Joint Modeling of Clinical Efficacy and Safety with an Application to Diabetes Studies

Abstract

The purpose of drug development is to evaluate a drug's efficacy and safety profile. For a personalized medicine, it is important for patients and health care providers to understand the efficacy and safety trade-off when selecting a dose for a patient. In this article, we propose three different methods for jointly modeling the clinical safety and efficacy endpoints. These three methods model the correlation relationship in three different ways: modeling the joint distribution by a copula method, modeling conditional distributions, and modeling their correlations through individual means by a hierarchical model. We compare these three methods through simulations and apply these methods to a data set from a diabetes study.

Key Words:

• Adverse events
• Bayesian methods
• Copula
• Efficacy and safety trade-off
• Hierarchical models
• Joint modeling

ACKNOWLEDGMENTS

The authors are grateful to the editor, associate editor, and referees for review of this article. They thank Yongming Qu, Cory R. Heilmann, and Leonard C. Glass for thoughtful discussions that improved the content of the article.

Notes

Note. The numbers in the table are the simulation scenarios which are referred by other figures such as Fig. 1.

Note. Asterisk indicates a statistically significant difference from zero. SD, standard deviation. HPD lower corresponds to the highest posterior density interval lower bound, and HPD upper corresponds to the upper bound.