Expert: Alon Mandes - 4/24/2009

Question
Hi Alon,

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
Hello Marc,
Sorry it took me little bit long to reply, I just had some extra
work to do in my company, & for that I apologize.
The formula you suggested above is wrong, & your explanation to it
below is correct. This term is called "moving average" It moves as
as a group envelope causing the mean daily dose to raise as a result.
Thus, you should calculate the averages individually. & then perform
average to the individual averages.
I'll attach you an image of an illustration with simple example.
I made a 2 dimension matrix : The rows represent the patients, &
the coulombs represent the days. In each day, each patient got different amount of doses. Calculating the individuals averages are
shown also.

Good day,
Alon.