146 Chapter 7 effect with a given level of power using a two sample t-test with ANCOVA correction for the correlation between S/F94 on day 0 and day 520. Ordinal variables (WHO scale) Values for the WHO ordinal scale were derived using information about oxygen support and mortality. Possible values in hospitalised patients range between 4 and 102. WHO scale - absolute value We fitted a proportional odds model with the WHO ordinal scale as the dependent variable, and age and sex as independent variables. We used this model to estimate the odds ratio associated with a 15% relative reduction in mortality21. WHO scale - sustained improvement We derived binary variables for sustained 1- or 2-level improvement on the WHO scale. To be considered sustained, an improvement had to be maintained until discharge or until day 28. We fitted a logistic regression model with mortality at day 28 as the dependent variable, and age, sex and sustained 1- or 2-level improvement on the WHO scale as independent variables. We used this model to estimate the difference in proportion of people who had a sustained improvement on the WHO ordinal scale that was associated with a 15% reduction in risk of mortality. We then calculated required sample size for this outcome using a two-sample test for proportions with a continuity correction22. Only patients who had WHO ordinal scale values on at least two separate days were included in this analysis. Mortality In order to compare these alternative outcome measures with a definitive outcome (mortality), we calculated the number of participants needed if 28-day mortality was the outcome measure, using a two-sample test for proportions with continuity correction. Results Relationship with the reference standard oxygenation measure (P/F) There is a consistent pattern in both synthetic (Figure 1) and real (Supplementary Figure 1) data: if no maximum cut-off value for SaO2 is used, spuriously low S/F values are seen in patients with good lung function, reflected in high P/F values (Figure 1A, Supplementary Figure 1A). This is due to the ceiling effect - SaO2 cannot rise above 100%. These misleading values are removed by excluding values with SaO2 above 94% (Figure 1B, Supplementary Figure 1B), which improves the correlation with the
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