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I have 102 patients that were expected to receive 8601 doses of a drug in total. In reality, they received 7992 doses. I understand this to be an overall compliance of 92.9% in this group. Is this an appropriate measure of "mean" compliance?

I have also considered taking each of the patients' individual percentage compliance, then taking a mean of those percentage measures, e.g. if 51 of the patients were 50% compliant and the other 51 patients were 90% compliant, the mean would be 70%. Intuitively I think this may be wrong, but I can't explain why.

Finally, depending on the correct way to calculate the mean, what would be the most appropriate way to work out standard deviation?

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  • $\begingroup$ Perhaps this will complicate your question even more. It seems the patients did not all have the same number of intended doses. Is missing one dose more important to you if the intended number of doses is small? $\endgroup$
    – Joel W.
    Commented Dec 16, 2020 at 22:55
  • $\begingroup$ An argument could be made that those with fewer intended doses are of less interest, as the effect of the drug is likely be harder to detect in those patients, but that's a bit beyond my task. I have only been asked to give a mean compliance figure with SD. $\endgroup$
    – jserv
    Commented Dec 16, 2020 at 23:01
  • $\begingroup$ Sorry, I misunderstood your question. You're right that a patient with a lower intended number of doses who misses a day will have a dramatically lower compliance percentage, e.g. 1/2 doses = 50% compliance. No, this is not more important in this case, as a lower number of "intended doses" indicates that the patient probably did not survive or withdrew. $\endgroup$
    – jserv
    Commented Dec 16, 2020 at 23:08

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We have a statistical consultant on the study that has said typically compliance is calculated the latter way (as a percentage figure for each individual patient). It is not relevant to show the numerator and denominator for compliance here, and instead they recommended giving the interquartile range (IQR) alongside the mean percentage and standard deviation of patient compliance percentages.

This is currently the best answer I have, so I will mark it accordingly.

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