sample size for continuous skewed data 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:

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*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?


Proving non-existence is always hard. But yes, I would assume there is no simple recipe to determine your sample size for as complicated a setup as you have.
So you will indeed need to simulate. Any first of all, you will need to decide what parameter you are interested in. The mean? The amount of zero inflation? Something else? Essentially, you will need to figure out which test statistic you are interested in.
Note that this is not only a question of simulating the power under different sample sizes. You will need to make assumptions as follows:

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*Distribution of predictors (if any)

*Relationship between predictors and observables, including the amount of zero inflation, and the non-zero distribution

*An effect size (in terms of the parameter you are looking at, see above) that you want to detect

Once you have made your assumptions, you can think about which model you will use to analyze your data.
And then you can start simulating along the assumptions, and analyzing with your chosen model. Tweak the sample size until you get the power you want.
And then add another 20% to the sample size, because there will always be data problems.
