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There are two groups: control and experimental, mean difference is 10% between experimental group and control group [if there are X successes in control group then there are 1.1 * X successes in experimental group], significance level is 0.05, power (sensitivity = (1 - beta)) is 0.8. The number of patients in groups are equal. Which is the minimum number of patients in group?

The known formulas for sample size include standard deviation (which is unknown in this case), so we can't apply computations directly. Can we estimate the SD with the "minimum number of patients" condition? Or we need to choose other way?

Thanks.

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It appears that you are trying to estimate power for a binary (dichotomous) outcome using the methods designed for a continuous outcome (i.e., one that produces means and standard deviations). The power in your situation will be affected by the base-rate, that is, the success rate in the control condition. A 10% difference around a base-rate of 50% will require a smaller sample than a 10% difference around a base-rate of 5%. The additional information you need to solve for sample size is the base-rate, not the standard deviation. You also need to be applying the method for a binary outcome.

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  • $\begingroup$ Thanks for response! But it seems that there is vice versa: difference around base-rate of 50% will require bigger sample than around any other base-rate. $\endgroup$
    – eiyawii
    Jun 17, 2017 at 14:10
  • $\begingroup$ sealedenvelope.com/power/binary-superiority This calculator shows approach which I needed. And if I don't know the base-rate then I should use base-rate = 50%, as it is the most uncertain condition to determine sample size, so the sample size in this case equal to 385 patients for each group. But it's quite large sample, is there some mistake? $\endgroup$
    – eiyawii
    Jun 17, 2017 at 14:29
  • $\begingroup$ This is true for detecting an absolute difference (say 5 percentage points) but not for a relative difference. Using your above example, you need a bigger sample size for a 10% difference around a base rate of 10% (thus comparing 10% success in control versus 11% success in treatment) then you do for a 10% difference around a 50% base rate (50% in control and 55% in treatment). $\endgroup$
    – dbwilson
    Jun 17, 2017 at 14:42
  • $\begingroup$ The main point is that you don't need the standard deviation. What you do need is the base rate. Once you have that, you can solve for sample size. $\endgroup$
    – dbwilson
    Jun 17, 2017 at 14:43
  • $\begingroup$ Yep, I've caught about standard deviation. We don't know base-rate at control group, so if we consider absolute difference (e.g. 50% successes in control vs 60% successes in treatment group) then we need to set base-rate on 50% as it is the maximization of sample size; if we consider relative difference (e.g. 50% successes in control vs 55% successes in treatment group) then we need to set base-rate at then minimum base-rate to maximize sample size. Right? and is there is some good explanation of the formula for computation of sample size? $\endgroup$
    – eiyawii
    Jun 18, 2017 at 14:42

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