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I have just had my viva and my sample size calculation was criticised as it was based on r2. I was told to base the sample size on the minimal magnitude of association. My outcome variable is HbA1c, a marker of blood glucose. The minimal magnitude of association is 6 mmol/mol. I am reporting unstandardised b. I have used mixed effects multi level models and have 15 covariates.

I am ok with accounting for clustering once i have a sample size but was wondering how i calculate the sample size? I think that i am getting confused with effect sizes.....Where would i enter my value thats considered of clinical importance? Or does this translate to the effect size? I am using GPower.

Any help would be greatly appreciated. Thank you!

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You did not state your goal. If the goal is estimation or prediction it is not appropriate to use a "difference to detect" but rather to solve for $N$ that will result in adequate estimation of the expected value of $Y$ given $X$, i.e., the regression equation. Another good approach is to solve for $N$ such that you can estimate $R^2$ with a good margin of error. I discuss a few approaches in https://hbiostat.org/rms including a simple calculation based on estimating $\sigma^2$ (this usually takes about $N=70$ or greater).

In the RMS book and course notes I also have a case study demonstrating that it is not appropriate to analyze HbA1c on the original scale, and that ordinal regression (semiparametric models such as the proportional hazards model) are superior. If you had to analyze HbA1c parametrically a transformation that comes close to working is to raise it to the minus 1.5 power. If you don't pay special attention you'll find that your model is not variance stabilized (i.e., you have heteroscedasticity).

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Check out Cohen 1988 and other references that provide formulas for effect sizes defined in various ways including % variance explained (R-sq) and standardized mean differences. For an important dichotomous variable it may be easier to formulate the effect size in terms of how large the mean difference is and then translate this to % of variance explained.

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