145 S/F94 as a proxy for COVID-19 severity 7 Association between S/F94 and 28-day mortality Two key assumptions underlie the use of S/F94 as an intermediate endpoint. Firstly, that pulmonary oxygenation function predicts mortality in COVID-19, and secondly, that S/F94 accurately reflects the pulmonary oxygenation function. If either of these assumptions are violated, then a strong relationship between S/F94 and subsequent mortality would not be expected. To evaluate this association, a logistic regression model was developed with 28-day all-cause mortality as the dependent variable and S/F94 measured on day 0 and day 5 as two separate covariates. We included both S/F94 on day 0 and day 5 due to the strong relationship between S/F94 on day 0 and S/F94 on days further in the disease trajectory. Linear dependence of log-odds on S/F94 measured on day 0 and day 5 was assessed both by visual inspection and using model selection criteria including the Bayesian Information Criterion (BIC) to compare to a restricted splines model. Finally, predicted models were made to assess the absolute change in risk of mortality with a change in S/F94. Sample size calculations We compared the sample sizes required for a range of different outcomes measures (S/F94, WHO ordinal scale, sustained improvement at day 28 and 28-day mortality). For the intermediate endpoints, we estimated the treatment effect associated with a 15% relative reduction in mortality. Below we give brief descriptions of the effect size calculations for the different outcome measures. All calculations assumed a 1:1 allocation of participants between treatment and control groups and are based on having 80% power at 2p=0.05 to detect the stated treatment effect. Details on effect size estimation can be found in the supplementary material. Quantifying uncertainty We bootstrapped 95% confidence for the effect size, and then used this to calculate 95% confidence intervals for required sample size using the fact that they are monotonically related. Continuous variables (S/F94) We fit a logistic regression with mortality at day 28 as the dependent variable, and age, sex, S/F94 on day 0 (baseline) and day 5 (or day 8) as independent variables. We used this to calculate the predicted probability of mortality, and the change in S/F94 associated with a relative reduction in predicted mortality of 15%, for each subject. Finally, we took the mean to find the average change in day 5 S/F94 that is associated with a 15% reduction in mortality across the sample. This was the target treatment effect in the clinical trial. We calculated the sample size required to see this treatment
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