Joint modeling under competing risks: Application to survival prediction in patients admitted in Intensive Care Unit for sepsis with daily Sequential Organ Failure Assessment score assessments

Joint models of longitudinal process and time‐to‐event data have recently gained attention, notably to provide individualized dynamic predictions. In the presence of competing risks, models published mostly involve cause‐specific hazard functions jointly estimated with a linear or generalized linear model. Here we propose to extend the modeling to full parametric joint estimation of a nonlinear mixed‐effects model and a subdistribution hazard model. We apply this approach on 6046 patients admitted in intensive care unit (ICU) for sepsis with daily Sequential Organ Failure Assessment (SOFA) score measurements. The joint model is built on a randomly selected training set of two thirds of patients and links the current predicted SOFA measurement to the instantaneous risks of ICU death and discharge from ICU, both adjusted on the patient age. Stochastic Approximation Expectation Maximization algorithm in Monolix is used for estimation. SOFA evolution is significantly associated with both risks: 0.37, 95% confidence interval (CI) = [0.35, 0.39] for the risk of death and −0.38, 95% CI = [−0.39, −0.36] for the risk of discharge. A simulation study, inspired from the real data, shows the good estimation properties of the parameters. We assess on the validation set the added value of modeling the longitudinal SOFA follow‐up for the prediction of death compared with a model that includes only SOFA at baseline. Time‐dependent receiver operating characteristic area under the curve and Brier scores show that when enough longitudinal individual information is available, joint modeling provides better predictions. The methodology can easily be applied to other clinical applications because of the general form of the model.