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A parallel-group randomized trial is design to compare parallel groups, not to compare change from baseline. You need to be using ANCOVA with Y=post score and X=baseline score. Change from baseline assumes linearity and a slope of 1.0 for post-pre. In depression studies I've seen strong nonlinearity. The most general analysis that is powerful is a ...
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Assuming treatment and control 3-month differences are nearly normally distributed, you want a power and sample size computation for a two-sample t test.
In order to get the sample size for each group you need the following:
Approximate variance of data in the two groups,
Significance level of the test [5% ?],
Size of difference you want
to detect, power (...
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In this analysis we will assume that we are making an inference about the population by forming the Welch-T confidence interval for the population mean, which is the standard interval estimator. We will first set out the form of that interval estimator for the present problem and we will then show how we can "optimise" the sample allocation ...
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In order to find sample size, in addition to the difference in proportions (given as .02), you need significance level (I suppose 5%) and desired power (let's say 80% or 90%). You do not state a target power, nor give enough explanation along with your computations to make your strategy clear (not to me, anyhow). So I can't say how to simplify your approach.
...
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Since I don't know the context, I cannot be sure, but I think it depends on how behaves whatever you are measuring. I think that you will probably run an analysis assuming that your data is uncorrelated. Thus, if you have $n=40$ with $t=1$ your data will very likely be uncorrelated (unless there are relations between the patients that lead to correlations in ...
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Q1. Would it be fine to conduct sample size calculation using simple ANOVA-based power analysis (like G*Power)? In this case, the random-effect won't be considered, and was wondering if this is important. If it is important, how much difference in sample size would it make? If it is not important, why?
No, it is not fine to ignore the random effects. The ...
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