151 S/F94 as a proxy for COVID-19 severity 7 F94 values on day 0. Sample size estimation Using the observed relationships in ISARIC4C data for eligible patients (see Methods), we quantified effect sizes associated with a 15% relative risk reduction in mortality for each of the following measures: S/F94 at 5 and 8 days after study enrolment, the WHO ordinal scale at 5 and 8 days after study enrolment, the proportion of patients who reached a sustained 1 or 2-level improvement on the WHO ordinal scale, and a definitive outcome, 28-day mortality. We chose a 15% relative risk reduction in mortality based on previous power calculations for the RECOVERY trial. We then estimated the sample sizes required to detect these effects with 80% power at 2p=0.05 (2p indicates a two-tailed test). Some examples of sample size estimations using different inclusion criteria can be found in the supplementary material (Supplementary Table 2 and Supplementary Table 3). We created an online tool, using synthetic data with similar characteristics to the ISARIC4C data (see Methods), to enable users to test any combination of inclusion criteria (age, frailty score and type of respiratory support) and outcome assessment timepoint: https://isaric4c.net/endpoints. For a 15% relative reduction in mortality, the required sample size was smallest for S/ F94 on day 5, needing 722 patients in each arm (1,444 in total, Table 1). The number of subjects required for S/F94 on day 8 was higher, with 1,342 subjects in each arm (Supplementary Table 4). For the WHO ordinal scale, 1,666 participants would be required in each arm on day 5, or 1,168 on day 8 to detect this mortality reduction. Required sample size was larger when 1-level sustained improvement was used as the outcome variable, with 3,378 patients in each arm, and 1,904 subjects in each arm when using 2-level sustained improvement (Table 1). Errors around the point estimates shown in Table 1 are shown in Figure 3 for a range of effect sizes. Estimated improvement with protocolied measurement of S/F94 We have developed a protocol for measurement of S/F94 (Appendix: Protocol). Protocolising measurements is likely to substantially improve the accuracy of measurements of oxygenation function, firstly by ensuring that an oxygen delivery mode is used for which FIO2 can be accurately quantified (e.g. Venturi systems), and secondly by ensuring that measurements are taken at steady state. Protocolised measurement also permits inclusion of all patients, since FIO2 is decreased until SpO2≤0.94, to a minimum of FIO2=0.21. We sought to estimate the magnitude of this improvement. We did this by fitting a measurement error model relating opportunistic and protocolised S/F94 measurements. A description of the estimation of effect size for the protocolised S/F94 measurement can be found in the supplementary methods. Based on this effect size estimate, the required sample size for a protocolised
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