Abstract
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.
Acknowledgment
WL acknowledges the support from Robert S Boas Center for Genomics and Human Genetics.
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Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: The data analysis work was not funded.
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Conflict of interest statement: Authors declare no conflicts of interests.
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Ethical approval: All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.
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Informed consent: As the study was a retrospective analysis of medical records, informed consent was waived.
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