Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am having difficulty in understanding the concept of Prevalence lately. Cambridge notes on Medical Statistics are not elaborate and I would really appreciate if any one of you can explain it to me.

The Question I am stuck on is related to two drugs: Ecstasy and Mephedrone.

Assume there are only 30 ecstasy related deaths in the UK per annum. If Mephedrone use is 60% as prevalent as ecstasy but half as dangerous, How many Mephedrone related deaths can you expect in the UK.

To my understanding, there is no definitive way to do this question. I haven't been taught any formulae or theory.

Can anyone explain how to tackle these kinds of questions.



share|cite|improve this question
up vote 2 down vote accepted

Prevalence is the proportion of a population for which some condition is true. The population of the UK is fixed, say $N$. If the prevalence of two drugs are $p_1$ & $p_2$, the frequency of usage is the same (say $f$ times per year), and the risk of death per use is $r_1$ and $r_2$ respectively, then the expected number of deaths from each drug per year (assuming users take only one or the other, otherwise we get into a counting war over which drug kills them) are $Nf\,p_ir_i$ for $i=1,2$. Perhaps it makes sense to define a drug's prevalence not by the number of users, but by the number of uses per year, the drug has. Then we can throw away the $f$ above, since it is modeled inside the $p_i$. But in any case, your problem becomes $$Nf\,p_1r_1=30$$ $$\frac{p_2}{p_1}=\frac35$$ $$\frac{r_2}{r_1}=\frac12$$ so that $$ Nf\,p_2r_2 =Nf\,p_1r_1\cdot\frac{p_2}{p_1}\cdot\frac{r_2}{r_1} =30\cdot\frac35\cdot\frac12 =9 $$ where you can cross out all the $f$'s if they're understood as part of the $p$'s.

share|cite|improve this answer
Thank you bgins! – Hassan Khan Mar 21 '12 at 18:14

You have 60% as many users and half as many of them die, so you expect 30*60%*(1/2)=9 deaths per year.

share|cite|improve this answer
Thank you Ross! =) – Hassan Khan Mar 21 '12 at 18:14

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.