Abstract: We consider a class of partially linear transformation models with interval-censored competing risks data. Under a semiparametric generalized odds rate specification for the cause-specific cumulative incidence function, we obtain optimal estimators of the large number of parametric and nonparametric model components by maximizing the likelihood function over a joint B-spline and Bernstein polynomial spanned sieve space. Our specification considers a relatively simpler finite-dimensional parameter space, approximating the infinite-dimensional parameter space as n → ∞. This allows us to study the almost sure consistency and rate of convergence for all parameters, and the asymptotic distributions and efficiency of the finite-dimensional components. We study the finite-sample performance of our method using simulation studies under a variety of scenarios. Furthermore, we illustrate our methodology by applying it to a data set on HIV-infected individuals from sub-Saharan Africa.

Key words and phrases: Bernstein polynomials, competing risks, cumulative incidence function, interval censoring, partially linear transformation model, semiparametric efficiency.