Testing the effect of treatment on survival time with an immediate intermediate event

ABSTRACT

In this paper, we consider testing the effects of treatment on survival time when a subject experiences an immediate intermediate event (IE) prior to death or predetermined endpoint. A two-stage model incorporating both (i) the effects of the covariates on the immediate IE and (ii) survival regression with the immediate IE and other covariates is presented. We study the likelihood ratio test (LRT) for testing the treatment effect based on the proposed two stage model. We propose two procedures: an asymptotic-based procedure and a resampling-based procedure, to approximate the null distribution of the LRT. We numerically show the advantages of the two stage modeling over the existing single stage survival model with interactions between the covariates and the immediate IE. In addition, an illustrative empirical example is provided.

KEYWORDS:

• Immediate intermediate event
• likelihood ratio test
• proportional hazards model
• two-stage model.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62N03

Acknowledgments

We are grateful to the associate editor and the reviewer for several thoughtful comments and suggestions which greatly help us to improve the paper. We also would like to express our sincere gratitude to the late Dr. Marvin Zelen for giving us the chance to consider the immediate intermediate event problem. This research would not have been possible without his introduction.

Johan Lim's research was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. 2011-0030810). Sungim Lee's research was supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2011-0025168).