We are performing a clinical intervention, that we believe will significantly improve some parameters in patients. We expect that the intervention will be successful 85% of the time (it will either be successful or not). We will be measuring the same parameters before and 3 months after the intervention. After that, we are planning to use paired t-test to determine whether the intervention results in a significant increase in these same parameters after the procedure compared to pre-procedure. We expect that if the intervention is successful (we know that the intervention is successful 85% of the time from preliminary studies), the parameters will improve to a certain degree, and we based our sample calculation on that effect estimate.
Specifically, I use pre-treatment (5000) and post-treatment (6500) means, pre and post group standard deviations (3000 each), correlation 0.5, alpha 0.05, power 0.95, one-sided (we expect an increase as indicated by prelim data. If there is a decrease, this well-known procedure would not be performed, thus one-sided). These numbers give me n=45 in STATA. After assuming a drop-out rate of 20%, I get n=54
However, I am not entirely sure how to incorporate the 85% procedural success rate into the sample size calculation. We know that the procedure will fail in approximately 15% of the patients, and they will not benefit from the procedure. In fact, there is a small chance (1-5%) that the parameters will get worse. The sample size calculation that I perform in STATA obviously does not factor in the procedural success rate.
I thought about multiplying the sample size by 100/85 to make up for the 85% procedural success. That is n=54 will be n=64.
Could you please tell me if this is acceptable? Is there a better way to do this?
Edit: After seeing the first reply, I felt I need to clarify: Our outcome variable is continuous. In sample size calculation, we are estimating that following the intervention, patients will be more physically active (measured by daily steps), and will have 1500 steps/day more (from say 5000 steps/day to 6500/day steps). However, with this estimated effect size, STATA output that I get (n=54), estimates that all participants on average will have to show this average effect size. On the other hand, if the procedure fails, daily steps will not improve. That is to say, if we enroll 54 patients, 54 x (0.85)= 45 patients will have successful intervention. If the 45 patients show +1500/day improvement, we will fall short of power. Therefore, I feel like an adjustment is needed in the sample size, for which I multiplied 54 with 100/85 (85% procedural success). I was meaning to ask if this adjustment (n x 100/85) would be an appropriate way to fix this issue.