Subject Classification:

• 62N02
• 62F12
• 62H12
• 63N86

Acknowledgment

We thank the referees and the Editor for their very constructive and insightful comments that greatly improved the manuscript.