An Estimation of Treatment Effect under the Additive Model

In this research, we propose an estimation procedure for the additive parameter under the additive hazards model for the two sample problem setting. For this purpose, first of all, we derive an equation which expresses a relationship between two survival or hazard functions with the additive parameter. Based on this expression, we obtain an estimator simply by substituting empirical ones for the survival or cumulative hazard functions. Then we discuss the asymptotic properties including the consistency with deriving the limiting variance of the normalized form for the estimator of the additive parameter. For doing this, we provide several necessary assumptions such as a relation between two sample sizes and behavior of the tail part of the estimator. Also we apply the large sample approximation theorem with the counting process approach. Then we illustrate our estimation procedure with an example. Finally we discuss some interesting features for our estimation procedure as concluding remarks.