Expert: Ahmed Salami - 4/24/2009

Question
Hi Ahmed,

I have a problem with a maths homework question.

If you know the average duration (in days) a large group of patients was on a drug, and you also know the average cumulative (total) dose this group of patients received while on the drug - from these two data do you know the average mean daily dose they received?  ie. can you do;

'average cumulative dose/average duration in days on drug = average mean daily dose'

Or, alternatively, to know the average mean daily dose the group of patients received while on the drug would you have to work out each individual's daily dose of the drug from their individual duration on the drug and their individual cumulative dose data and then work out the mean of this?

Because I can't help thinking that if you just divided the mean cumulative dose by the mean duration on the drug that - if, for example, the few patients with much higher cumulative doses were the same few patients who were on the drug for a much shorter duration, then your average mean daily dose figure would turn out higher than it should.

Which method should I use to work out the average mean daily dose the patients received?

Thanks for your time.

From Marc

Answer
Hi Marc,
Sorry for the delay.
The formula would be incorrect like you suggested. To get the average daily dose, you need to work out each patient's daily dose and then find the mean of all of it.
The value of 'average cumulative dose/average duration in days on drug' would be different from the value of the average daily dose. The difference would certainly depend on the distribution of the data.
The paragraph 'Because I can't help thinking that if you just divided the mean cumulative dose by the mean duration on the drug that - if, for example, the few patients with much higher cumulative doses were the same few patients who were on the drug for a much shorter duration, then your average mean daily dose figure would turn out higher than it should.' is actually quite spot on and the opposite would also be true.
Of course all of these can be verified with a sample set of data.

Regards