Sieve Estimation of the Additive Hazards Model with Bivariate Current Status Data

In this paper, we study sieve maximum likelihood estimators of both finite and infinite dimensional parameters in the marginal additive hazards models for bivariate current status data, where the joint distribution of the bivariate survival times is modeled by a nonparametric copula. We assume the two baseline hazard functions and the copula are unknown functions, and use constrained Bernstein polynomials (BP) to approximate these functions. Compared to the existing methods, our proposed method has three main advantages. First, our method provides sufficient flexibility; we bypass the specification of a specific copula structure via efficient BP approximations. Next, we establish strong consistency and optimal rate of convergence of the estimators, along with asymptotic normality and semiparametric efficiency of the regression parameter estimators. Finally, the computational framework relies on the augmented Lagrangian minimization algorithm for optimizing smooth nonlinear objective functions with constraints, leading to faster convergence. Simulation studies conducted using synthetic data reveal that the proposed estimators exhibit nice finite-sample properties. We also illustrate our methodology via application to a real dataset evaluating prevalence of antibodies to hepatitis B and HIV among Irish prisoners.