A joint test for progression and survival with interval-censored data from a cancer clinical trial

Clinical trials often assess efficacy by comparing treatments on the basis of two or more event-time outcomes. In the case of cancer clinical trials, progression-free survival (PFS), which is the minimum of the time from randomization to progression or to death, summarizes the comparison of treatments on the hazards for disease progression and mortality. However, the analysis of PFS does not utilize all the information we have on patients in the trial. First, if both progression and death times are recorded, then information on death time is ignored in the PFS analysis. Second, disease progression is monitored at regular clinic visits, and progression time is recorded as the first visit at which evidence of progression is detected. However, many patients miss or have irregular visits (resulting in interval-censored data) and sometimes die of the cancer before progression was recorded. In this case, the previous progression-free time could provide additional information on the treatment efficacy. The aim of this paper is to propose a method for comparing treatments that could more fully utilize the data on progression and death. We develop a test for treatment effect based on of the joint distribution of progression and survival. The issue of interval censoring is handled using the very simple and intuitive approach of the Conditional Expected Score Test (CEST). We focus on the application of these methods in cancer research.