Inferences for the distribution of the duration of response in a comparative clinical study

Duration of response is an important endpoint used in drug development. Prolonged duration for response is often viewed as an early indication of treatment efficacy. However, there are numerous difficulties in studying the distribution of duration of response based on observed data subject to right censoring in practice. The most important obstacle is that the distribution of the duration of response is in general not identifiable in the presence of censoring due to the simple fact that there is no information on the joint distribution of time to response and time to progression beyond the largest follow-up time. In this article, we introduce the restricted duration of response as a replacement of the conventional duration of response. The distribution of restricted duration of response is estimable and we have proposed several nonparametric estimators in this article. The corresponding inference procedure and additional downstream analysis have been developed. Extensive numerical simulations have been conducted to examine the finite sample performance of the proposed estimators. It appears that a new regression-based two-step estimator for the survival function of the restricted duration of response tends to have a robust and superior performance, and we recommend its use in practice. A real data example from oncology has been used to illustrate the analysis for restricted duration of response.