Efficient estimation of left-truncated and right censored data with additive hazard model

الملخص EN

In this paper, an additive hazard model is considered as a semiparametric model in which the unknown parameter consists of finite dimensional and infinite dimensional parts with left truncated and right censored data.

The full likelihood function for the model is obtained for the parametric part and also for the nonparametric part using linear sieve procedure and then compute the maximum likelihood estimators for the two parts.

The consistency of the maximum likelihood estimators is also proved for the two type of parameters.

The score operators for the parametric and nonparametric parts are obtained and their adjoint score operators are computed.

Finally, a simulation study using Monti-Carlo method and R language is implemented to compute the maximum likelihood estimators and compare the results of the proposed method with the true values.

As a real life application, Stanford Heart transplant data is considered and the maximum likelihood estimators are computed