A simulation study showed that linear regression and Mann-Whitney test can be used to analyse the Days Alive and at Home by day 30 (DAH30) outcome in a randomized controlled trial

Objective: The aims of the work were to consider the properties of the DAH30 from a statistical perspective, and to conduct a simulation study exploring the use of simple (unadjusted) linear regression and Mann-Whitney test as the method of analysis reflect realised analysis options.

Study design and setting: The days alive and at home by day 30 (DAH30) has been proposed a patient-centric outcome, and clinically relevant outcome suitable for clinical trials. It has unusual statistical properties, and suitability of standard statistical analysis methods is unclear. The properties of DAH30 were reviewed. Simulations based upon 1:1 allocation in a RCT based upon empirical data were conducted reflecting different additive and realised (reflecting the DAH30) treatment effects, sample sizes and distributions with varying and central locations and zero value level. A variety of metrics were used to assess performance (including bias, coverage, rejection rate).

Results: Linear regression provided a valid estimate of the unadjusted average treatment effect with an additive treatment. This was confirmed in terms of bias, estimation of variance, rejection rate in the absence of an effect, and coverage of the 95% confidence interval for the true realised effect. Mann-Whitney provided greater (power) than linear regression in some situations.

Conclusion: Simple linear regression is a reasonable analytic option for the DAH30 for estimating the average treatment effect in the RCT cohort (i.e. an intention to treat, or "treatment policy" estimand) where zero-inflation is relatively low. Mann-Whitney test in some circumstances (small effects and smaller samples sizes) provides better ability (like for like) to detect a difference between the groups.