In the literature much work has been devoted to the non-parametric estimation of survival analysis functions and has been considered the estimation of the maximum hazard rate under random censorship with covariate. The aim of the present paper is to generalize these works to the case of right censored and left truncated data with covariate.  Via a consistently Nadaraya-Watson weighted type estimator of the conditional hazard function, we get a non-parametric estimator of its maximum value. We investigate strong representation and strong uniform consistency results for our estimators, which generalizes these results obtained in the literature.

conditional hazard rate, maximum conditional hazard rate, non-parametric estimation, kernel, right-censoring, left-truncation.