We consider the problem of hazard rate estimation in presence of covariates, for survival data with censoring indicators missing at random. We propose in the context usually denoted by MAR (missing at random, in opposition to MCAR, missing completely at random, which requires an additional independence assumption), nonparametric adaptive strategies based on model selection methods for estimators admitting finite dimensional developments in functional orthonormal bases. Theoretical risks bounds are provided, they prove that the estimators behave well in term of Mean Square Integrated Error (MISE). Simulation experiments illustrate the statistical procedure.