Two-sample survival probability curves: a graphical method for survival data beyond right censoring

Abstract Background Studies with complex censoring or truncation mechanisms in survival data have historically simplified their data to use right censoring methods and to report treatment effect measures such as the hazard ratio calculated under the right-censoring mechanism. This can lead to loss of information, potential biases, and difficulties with interpretation of study results. In a previous study, we developed a graphical method called “two-sample survival probability curve” to complement current practice in treatment comparisons under right censoring and improve the communication of trial results. Methods In this paper, we extend this novel two-sample graphical approach, which allows visualization of treatment effects and the adequacy of model fits in a [0,1] $$\times$$ [0,1] space, to the analysis of arbitrarily censored and truncated time-to-event data. We first review one-sample nonparametric maximum likelihood estimators (NPMLEs), the analog of the Kaplan-Meier estimator, for a variety of censoring and truncation mechanisms. Then we propose the two-sample survival probability curves based on these NPMLEs and perform Monte-Carlo simulations to examine their performance. Results We demonstrate the proposed graphical method for interval censored, doubly censored, doubly interval censored, and singly truncated, singly censored data using some well-known survival data examples. An R package has been developed for our graphical method for both right censored data and the other types of censored or truncated data discussed in this paper. Conclusions We successfully extended a novel graphical tool to complement the analysis of different types of survival data for two-sample treatment comparisons.