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I have a null result for a negative binomial regression model and I would like to give evidence that my sample is large enough to detect even small effects.

I've found a few online calculators for power analysis, but I'd prefer to use simulation. I haven't been able to find many resources about how to do this.

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For your given sample size and the observed effect size your power was <50%, no need for simulation. If that's a meaningful effect size, the study was under-powered.

If that is not the case and the confidence intervals exclude a meaningful effect size, then you have a pretty good argument that the study had provided a pretty clear answer.

What's the particular problem with simulating? Simulate your drop out/ censoring process, condition on the simulated drop out times, then either simulate straight from a negative binomial, or simulate as a Gamma-Poisson mixture (useful if you also have a baseline period and need to capture the within subject correlation for that). Then apply your analysis model to each simulated dataset.

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    $\begingroup$ For your second statement, the pretty clear answer is that there is no effect? $\endgroup$ – Isabella Ghement Nov 10 '18 at 14:00

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