Discussion
REGRESSION, HAND PRESENTATION
We have provided an overview of the necessary methodological considerations and a discussion of four different regression models for assessing skewed and non-trivially distributed outcomes such as DAWOLS and compared these models in real data from the COVID STEROID 2 trial [Linear regression is easy to interpret, simple to work with, and may be used if separate estimates for specific counts, such as minimum/maximum values, are not needed. While the assumption of normally distributed residuals (Table S1 in Additional file Multi-part models, including hurdle-negative binomial and zero–one-inflated beta models may better generatively replicate data and provide combined and separate estimates for each sub-model. This may be important if a treatment has opposite effects on, e.g., mortality and the duration of organ support in survivors/non-survivors, leading to opposing differences in the probabilities of 0 days and the mean number of days in all other patients. Such opposing effects may hamper the interpretation of the combined estimate and decrease power [The cumulative logistic regression model assessed has the least distributional assumptions and may fit data well overall. However, the ordinal odds ratio is somewhat difficult to interpret, as it is not on an absolute or clinically interpretable scale. Thus, defining a clinically relevant difference is difficult, unless mean values are estimated by combining the probabilities of all counts in the data. The central assumption of this model (i.e., odds being proportional) may not hold, and, from a clinical perspective, treatment effects may plausibly be different, at least in magnitude, on mortality and the number of days alive and without life support in survivors. Thus, while violations of the proportional odds assumption do not necessarily invalidate the model (Table S1 in Additional file In addition to the overall statistical model used, detailed graphical presentation of the overall and daily raw data and presentation of probabilities of minimum/maximum values and overall mortality for the same period of follow-up is advisable to ease interpretation and to ensure that opposing directions of effects on mortality and the number of days in survivors are not present, as the combined estimate may not be clinically meaningful if this is the case [