Quantile Effect on Duration of Response: A Zero-Inflated Censored Regression Approach

Duration of response (DOR) has been increasingly used as a useful measure of response to treatments in randomized clinical trials (RCT). Some estimands for DOR, such as the restricted mean DOR, although simple to use, may be sensitive to outliers and may not correctly measure treatment effects on the quantiles of DOR, such as the proportion of patients with DOR of at least 3 months. Quantile regression for survival data has been well developed. However, it is not directly applicable to DOR data in RCTs, due to the presence of non-responders for whom DOR is not defined. Although they can be treated as having zero DOR in a standard quantile regression, such an approach may not be flexible to model these subset of patients. To mitigate this issue, we propose an approach similar to the two-parts zero-inflated models, for example, for count data, so that the nonresponders are modeled as a part of the model, while DOR is modeled using quantile regression. A simulation study is conducted to examine the performance of the proposed approach. For illustration, we apply our approach to a simulated dataset of an acute myeloid leukemia trial, since the true dataset cannot be used due to confidentiality. The asymptotic properties of the proposed approach are also derived.