A number of recent media stories
have brought attention to the risk of unnecessary or inappropriate medication
use in older patients (1). The
Canadian Deprescribing Network estimates that âamong those 85 and older, nearly
40 per cent were taking 10 or more drugsâ. This network has announced a
âfour-year plan with a goal of reducing unnecessary or inappropriate medication
use in older patients by 50 per cent by 2020â(2).
You read these articles and canât
believe these staggering numbers. You decide to follow up and take a couple of
samples to see for yourself what the proportion of seniors taking 10 or more
drugs is. You draft a short questionnaire, including the question âHow many
drugs do you take on a regular basis?â. You first go to a retirement home and
ask 20 seniors over 85 to fill in a short questionnaire for you. Then you ask
an elderly neighbour to get her friends over 85 to fill in the questionnaire,
as well. She is able to collect responses from 10 people
(a) (3 points) Please comment on the
methodology. Is it appropriate to answer your question? What kind of sampling
are you using? Are there issues with this methodology?
(b) (6 points) ] You go over the
results from your study, and find that in the seniors home sample 47%, and in
the neighbourâs sample 12% of respondents take more than 10 drugs. If the
Canadian Deprescribing Network is right, what is the probability of obtaining
these results? Would you believe that both your samples are representative of
the overall population of seniors over 85? Make suitable assumptions to perform
the calculations and comment on their validity.
Another news outlet reports that
âThe average senior household spends $500 each year on prescription drugsâ(3) .
(2 points) You pick a random senior
household and ask about their yearly drug costs. What is the probability that
this household spends more than $700 each year on prescription drugs? (Assume a
normal distribution with a standard deviation of $400.)
(4 points) What is the probability
that the average spending among senior households in a random sample with 30
respondents is between $600 and $800? (Continue to assume a normal distribution
with a standard deviation of $400.)
The news report actually did not
contain any reference to a standard deviation, so do not assume you know the
standard deviation for this question. You come across a sample of 7 senior
households on the internet. It lists the following yearly drug costs for the
households: 1156, 387, 2343, 976, 2823, 84, 876. .
(a) (4 points) As you know, it can
be difficult to obtain proper random samples. Would you believe that this
sample could have been randomly selected from the same population mentioned in
the news report?