What is the statistical test to compare waterfall plots as used in clinical trials?

[mjtaws]

The blog article by Rick Wicklin https://blogs.sas.com/content/iml/2015/04/20/waterfall-plot.html explains what waterfall plots are.

My question is, what is the appropriate statistical test which could be applied to assess differences between placebo and treated group by comparing corresponding watterplots (considering each set having data for at least 50 subjects)? 

ChatGPT sugests: 'To compare waterfall plots, one approach is to use a statistical test that compares the distribution of the changes in tumor size or marker levels between two treatment groups. One such test is the Wilcoxon rank-sum test, also known as the Mann-Whitney U test. This non-parametric test compares the ranks of the changes in tumor size or marker levels between the two groups, and can be used to determine if there is a statistically significant difference in tumor response between the two treatments.'

Is it all one can do or is there a more tailored test taking into account the characteristic distribution of the data, i.e. bound from below and above tumor growth/shrinkage (there is at maximum 100% reduction of tumour and it is only open in theory on the other side but of course limited physically from unrestricted growth)?

[StatDave · Accepted solution]

If you used the actual tumor size or (percent size INCREASE) + 100 so that your response has a minimum of zero, then you could use something like the Tweedie distribution to model that response as discussed in this note. If you don't have any other variables than group, then you just need the group variable in both the CLASS and MODEL statements for your model. You could add an LSMEANS statement with the ILINK and DIFF options to estimate the group means and test their difference. For more on the Tweedie distribution, see "Tweedie Distribution for Generalized Linear Models" in the Details section of the PROC GENMOD documentation.

[mjtaws]

Here the data in question in histograms and waterfall plots for all interested. Left, treatment A related, right treatment B.