Testing for a time-dependent covariate effect in the linear risk model

We propose two tests to identify a time dependent covariate effect in the partly parametric linear risk model, and derive asymptotic distributions of the test statistics under the assumption that the covariate effect of interest is constant. One of the asymptotic distributions depends on unknown functions and we devise a weighted bootstrap procedure to estimate its quantiles. We also derive rates of convergence of maximum likelihood estimators of regression coefficients in both the nonparametric and the partly parametric linear risk models using the method of sieves. We carry a simulation study to assess the performance of the proposed test and apply it to real data from a clinical trial on myelomatosis.