A Cure Time Model for Joint Prediction of Outcome and Time-to-Outcome

The Cox model has been widely used in time-to-outcome predictions, particularly in studies of medical patients, where prediction of the time of death is desired. In addition, the cure model has been proposed to model times of death for discharged patients. However, neither the Cox model nor the cure model allow explicit cure information and prediction of patient cure times (discharge times). In this paper we propose a new model, the "cure time model", which models the static data for dying patients, surviving patients, and their death/cure times jointly. It models (1) mortality via logistic regression and (2) death and discharge times via Cox models. We extend the cure time model to situations with censored data, where neither time of death nor discharge time are known, as well as to multiple (>2) outcomes. In addition, we propose a joint log-odds ratio which can predict the mortality of patients using the information from both the logistic regression and Cox models. We compare our model with the Cox and cure models on a trauma patient dataset from UCSF/San Francisco General Hospital. Our results show that the cure time model more accurately predicts both mortality and time-to-mortality for patients from these datasets.