Statistical analysis
REGRESSION, REMISSION
The analyses used all participants who were randomised to a treatment arm and received at least one treatment (modified intention to treat).The primary outcome was modelled using penalised logistic regression in the multiply imputed data-sets, with treatment, baseline MADRS score and site as covariates. A number needed to treat (NNT) was calculated from the difference in proportions with remission estimated from the multiply imputed data-sets. Heterogeneity of the primary outcome across cohorts was examined using logistic regression in the multiply imputed data-sets, with cohort, site, treatment arm, baseline MADRS score and treatment arm × cohort as covariates. Change in MADRS score from baseline to end of RCT was estimated from a linear mixed-effects model that included all baseline-to-session change scores as repeats (with an unstructured covariance matrix), and session, treatment, site, baseline MADRS, and the session × treatment and session × baseline MADRS interactions as covariates.CGI-S and CGI-I scores were treated as ordinal categories and the odds of a lower severity or greater improvement for ketamine versus midazolam were modelled using ordinal regression (with baseline CGI-S and site as fixed factors). Further details are available in the Supplementary material; see 