A Cox-Aalen Model for Interval-censored Data

The Cox-Aalen model, obtained by replacing the baseline hazard function in the well-known Cox model with a covariate-dependent Aalen model, allows for both fixed and dynamic covariate effects. In this paper, we examine maximum likelihood estimation for a Cox-Aalen model based on interval-censored failure times with fixed covariates. The resulting estimator globally converges to the truth slower than the parametric rate, but its finite-dimensional component is asymptotically efficient. Numerical studies show that estimation via a constrained Newton method performs well in terms of both finite sample properties and processing time for moderate-to-large samples with few covariates. We conclude with an application of the proposed methods to assess risk factors for disease progression in psoriatic arthritis.