Copula graphic estimation of the survival function with dependent censoring and its application to analysis of pancreatic cancer clinical trial

Abstract

In this article, we consider a survival function estimation method that may be suitable for analyses of clinical trials of cancer treatments whose prognosis is known to be poor such as pancreatic cancer treatment. Typically, these kinds of trials are not double-blind, and patients in the control group may drop out in more significant numbers than in the treatment group if their disease progresses (DP). If disease progression is associated with a higher risk of death, then censoring becomes dependent. To estimate the survival function with dependent censoring, we use copula-graphic estimation, where a parametric copula function is used to model the dependence in the joint survival function of the event and censoring time. In this article, we propose a novel method that one can use in choosing the copula parameter. As an application example, we estimate the survival function of the overall survival time of the KG4/2015 study, the phase 3 clinical trial of the efficacy of GV1001 as a treatment for pancreatic cancer. We provide both statistical and clinical pieces of evidence that support the violation of independent censoring. Applying the estimation method with dependent censoring, we obtain that the estimates of the median survival times are 339 days in the treatment group and 225.5 days in the control group. We also find that the estimated difference of the medians is 113.5 days, and the difference is statistically significant at the one-sided level with size 2.5%.