On the Information Matrix of Exponential Mixture Models with Long-term Survivors

The aim of this paper is to study the properties of the asymptotic variances of the maximum likelihood estimators of the parameters of the exponential mixture model with long-term survivors for randomly censored data. In addition, we study the asymptotic relative efficiency of these estimators versus those which would be obtained with complete follow-up. It is shown that fixed censoring at time T produces higher precision as well as higher asymptotic relative efficiency than those obtainable under uniform and uniform-exponential censoring distributions over (0, T). The results are useful in planning the size and duration of survival experiments with long-term survivors under random censoring schemes.