|
Abstract:
|
In making inference on the relation between failure and exposure histories in the Cox model, the maximum partial likelihood estimator (MPLE) of the finite dimensional odds parameter, and the Breslow estimator of the baseline survival function, are known to achieve full efficiency when data is available for all time on all cohort members. However, under the sampling designs, the MPLE is not efficient in general. In this paper, we show that, when using the nested case-control design, it approaches efficiency in highly stratified situations, where the covariate values are increasingly less dependent upon the past, when the covariate distribution is unknown, and there is no censoring. In particular, in such situations, both the MPLE and the Breslow estimator achieve the information lower bound both in the distributional and the minimax senses when the cohort size tends to infinity.
|
