Approximate reciprocal relationship between two cause-specific hazard ratios in COVID-19 data with mutually exclusive events.

COVID-19 survival data presents a special situation where not only the time-to-event period is short, but also the two events or outcome types, death and release from hospital, are mutually exclusive, leading to two cause-specific hazard ratios (csHR d and csHR r ). The eventual mortality/release outcome is also analyzed by logistic regression to obtain odds-ratio (OR). We have the following three empirical observations: (1) The magnitude of OR is an upper limit of the csHR d : |log(OR)| ≥ |log(csHR d )|. This relationship between OR and HR might be understood from the definition of the two quantities; (2) csHR d and csHR r point in opposite directions: log(csHR d ) ⋅ log(csHR r ) < 0; This relation is a direct consequence of the nature of the two events; and (3) there is a tendency for a reciprocal relation between csHR d and csHR r : csHR d ∼ 1/csHR r . Though an approximate reciprocal trend between the two hazard ratios is in indication that the same factor causing faster death also lead to slow recovery by a similar mechanism, and vice versa, a quantitative relation between csHR d and csHR r in this context is not obvious. These results may help future analyses of data from COVID-19 or other similar diseases, in particular if the deceased patients are lacking, whereas surviving patients are abundant.

A comparison of two frameworks for multi-state modelling, applied to outcomes after hospital admissions with COVID-19.

We compare two multi-state modelling frameworks that can be used to represent dates of events following hospital admission for people infected during an epidemic. The methods are applied to data from people admitted to hospital with COVID-19, to estimate the probability of admission to intensive care unit, the probability of death in hospital for patients before and after intensive care unit admission, the lengths of stay in hospital, and how all these vary with age and gender. One modelling framework is based on defining transition-specific hazard functions for competing risks. A less commonly used framework defines partially-latent subpopulations who will experience each subsequent event, and uses a mixture model to estimate the probability that an individual will experience each event, and the distribution of the time to the event given that it occurs. We compare the advantages and disadvantages of these two frameworks, in the context of the COVID-19 example. The issues include the interpretation of the model parameters, the computational efficiency of estimating the quantities of interest, implementation in software and assessing goodness of fit. In the example, we find that some groups appear to be at very low risk of some events, in particular intensive care unit admission, and these are best represented by using 'cure-rate' models to define transition-specific hazards. We provide general-purpose software to implement all the models we describe in the flexsurv R package, which allows arbitrarily flexible distributions to be used to represent the cause-specific hazards or times to events.

Absolute mortality risk assessment of COVID-19 patients: the Khorshid COVID Cohort (KCC) study.

BACKGROUND: Already at hospital admission, clinicians require simple tools to identify hospitalized COVID-19 patients at high risk of mortality. Such tools can significantly improve resource allocation and patient management within hospitals. From the statistical point of view, extended time-to-event models are required to account for competing risks (discharge from hospital) and censoring so that active cases can also contribute to the analysis. METHODS: We used the hospital-based open Khorshid COVID Cohort (KCC) study with 630 COVID-19 patients from Isfahan, Iran. Competing risk methods are used to develop a death risk chart based on the following variables, which can simply be measured at hospital admission: sex, age, hypertension, oxygen saturation, and Charlson Comorbidity Index. The area under the receiver operator curve was used to assess accuracy concerning discrimination between patients discharged alive and dead. RESULTS: Cause-specific hazard regression models show that these baseline variables are associated with both death, and discharge hazards. The risk chart reflects the combined results of the two cause-specific hazard regression models. The proposed risk assessment method had a very good accuracy (AUC = 0.872 [CI 95%: 0.835-0.910]). CONCLUSIONS: This study aims to improve and validate a personalized mortality risk calculator based on hospitalized COVID-19 patients. The risk assessment of patient mortality provides physicians with additional guidance for making tough decisions.