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.