We suggest a new simple approach for estimation and assessment of covariate effects for the cumulative incidence curve in the competing risks model. We consider a semiparametric regression model where some effects may be time-varying and some may be constant over time. Our estimator can be implemented by standard software. Our simulation study shows that the estimator works well and has finite-sample properties comparable with the subdistribution approach. We apply the method to bone marrow transplant data and estimate the cumulative incidence of death in complete remission following a bone marrow transplantation. Here death in complete remission and relapse are two competing events.