Assessing covariate effects using Jeffreys-type prior in the Cox model in the presence of a monotone partial likelihood

ABSTRACT

In medical studies, the monotone partial likelihood is frequently encountered in the analysis of time-to-event data using the Cox model. For example, with a binary covariate, the subjects can be classified into two groups. If the event of interest does not occur (zero event) for all the subjects in one of the groups, the resulting partial likelihood is monotone and consequently, the covariate effects are difficult to estimate. In this article, we develop both Bayesian and frequentist approaches using a data-dependent Jeffreys-type prior to handle the monotone partial likelihood problem. We first carry out an in-depth examination of the conditions of the monotone partial likelihood and then characterize sufficient and necessary conditions for the propriety of the Jeffreys-type prior. We further study several theoretical properties of the Jeffreys-type prior for the Cox model. In addition, we propose two variations of the Jeffreys-type prior: the shifted Jeffreys-type prior and the Jeffreys-type prior based on the first risk set. An efficient Markov-chain Monte Carlo algorithm is developed to carry out posterior computation. We perform extensive simulations to examine the performance of parameter estimates and demonstrate the applicability of the proposed method by analyzing real data from the SEER prostate cancer study.

KEYWORDS:

• Bayesian estimates
• cause-specific hazards model
• first risk set
• penalized maximum likelihood
• shifted Jeffreys-type prior
• zero events

AMS SUBJECT CLASSIFICATION:

• 62N02

Acknowledgments

We would like to thank the editor in chief, the guest editor, the associate editor, and the two anonymous reviewers for their very helpful comments and suggestions, which have led to a much improved version of the article.

Funding

Dr. de Castro’s research was partially supported by CNPq, Brazil, grant 306579/2014-6. Dr. Chen’s research was partially supported by US Nationsal Institutes of Health grants GM 70335 and P01 CA142538.

Additional information

Funding

Dr. de Castro’s research was partially supported by CNPq, Brazil, grant 306579/2014-6. Dr. Chen’s research was partially supported by US Nationsal Institutes of Health grants GM 70335 and P01 CA142538.