<p>This paper considers regression analysis of interval-censored competing risks data, which arise in many areas. For the problem, we consider an additive–multiplicative Cox–Aalen model for the subdistribution of a competing risk, and for inference, we propose a sieve maximum likelihood estimation procedure. In the method, B-splines are used to approximate unknown functions, or a finite-dimensional parameter space is employed to approximate the infinite-dimensional parameter space. The developed methodology allows for incorporating and measuring the additive effects of covariates, while preserving its applicability to conventional multiplicative effects of covariates. Furthermore, we establish the asymptotic normality and semiparametric efficiency of the estimated regression parameter. A series of simulation studies are conducted to assess the finite-sample performance of the proposed approach, and it is illustrated by a set of bone marrow transplantation data.</p>