162 Chapter 7 day time period (e.g comorbidities such as obesity, dementia, liver disease etc) were imputed by chained equations. New rows were added for day 5 and day 8 for each simulated record, with the constant variables imputed in the previous step repeated. After this, there were multiple rounds of partitioning the full dataset, containing both real and simulated records, and carrying out imputation by chained equations separately within each piece. For example, a binary variable indicating whether an individual died was imputed, then the full dataset was split into those who died and those who didn’t, and a day of death was imputed for the former. Similarly, binary variables indicating whether or not the individual had a one/two level sustained improvement in WHO ordinal severity score were imputed, and used to partition the full dataset. Then the minimum time taken for patients to have a sustained one/ two level improvement was imputed amongst those that had this event occur. Appropriate care was taken in order to respect variable bounds, interdependence and the time series structure of the data. For example, if an individual had a sustained two level improvement, they necessarily must also have had a sustained one level improvement, and the time taken for the former to occur must necessarily be greater than or equal to the time taken for the latter to occur. In order to handle this appropriately, we first imputed the time taken for a sustained one level improvement, and after appropriate partitioning, we then imputed the difference in time taken for a sustained one and two level improvement using predictive mean matching. This guaranteed a positive difference, as required. In each imputation by chained equations, predictive mean matching was used for continuous variables and logistic or multinomial logistic regression was used for categorical variables. Supplementary Notes Physiology Evaluation in ISARIC 4C data Respiratory Rate There is large variation in respiratory rate, which is independent of S/F94. As expected, there is a tendency of higher respiratory rates for patients with a lower S/F94. (Supplementary Figure 3) Association between mortality at day 28 and S/F94 The relationship between S/F94 on day 0 and mortality in the multivariable model appears counter-intuitive (Supplementary Figure 4A). A univariable regression model with mortality on day 28 as the outcome variable and S/F94 on day 0 as the predictor, shows a relationship as expected: there is an increase in mortality risk with a decrease in S/F94 on day 0 (Supplementary Figure 4B). Hence the reversed direction in the multivariable model is explained by the effect of change in S/F94 between day 0 and day 5, suggesting that patients who are admitted to hospital with moderate
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