Multivariate joint model under competing risks to predict death of hospitalized patients for SARS‐CoV‐2 infection

Abstract During the coronavirus disease 2019 (COVID‐19) pandemic, several clinical prognostic scores have been proposed and evaluated in hospitalized patients, relying on variables available at admission. However, capturing data collected from the longitudinal follow‐up of patients during hospitalization may improve prediction accuracy of a clinical outcome. To answer this question, 327 patients diagnosed with COVID‐19 and hospitalized in an academic French hospital between January and July 2020 are included in the analysis. Up to 59 biomarkers were measured from the patient admission to the time to death or discharge from hospital. We consider a joint model with multiple linear or nonlinear mixed‐effects models for biomarkers evolution, and a competing risks model involving subdistribution hazard functions for the risks of death and discharge. The links are modeled by shared random effects, and the selection of the biomarkers is mainly based on the significance of the link between the longitudinal and survival parts. Three biomarkers are retained: the blood neutrophil counts, the arterial pH, and the C‐reactive protein. The predictive performances of the model are evaluated with the time‐dependent area under the curve (AUC) for different landmark and horizon times, and compared with those obtained from a baseline model that considers only information available at admission. The joint modeling approach helps to improve predictions when sufficient information is available. For landmark 6 days and horizon of 30 days, we obtain AUC [95% CI] 0.73 [0.65, 0.81] and 0.81 [0.73, 0.89] for the baseline and joint model, respectively ( p = 0.04). Statistical inference is validated through a simulation study.