152 Chapter 7 measurement of day 5 S/F94 would be around 988 subjects in total (Figure 3). Discussion In synthetic (Figure 1) and real (Supplementary Figure 1) physiological data, we found that SaO2≤0.94 is a pragmatic cut-off threshold, lying within a safe range, excluding the majority of obviously misleading values caused by the ceiling effect, and optimising predictive validity. Using observational data from the ISARIC4C study, we demonstrate that S/F94 fulfills our initial requirements for an intermediate outcome: a continuous outcome measure that is closely related to mortality and can be modified by therapy3. Testing predicted statistical power for a range of effect sizes in observational data, we found that S/F94 is more sensitive than other widelyused outcomes. Comparing both the WHO ordinal scale and S/F94 to the definitive outcome of mortality at day 28, we found that the same predicted treatment effect can be detected with fewer patients using S/F94, even when measurements are not protocolised. In a clinical trial setting, where both SpO2 and FIO2 measurement can be protocolised, sensitivity is predicted to improve because protocolised measurement are less noisy and are therefore expected to have a stronger relationship with mortality. Using the SD for protocolised S/F94 during the RECOVERY trial, together with the assumed error measurement model relating protocolised and opportunistic S/F94 measurements, we predict a substantial additional improvement in statistical power using a protocolised measurement. Our analyses may underestimate the statistical power of mortality, since time-toevent analyses would be used in most circumstances to maximise statistical power. Due to the large proportion of missing data after day 10, it was not possible to carry out survival modelling in our data. Ideally, we would have performed a mediation analysis with treatment effect, to determine the extent to which the treatment effect on mortality is explained by the intermediate endpoint S/F94. However, since there is no S/F94 data available from clinical studies showing significant treatment effect, it is not possible to perform this analysis. Some important sources of error exist in the outcome measures we considered. Firstly, SpO2 and FIO2 are both subject to measurement error, particularly in opportunistic data. For example, estimating FIO2 for patients receiving supplemental oxygen via nasal cannula or simple (Hudson) masks is inaccurate, because the FIO2 is profoundly affected by inspiratory flow rate, which varies between patients. This error would be eliminated by protocolised measurement, which mandates the use of devices delivering a fixed FIO2. Secondly, the position of a patient on the ordinal WHO scale is influenced by both availability of resources and the decision by the patient and the clinician whether to escalate the level of care or provide organ support. This may explain the wide range of S/F94 values for patients at the same position on the WHO scale.
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