Estimating the Distribution of Ratio of Paired Event Times in Phase II Oncology Trials

With the rapid development of new anti-cancer agents which are cytostatic, new endpoints are needed to better measure treatment efficacy in phase II trials. For this purpose, Von Hoff (1998) proposed the growth modulation index (GMI), i.e. the ratio between times to progression or progression-free survival times in two successive treatment lines. An essential task in studies using GMI as an endpoint is to estimate the distribution of GMI. Traditional methods for survival data have been used for estimating the GMI distribution because censoring is common for GMI data. However, we point out that the independent censoring assumption required by traditional survival methods is always violated for GMI, which may lead to severely biased results. In this paper, we construct nonparametric estimators for the distribution of GMI, accounting for the dependent censoring of GMI. We prove that the proposed estimators are consistent and converge weakly to zero-mean Gaussian processes upon proper normalization. Extensive simulation studies show that our estimators perform well in practical situations and outperform traditional methods. A phase II clinical trial using GMI as the primary endpoint is provided for illustration.