Statistical considerations

In the literature, incidence rates of delirium in elderly populations in control groups in the first week after surgery or hospital admission range from 20.8% to 32.6%.^{19 20 29} We therefore expect a cumulative incidence of delirium of 25% at day 10 after surgery in the control group.

Literature data are discordant on melatonin’s effect on the risk of delirium. In medical wards, meta-analyses^{11 30} found in elderly patients a decreased in the incidence of delirium between 60% and 75% with melatonin supplementation. In a postoperative setting the effect seems smaller but there are fewer studies, with discordant results, going from no effect to a 70% decrease of delirium incidence.^{19 20 29} We therefore expect a 40% risk reduction in the melatonin group with respect to placebo, which corresponds to a cumulative incidence of delirium of 15% at day 10 after surgery in the melatonin group. Adding to this assumption a bilateral type I error of 5% and a power 90%, we need to randomise 718 patients (359/group) in order to have 129 events and to detect a significant difference between arms (including 10% of patients that could not be evaluated). Sample size was computed with a Fine and Gray methods using R package cmprsk.³¹ We expect that 10% of included subjects will be secondarily excluded (not randomised) due to presence of delirium at inclusion. Therefore, we need to include 790 patients in order to randomise 718 subjects. Inclusions will continue until 718 patients are randomised.

The analyses will follow the intention-to-treat principle.

Postoperative delirium cumulative incidence function (CIF) will be compared at day 10 between the two randomised arms (melatonin vs placebo) by means of a competing risks framework, using the Fine and Grey model, that allows to estimate CIF on the presence of other cause of failure (deceased in our study), altering the probability of experiencing the event of interest, delirium.

The significant level of all statistical analyses will be a 2-sided 5%. All statistical analyses will be performed using SAS software (SAS Institute) V.9.4 or later, or R software (R Foundation for Statistical Computing, Vienna, Austria. http://www.r-project.org/) V.4.0 or later.

The economic evaluation is planned, undertaken and analysed according to the intention-to-treat principle, with the primary aim to estimate the 30-day incremental cost-utility and cost effectiveness of melatonin. Because of the short duration of the follow-up (30 days) the difference in quality-adjusted life year is likely to be small; we will therefore add a measure of clinical effectiveness based on a composite of the primary and secondary clinical outcomes: incidence of delirium, need for sedatives, need for physical restraints, fall and death.

All analyses will be conducted by a statistician according to a prespecified statistical analysis plan. A full statistical analysis plan including the health economics analysis has been written and is available in online supplemental material 2.

bmjopen-2021-053908supp002.pdf

All analyses results will be reported according to the Consolidated Standards of Reporting Trials 2010 guidelines and the Consolidated Health Economic Evaluation Reporting Standards guidelines on economic evaluation in healthcare.³²