Existing likelihood methods for the additive hazards model with interval censored survival data are limited and often ignore the non-negative constraints on hazards. This paper proposes a maximum penalized likelihood method to fit additive hazards models with interval censoring. Our method firstly models the baseline hazard using a finite number of non-negative basis functions, and then regression coefficients and baseline hazard are estimated simultaneously by maximizing a penalized log-likelihood function, where a penalty function is introduced to regularize the baseline hazard estimate. In the estimation procedure, non-negative constraints are imposed on both the baseline hazard and the hazard of each subject. A primal–dual interior-point algorithm is applied to solve the constrained optimization problem. Asymptotic properties are obtained and a simulation study is conducted for assessment of the proposed method.
- Additive hazards model
- Interval censoring
- Maximum penalized likelihood estimation
- Primal–dual interior point algorithm
- Automatic smoothing value selection