Multilevel Bayesian Models for Survival Times and Longitudinal Patient-Reported Outcomes With Many Zeros

Abstract

Regulatory approval of new therapies often depends on demonstrating prolonged survival. Particularly when these survival benefits are modest, consideration of therapeutic benefits to patient-reported outcomes (PROs) may add value to the traditional biomedical clinical trial endpoints. We extend a popular class of joint models for longitudinal and survival data to accommodate the excessive zeros common in PROs, building hierarchical Bayesian models that combine information from longitudinal PRO measurements and survival outcomes. The model development is motivated by a clinical trial for malignant pleural mesothelioma, a rapidly fatal form of pulmonary cancer usually associated with asbestos exposure. By separately modeling the presence and severity of PROs, using our zero-augmented beta (ZAB) likelihood, we are able to model PROs on their original scale and learn about individual-level parameters from both presence and severity of symptoms. Correlations among an individual's PROs and survival are modeled using latent random variables, adjusting the fitted trajectories to better accommodate the observed data for each individual. This work contributes to understanding the impact of treatment on two aspects of mesothelioma: patients’ subjective experience of the disease process and their progression-free survival times. We uncover important differences between outcome types that are associated with therapy (periodic, worse in both treatment groups after therapy initiation) and those that are responsive to treatment (aperiodic, gradually widening gap between treatment groups). Finally, our work raises questions for future investigation into multivariate modeling, choice of link functions, and the relative contributions of multiple data sources in joint modeling contexts.

KEY WORDS:

• Beta distribution
• Cancer
• Failure time
• Random effects model
• Repeated measures
• Weibull distribution

Acknowledgments

The work of Hatfield and Carlin was supported by a grant from Eli Lilly and Company, Global Health Outcomes—Oncology #2010-103, while that of Carlin was also supported by the National Cancer Institute grant. The authors thank the associate editor and two anonymous referees for their particularly insightful and constructive suggestions.