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I'm looking at patients that have attended a pain clinic for assessment and treatment program. I want to look for differences between the population that complete the program and the non-completers. I want to compare completers vs non-completers on a number of variables, e.g. age, sex, employment status, number of medications, +/- mental health diagnosis etc. Can anyone help me with a sample size calculation. I have been reading up trying to figure out an answer for hours and i honestly feel more confused now than before i started.

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    $\begingroup$ Do you mean you are trying to determine a proper sample size so the results have enough statistical power? $\endgroup$ Nov 19, 2023 at 8:19
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    $\begingroup$ What are you trying to sample size here; whether there's a difference in proportion of subjects that complete vs. those who don't (one comparison) or if those two populations differ in these several variables (many comparisons which will likely have a different adequate sample size each)? $\endgroup$
    – PBulls
    Nov 19, 2023 at 11:00

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This is an age old dilemma. It's all up to the way you want to pose the problem. First, do you have a fixed maximal model in mind based upon good science or are you hypothesis generating? I'm guessing that because you want to do a sample size calculation then it's the former and your desire to cast it as a well designed study. Are you powering for all coefficients or is there a main variable or two? Let's first assume that you desire power for the coefficient of a single variable adjusted for potential co-founders (the rest). Then you'll want to consult Self and Mauritsen, BIOMETRIcs 44, 79-86 "Power/Sample Size Calculations for Generalized Linear Models".

If you want power for more than a single variable's coefficient then you have to decide how many. Say two of the p variables. A simple approach is to use the conjunctive power e.g.

p( both variables are significant | both nulls are false )

~ p( a single variable is significant | its null is false)^2

So for 80% power just do the single variation calculation at 0.8^0.5 ~ 0.9 power. This of course assumes independence which is conservative if there is positive correlation. It's probably good enough even if not. Want to be sure, do simultaneous under some kind of dependence model.

Good luck and happy reading.

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