Estimation of the Conditional Survival Function of a Failure Time Given a Time-varying‎ ‎Covariate with Interval-censored Observations

In this paper, we propose an approach for the nonparametric estimation of the conditional survival function of a time to failureý ýgiven a time-varying covariate under interval-censoring for the failure time. Our strategy consists iný ýmodeling the covariate path with a random effects model, ýas is done in the degradation and joint longitudinal and survival data modelingý ýliterature, ýthen in using a nonparametric estimator of the conditional survival function for time-fixed covariate. ýWe derive the large sample bias and variance of the estimator under simplifying assumptions and we investigateý ýits finite sample efficiency and robustness by simulation. ýWe show how the proposed method can be useful iný ýthe early stages of data exploration and model specification by applying it to two real datasets, ýone oný ýthe time to infestation of trees by pine weevil and one on the reliability of a piece of electrical equipment. ýWe conclude by suggesting avenues to make this data exploration method more suitable for formal inferencesý.