Incorporating delayed entry into the joint frailty model for recurrent events and a terminal event

Area of Science:

• Biostatistics
• Survival Analysis
• Epidemiology

Background:

• Joint modeling is essential for recurrent events with dependent censoring, like death.
• Frailty models for recurrent events and death are established but often assume observation from the start.
• Delayed entry (left truncation) is common in real-world samples, affecting frailty distribution.

Purpose of the Study:

• To investigate the impact of unadjusted delayed entry in joint frailty models.
• To derive a correctly adjusted marginal likelihood for left-truncated recurrent event and terminal event data.
• To extend existing estimation methods to accommodate left truncation.

Main Methods:

• A comprehensive simulation study was conducted to assess the effects of delayed entry.
• The marginal likelihood was derived as a ratio of integrals over the frailty distribution.
• An existing estimation method was extended to include left truncation, using Gaussian quadrature for numerical integration.

Main Results:

• Failure to adjust for delayed entry can significantly bias results in joint frailty models.
• The derived adjusted marginal likelihood provides a statistically sound approach for left-truncated data.
• The extended method successfully estimated age-specific intensities of recurrent urinary tract infections and mortality.

Conclusions:

• Accurate analysis of recurrent events with dependent censoring requires accounting for delayed entry.
• The proposed method offers a robust solution for left-truncated joint frailty models.
• This approach is valuable for epidemiological studies involving older populations and recurrent health events.