A Threshold Regression Mixture Model for Assessing Treatment Efficacy in a Multiple Myeloma Clinical Trial

Abstract

A first-hitting-time (FHT) survival model postulates a health status process for a patient that gradually declines until the patient dies when the level first reaches a critical threshold. Threshold regression (TR) is a new regression methodology that incorporates the effects of covariates on the threshold and process parameters of this FHT model. In this study, we use TR to analyze data from a randomized clinical trial of treatment for multiple myeloma. The trial compares VELCADE and high-dose Dexamethasone, the former a new therapy and the latter an established therapy for this disease. Patients are switched between the two drugs based on patient response. The novel contribution of this work is the modeling of this clinical trial design using a mixture of TR models. Specifically, we propose a mixture FHT model to fit the survival distribution. The model includes a composite time scale that differentiates the rate of disease progression before and after switching. The analysis shows significant benefit from initial treatment by VELCADE. A comparison is made with a Cox proportional hazards regression analysis of the same data.

Key Words:

• Analysis time
• Composite time
• Cox regression
• Data analysis
• Disease progression
• Duration
• First hitting time
• Lifetime
• Maximum likelihood
• Mixture model
• Multiple myeloma
• Proportional hazards
• Randomized clinical trial
• Stochastic process
• Stopping time
• Survival
• Threshold regression
• Time-to-event
• Treatment switching
• Wiener diffusion process

ACKNOWLEDGMENTS

This research is supported in part by NIOSH Grant OH008649 (Lee) and by NSERC Grant 4032-05 (Whitmore). The authors thank Millennium Pharmaceutical Inc. for making background information on multiple myeloma, the study protocol and the data set available to the authors and for its financial support of the research.

Notes

Initial health status for each component depends on baseline covariates representing previous treatments prev, level of beta-2 microglobulin lgb2, and baseline age age. The mean parameter for each component depends on treatment trt, whether PD occurred pd, and their interaction trt-pd.