Bayesian analysis of survival data with missing censoring indicators

Abstract

In some large clinical studies, it may be impractical to perform the physical examination to every subject at his/her last monitoring time in order to diagnose the occurrence of the event of interest. This gives rise to survival data with missing censoring indicators where the probability of missing may depend on time of last monitoring and some covariates. We present a fully Bayesian semi-parametric method for such survival data to estimate regression parameters of the proportional hazards model of Cox. Theoretical investigation and simulation studies show that our method performs better than competing methods. We apply the proposed method to analyze the survival data with missing censoring indicators from the Orofacial Pain: Prospective Evaluation and Risk Assessment study.

Keywords: interim event adjudication; missing data; proportional hazards; semiparametric Bayes; time-to-event.

Figure 1.

Study design flowchart: Patient i has been followed-up until V_i when the patient is either diagnosed with TMD or lost to follow-up, or the study ends. This figure appears in color in the electronic version of this article, and any mention of color refers to that version.

Figure 2.

Diagnostic plots for Bayesian analysis of the OPPERA study: figure (a) is a plot of $-\log [\widehat{S}\{\widehat{\Lambda }(V_i)\}]$ versus $\widehat{\Lambda }(V_i)$ for one binary clinical covariate, chronic pain. Figure (b) is the martingale residual versus covariate plot for chronic pain. This figure appears in color in the electronic version of this article, and any mention of color refers to that version.