Efficient t0$$ {t}_0 $$‐year risk regression using the logistic model

In some clinical studies patient survival beyond a specific point in time, t0$$ {t}_0 $$, say, may be of special interest as it may for instance indicate patient cure. To analyze the t0$$ {t}_0 $$‐year risk for such patients may be accomplished using logistic regression with appropriate weights (IPWCC) that may further be augmented (AIPWCC) to improve efficiency. In this paper, we derive the most efficient estimator for this problem, which is different from the AIPWCC based on the full data efficient influence function. We first give the result for a survival endpoint and then generalize to the competing risk setting. The proposed estimators superior behavior is illustrated using simulations as well as applying it to some real data concerning the survival of blood and marrow transplanted patients.