I have an outcome which takes values from 0 - 100. I have added a figure of the distribution (below). However, 30% or more will have a value of 0 (so zero inflated). Then the next lowest value it can take is 9 (numbers in between not possible), with all other values being possible. We do expect that the mode will be around 8 – 15 and 5% will have a value of 100.
I am trying to calculate the sample size required (varying levels of alpha, power, MCD and other parameters that one requires for sample size) for a study having this index as primary outcome. The Sample size will also have to account for the fact that data is likely to be cluster randomised, therefore need to take a note of that.
In my search, I have come across a few things that allow modelling of zero inflated and skewed data:
Use of Tobit, Tweedie and others
I found an approach that use modelling to calculate sample size: https://www.tandfonline.com/doi/full/10.1080/03610918.2019.1577975 - sample size for hierarchical modelling of (zero inflated) Poisson distribution
But I have not been able to find a way to calculate the sample size based on those distributions that would account for clustering within the data.
I found the following which seems to be non-parametric approach:
https://www.jstor.org/stable/41242503?seq=3#metadata_info_tab_contents (Power and Sample Size Estimation for the Clustered Wilcoxon Test)
However, when modelling, the wilcoxon test doesn't allow for adjustment for other variables?
So my questions are:
Is it possible to accurate calculate the sample size for a data set such as above without the use of simulation? If so, can anyone point me in the right direction?
If I have to simulate data, am I right to assume that essentially, I will be fixing my sample size and calculating the power under different sample sizes?