• Derek Hazard, Klaus Kaier, Maja von Cube, Marlon Grodd, Lars Bugiera, Jerome Lambert, and Martin Wolkewitz.
• Institute of Medical Biometry and Statistics, Faculty of Medicine and Medical Center - University of Freiburg, Stefan-Meier-Str. 26, 79104, Freiburg, Germany. hazard@imbi.uni-freiburg.de.
• Bmc Med Res Methodol. 2020 Aug 11; 20 (1): 206.

BackgroundThe clinical progress of patients hospitalized due to COVID-19 is often associated with severe pneumonia which may require intensive care, invasive ventilation, or extracorporeal membrane oxygenation (ECMO). The length of intensive care and the duration of these supportive therapies are clinically relevant outcomes. From the statistical perspective, these quantities are challenging to estimate due to episodes being time-dependent and potentially multiple, as well as being determined by the competing, terminal events of discharge alive and death.MethodsWe used multistate models to study COVID-19 patients' time-dependent progress and provide a statistical framework to estimate hazard rates and transition probabilities. These estimates can then be used to quantify average sojourn times of clinically important states such as intensive care and invasive ventilation. We have made two real data sets of COVID-19 patients (n = 24* and n = 53**) and the corresponding statistical code publically available.ResultsThe expected lengths of intensive care unit (ICU) stay at day 28 for the two cohorts were 15.05* and 19.62** days, while expected durations of mechanical ventilation were 7.97* and 9.85** days. Predicted mortality stood at 51%* and 15%**. Patients mechanically ventilated at the start of the example studies had a longer expected duration of ventilation (12.25*, 14.57** days) compared to patients non-ventilated (4.34*, 1.41** days) after 28 days. Furthermore, initially ventilated patients had a higher risk of death (54%* and 20%** vs. 48%* and 6%**) after 4 weeks. These results are further illustrated in stacked probability plots for the two groups from time zero, as well as for the entire cohort which depicts the predicted proportions of the patients in each state over follow-up.ConclusionsThe multistate approach gives important insights into the progress of COVID-19 patients in terms of ventilation duration, length of ICU stay, and mortality. In addition to avoiding frequent pitfalls in survival analysis, the methodology enables active cases to be analyzed by allowing for censoring. The stacked probability plots provide extensive information in a concise manner that can be easily conveyed to decision makers regarding healthcare capacities. Furthermore, clear comparisons can be made among different baseline characteristics.

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