Question regarding PSA and dirichlet distributions
Hi,
Sorry in advance, this is a bit of a read. I have several questions about performing a PSA, and I’d also appreciate some feedback on the results of a PSA I ran. The results look a bit off so I’m not sure if I did everything correctly.
Currently, my ICE scatterplot shows more variability along the x-axis than I expected. Since this is related to effectiveness/QALYs, my line of thinking was that it was related to one of the distributions I had assigned either to event probabilities (dirichlet distribution), study discontinuation (beta distribution), disabling/non-disabling stroke (beta distribution) or utilities (beta distribution).
After trying to reduce the variability by replacing each of the beta distributions with their mean values from the deterministic analysis, it seemed likely that the main source of the variability was from the Dirichlet distribution I had used.
Initially as I did not have quarterly counts of the events readily available to inform the alpha list of my Dirichlet distribution I used quarterly probabilities I calculated from trial data I have access to. The variability along the x-axis was so wide my ICE scatterplot looked more like a line, so I looked into it a bit and realized I can scale the concentration parameters. I tried what I thought would be logical scaling factors: x100, x543 [the average number of patients in each arm of the trial; this would technically also convert my probabilities to counts (though the time frame doesn’t match my model)], but the variability, while less, still seemed excessive.
So after all that, I’m just wondering if it sounds like I’ve performed this PSA correctly? Is my scaling factor too high? Too low? Is there something else I should look at or is this variability I’m seeing just part of the data I have?
Thanks!
Comments
Yes, you are correct that putting probabilities as the list entries for the Dirichlet distribution will generate far more uncertainty than you want. Multiplying those probabilities by 100 will give you more reasonable uncertainty, but you can change that factor up and down until your are comfortable with the ranges.
I would recommend you use the Graph It function for the Dirichlet distribution to examine the uncertainty for the sampled probabilities. Then you can adjust the multiplicative factor until you are comfortable with the uncertainty plots from Graph It. The Graph It function is a toolbar icon in the Distributions View.
Andrew
Thanks for taking the time to read all that and confirming that I'm on the right track.
When it comes to choosing a multiplicative factor is there an upper limit to keep in mind or is any number fine as long as I'm comfortable with the uncertainty plots?
There is no general rule for uncertainty distributions. Every input is different.
You have to do the best you can to estimate uncertainty. The Graph It option will give you a good feel for the uncertainty you are using.
Andrew
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