Authors

• Mohammad Hossein Dehghan
• ‎Thierry Duchesne

Statistics Department‎, ‎University of Sistan and Baluchestan‎, ‎Iran

Abstract

In this paper, we propose an approach for the nonparametric estimation of the conditional survival function of a time to failure‎ ‎given a time-varying covariate under interval-censoring for the failure time. Our strategy consists in‎ ‎modeling the covariate path with a random effects model, ‎as is done in the degradation and joint longitudinal and survival data modeling‎ ‎literature, ‎then in using a nonparametric estimator of the conditional survival function for time-fixed covariate. ‎We derive the large sample bias and variance of the estimator under simplifying assumptions and we investigate‎ ‎its finite sample efficiency and robustness by simulation. ‎We show how the proposed method can be useful in‎ ‎the early stages of data exploration and model specification by applying it to two real datasets, ‎one on‎ ‎the time to infestation of trees by pine weevil and one on the reliability of a piece of electrical equipment. ‎We conclude by suggesting avenues to make this data exploration method more suitable for formal inferences‎.

Keywords

• Degradation
• Generalized Kaplan-Meier estimator
• Generalized Turnbull estimator
• Joint modeling
• Nadaraya-Watson estimator
• Reliability‎