A two-stage machine learning framework to predict heart transplantation survival probabilities over time with a monotonic probability constraint

The overarching goal of this paper is to develop a modeling framework that can be used to obtain personalized, data-driven and monotonically constrained probability curves. This research is motivated by the important problem of improving the predictions for organ transplantation outcomes, which can inform updates made to organ allocation protocols, post-transplantation care pathways, and clinical resource utilization. In pursuit of our overarching goal and motivating problem, we propose a novel two-stage machine learning-based framework for obtaining monotonic probabilities over time. The first stage uses the standard approach of using independent machine learning models to predict transplantation outcomes for each time-period of interest. In the second stage, we calibrate the survival probabilities over time using isotonic regression. To show the utility of our framework, we applied it on a national registry of U.S. heart transplants from 1987 to 2016. The first stage produces an area under the receiver operating curve ( AUC ) between 0.60 and 0.71 for years 1–10. While the 1-year prediction AUC result is comparable to the reported results in the literature, our 10-year AUC of 0.70 is higher than the current state-of-the-art results. More importantly, we show that the application of isotonic regression to calibrate the survival probabilities for each patient over the 10-year period guarantees monotonicity, while capitalizing on the data-driven and individualized nature of machine learning models. To promote future research, our code and analysis are publicly available on GitHub. Furthermore, we created a web app titled “H-TOP: Heart Transplantation Outcome Predictor” to encourage practical applications.