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I determined the sample size already (25), but I want to know if it has to be increased because of a minor change. Our study consists of two groups - one will be sedated and the other will not. For the group that will be sedated, three drugs will be used. One of those three drugs (K) can be replaced by another drug (P) that does the same thing. If patients prefer, P can be used instead of K (original plan was to use K for everyone, but we decided to have P as an option/alternative treatment). The PI asked me if it's possible to use K for half of the patients and P for the other half or something like 15 receiving K and 10 receiving P where the total still remains as 25 for each group. Is it okay to keep the sample size as 25 for each group or will the sample size have to increase if the sedated group uses P for some patients instead of K? I should probably add that all of the drugs that will be used in this study have already been approved and marketed. We are simply comparing two types of anesthesia techniques. It makes sense to increase the sample size (maybe double it?), but I am not sure how to determine if it requires doubling or something else because the study design didn't change for the non-sedated group (only one of the drugs in the sedated group will/might be varied).

Please let me know what you think. I appreciate any help you may have.

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    $\begingroup$ If you also want to contrast P & K, you are asking for more information from your data. That means you would have less information left over for other contrasts. So if you want to have the same power, you would need to have more data to start with. $\endgroup$ Aug 24 '15 at 20:03
  • $\begingroup$ So, does this mean my sample size would have to become 50 if we use P as well instead of just K? I'm just not sure how to take this into account into my sample size calculation. $\endgroup$
    – user86738
    Aug 24 '15 at 20:28
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It's not clear from the problem description whether P vs K is actually part of the experimental design/statistical question. If it isn't, then a proper experimental design might block on K vs P, but randomizing the condition is unethical and produces invalid inference.

As an example, suppose a study inspects early diabetes outcomes. Treating physicians might prefer to use D: drug (metformin), I: insulin, or B: both to manage blood sugars. There are clear indications for one vs. the other, but there's also grey area where the decision comes down to treating physician and patient's preference. This is an important for capturing real-life effectiveness of an experimental drug. If I force the treating physician to choose a treatment that is not germane to the question, I will do harm, a violation of the beneficence principal of the Declaration of Helsinki.

If you are really willing to make the assumption that P/K are equivocal treatments (create a new variable T and call it "treated" if a patient receives either P or K), then no you do not need to increase your sample size. The primary analysis will be a comparison of T versus not T using the appropriate test(s). Then you can conduct a post hoc test of either P vs. K or P vs. K vs. not T. The last analysis will be underpowered and it would be advisable to interpret any findings as hypothesis generating and exploratory.

On the other hand, if you do a 3 way ANOVA of P vs K vs not T, you will need to redo the sample size calculation for 2 degree of freedom test of heterogeneity. This analysis would be amenable to subsequent post hoc comparisons as well.

A third hybrid option is to perform an adaptive design. In the adaptive design, one can plan for a run-in period to inspect P vs K and, providing no heterogeneity, pool or drop arms accordingly for a final analysis, budgeting for appropriate stopping rules and alpha-spending. This method is a costly form of insurance to protect against model misspecification.

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