Rationale: Oxygen saturation to fraction of inspired oxygen ratio (SpO 2 /FiO 2) has been described as potential predictor of poor outcome for COVID-19, without considering its time-varying behavior though. Methods: Prognostic value of SpO 2 /FiO 2 was evaluated by jointly modeling the longitudinal responses of SpO 2 / FiO 2 and time-to-event data retrieved from 280 severe and critically ill (intensive care) patients with COVID-19. Results: A sharply decrease of SpO 2 /FiO 2 from the first to second measurement for non-survivors was observed, and a strong association between square root SpO 2 /FiO 2 and mortality risk was demonstrated, with a unit decrease in the marker corresponding to 1.82-fold increase in mortality risk (95% CI: 1.56-2.13). Conclusions: The current study suggested that SpO 2 /FiO 2 could serve as a non-invasive prognostic marker to facilitate early adjustment for treatment, thus improving overall survival.

Ovarian epithelial cancer is a gynecological tumor with a high risk of recurrence and death. In the clinical diagnosis of ovarian epithelial cancer, CA125 has become an important indicator of disease burden. To account for patient recurrence and death, a proper method is needed to integrate information from biomarkers and recurrence simultaneously. In the past 10 years, many methods have been proposed for joint modeling of longitudinal biomarkers and survival data, but few of them are applicable to longitudinal data and disease processes, including recurrence and death. In this article, we proposed a new joint frailty model based on functional principal component analysis for dynamic prediction of survival probabilities on the total time scale, which took recurrent history and longitudinal data into account simultaneously. The estimation of the joint frailty model is achieved by maximizing the penalized log‐likelihood function. The simulation results demonstrated the advantages of our method in both discrimination and accuracy under different scenarios. To indicate the method's practicality, it is applied to an actual dataset of patients with ovarian epithelial cancer to predict survival dynamically using longitudinal data of biomarker CA125 and recurrent history data.