Efficient analysis of time-to-event endpoints when the event involves a continuous variable crossing a threshold.

In many trials, the duration between patient enrolment and an event occurring is used as the efficacy endpoint. Common endpoints of this type include the time until relapse, progression to the next stage of a disease, or time until remission. The criteria of an event may be defined by multiple components, one or more of which may be a continuous measurement being above or below a threshold. Typical analyses consider all components as binary variables and record the first time at which the patient has an event. This is analysed through constructing and testing survival functions using Kaplan-Meier, parametric models or Cox models. This approach ignores information contained in the continuous components. We propose a method that makes use of this information to improve the precision of analyses using these types of endpoints. We use joint modelling of the continuous and binary components to construct survival curves. We show how to compute confidence intervals for quantities of interest, such as the median or mean event time. We assess the properties of the proposed method using simulations and data from a phase II cancer trial and an observational study in renal disease.