Dynamic lifetime prediction using a Weibull-based bivariate failure time model: a meta-analysis of individual-patient data

Abstract

Predicting time-to-death for patients is one of the most important issues in survival analysis. A dynamic prediction method using a bivariate failure time model allows one to build a prediction formula based on tumor progression status observed during the follow-up. However, the existing spline models for the baseline hazard functions are not convenient for predicting long-term survival probability exceeding the largest follow-up time. Therefore, we proposed a parametric method based on the Weibull model to achieve long-term prediction. The present study aims to develop a prediction formula based on a Weibull-based bivariate failure time model, which is designed for individual patient data meta-analysis. We also consider prediction of residual life expectancy that is not possible by the nonparametric models. We conducted Monte Carlo simulations to compare the performance of the proposed model with the spline model. In addition, we illustrate the proposed methods through the analysis of breast cancer patients.

KEYWORD:

• Copula
• Increasing hazard rate
• Residual life
• Semi-competing risk
• Weibull probability plot

MATHEMATICS SUBJECT CLASSIFICATION:

• 62N01
• 62H12
• 62N05

Acknowledgments

The authors kindly thank the two anonymous referees for their careful reading and valuable suggestions that improved the presentation of our study. The authors are deeply grateful to professor Takeuchi Masahiro who provided carefully considered feedback and valuable comments. I also have had the support and encouragement of assistant professor Pak Kyongsun. Advice and comments given by the Department of Clinical Medicine (Biostatistics) have been a great help for me.