Multi-state model for studying an intermediate event using time-dependent covariates: application to breast cancer

Area of Science:

• Biostatistics
• Survival Analysis
• Medical Statistics

Background:

• Intermediate events in disease progression can influence patient outcomes.
• The impact of intermediate events on prognosis is often dependent on timing and duration.
• Investigating these time-dependent effects is crucial for accurate survival analysis.

Purpose of the Study:

• To propose and evaluate statistical methods for analyzing the time-dependent hazard ratio after an intermediate event.
• To assess the influence of waiting time and sojourn time on the hazard ratio.
• To apply these methods to breast cancer data, specifically focusing on isolated locoregional recurrence (ILRR).

Main Methods:

• Utilized a multi-state illness-death model as a framework.
• Employed Cox regression-based approaches, extending beyond standard Markov models by incorporating different time-scales.
• Included time-varying covariates using fractional polynomials and applied to German Breast Cancer Study Group (GBSG) data.

Main Results:

• Time-dependent structures significantly altered hazard functions for breast cancer.
• Early ILRR substantially increased the risk of death, while late ILRR had a lesser impact.
• Successful treatment of ILRR minimally increased mortality risk concerning distant disease.

Conclusions:

• Multiple modeling strategies exist for intermediate events, each with limitations and potential for divergent results.
• Time-dependency in statistical analyses, often neglected in breast cancer literature, is critical for ILRR.
• Fractional polynomials are effective for modeling time-varying variables in survival analyses.