Nonparametric analysis of covariance for censored data

The fully nonparametric model for nonlinear analysis of covariance, proposed in Akritas et al.(2000), is considered in the context of censored observations. Under this model, the distributions for each factor level combination and covariate value are not restricted to comply to any parametric or semiparametric model. The data can be continuous or ordinal categorical. The possibility of different shapes of covariate effect in different factor level combinations is also allowed. This generality is useful whenever modelling assumptions such as additive risks, proportional hazards or proportional odds appear suspect. Test statistics are obtained for the nonparametric hypotheses of no main effect and of no interaction effect which adjusts for the presence of a covariate. They are quadratic forms based on averages over the covariate values of Beran estimators of the conditional distribution of the survival time given each covariate value. The derivation of the asymptotic (chi)^2 distribution of the test statistics uses a recently-obtained asymptotic representation of the Beran estimator as average of independent random variables. A real-data set is analysed and results of simulation studies are reported.