A Quirky Maths Exam Question

Well, yesterday was my maths paper. During the paper, one thing that caught my attention (or rather, one 'interesting' thing. I mean, every question in the examination would have taken my attention, and I would also want that to be the case. Or else, I might end up banging my head against the table. Worse still, I end up leaving a bloody mess on the table/wall from a bleeding nose or head - which is really bad and definitely painful. Oops getting off track. Anyway, back to the topic.) was a particular question (hmmm, sounds obvious - what else could it possibly be during the paper?) being asked in the statistics part of it. The interesting thing was, it was probably the most un-mathematical question I've ever seen in a maths paper.

And somehow, it also stimulated the crappy side of my brain to generate some great (or 'great' - ie. great in inverted commas, since such an answer would be seen as great to crappers alike, or 'great' to examiners reading this) answer.

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Q: A study is carried out to determine whether an experimental drug developed by a team of medical researchers works better than the simple aspirin tablet in warding off heart attacks and strokes. The study involves 10000 people who have suffered heart attack, strokes, or pain from clogged arteries. Each person is randomly assigned to take either aspirin or the experimental drug for a period of 1 to 3 years. Assume that each person is equally likely to be assigned one of the two medications.

Devise a randomization plan to assign the medications to the patients to the patients (that is, how each patient is to be assigned to take aspirin or the experimental drug). Will there be an equal number of patients on each treatment group? (6 marks)

Initially, there were some questions I had on this question:

1) Based on my medical knowledge, why are only people with pain from clogged arteries in the study? Aren't people with pain in the chest and/or heart with/without pain spreading to the upper jaw and left arm in as much danger (if not, more) of a heart attack as those with pain from clogged arteries?

2) Does aspirin clear clogged arteries? As much as I know, aspirin is a anti-coagulant in blood.

3) Since it's already mentioned that people are randomly assigned to take aspirin or the experimental drug, why am I asked to devise a plan to redo all that's already been done?

4) When they ask me to assign medications, are they referring to the nursing aspect of it (ie. how do you administer a random drug to a patient - which is a serious no-no in the medical line)? Smoke the patient? Force feeding the poor soul with the medication? Or jab it in his IV-line (the water bag and tube that goes into his arm/hand)?... etc.

5) Why aren't the patients asked for/giving consent for experimental drugs being used on them, and instead, I am asked to assign them the drug? The hospital could be sued, blacklisted, people (and quite possibly the poor nurse who was arrowed to administer the drug) getting fired/charged/jailed, news hitting the headlines... etc. Worse still, I may get into trouble if my suggestion was actually taken into account because for some unknown reason, the lecturer simply loved my answer, and someone died as a result.

6) Why do they ask me if there would be an equal number of patients on each treatment group when each person is equally likely to be assigned either drug, meaning 50% would get one and 50% the other and hence there would be an equal number of patients statistically speaking? And from another aspect, isn't that (ie. the number) supposed to be dependent on what they ask me to do - to assign it?

But although I had such queries, I simply couldn't spend too much time thinking about them or asking the invigilators. So, I merely answered that there would be 5000 lots for each medication and they're randomly assigned by someone or asked to pick their lot. I can't remember what else I wrote. But shortly after the paper, my crappy mind generated the following 6 marks answer (in terms of length):

For the 10000 people, they should be split into groups of 4. Gather them in their groups and allow them to play a game of 10 rounds of heart attack (which is an appropriate title anyway). For those who lose, it is based on the least number of wins, and vice versa. If the people in second and third ranking has the same score, they will play 1 round of heart attack among themselves to determine the winner. Should people lose the game (well, losers are the more appropriate bunch to get it since, well, they lost), or get too excited and could not take the stress (and hence quit the game), they would be assigned the experimental drug since they're in a greater danger of a heart attack. In such a situation, they may die anyway, and hence they should try the new drug. Who knows, if the drug is successful, it may even save them. If the drug failed or gave adverse effects, their fate is the same as without the drug anyway.

In answer to "Will there be an equal number of patients in each treatment group" - No. People may die of heart attack after a heart stopping game of heart attack (which is very likely, especially so for those who live to win) and hence, the distribution would most likely be unequal.

Thought: Oh well, I only hope I do not get a heart attack upon seeing my result slip at the end of it all.