Classroom activity: What's the best medicine?

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This activity explores the difficult decisions facing health authorities when it comes to deciding which drugs should be made available to patients. Mathematically, the activity involves basic arithmetic and manipulation of averages.

Pill bottles

What's the best drug?

A medical breakthrough has enabled scientists to start working on treatments for a rare and dangerous cancer, which when untreated kills patients within just a few months. After extensive research and clinical trials, three drug companies have come up with their version of a drug to treat the cancer. The table below shows the average number of years patients survive after diagnosis for each of the three drugs. It also shows how much each drug costs per patient per year.

It's your job to decide which of the three drugs patients should be given this year. Your budget for this year is £1,000,000, which you must not exceed, and there are currently 2150 patients that need to be treated. Which drug would you choose to maximise the average survival time while still remaining within budget?

Drug A Drug B Drug C
Average survival time in years 2.8 3.5 4.2
Cost per patient per year £350 £400 £470

Just as you are going to communicate your decision to doctors, some new research results are published. It turns out that the three drugs affect men and women differently. The differences are shown in the table below. Out of the 2150 patients 800 are men and 1350 are women. Work out which combination of drugs (drug X for men and drug Y for women) gives the greatest average survival time calculated over all patients. Can you use this to come up with a final choice of drug for both groups? What other considerations might you make when allocating the drugs?

Men (800)
Women (1350)
Drug A Drug B Drug C
Average survival time in years 3.9 3.5 4.0
Cost per patient per year £350 £400 £470
Drug A Drug B Drug C
Average survival time in years 2.1 3.5 4.3
Cost per patient per year £350 £400 £470

A year has passed when you receive the news that the drug companies that produce drugs B and C have lowered their prices to match that of drug A. The average cost per patient per year is now the same for all three drugs. This would suggest that everyone should be treated with drug C, since this maximises the overall survival time.

However, the drug companies have also been forced to publish the results of a study into the side effects of their drugs. These can be severe, causing patients pain and even confining them to bed. The results of the study show how patients have rated their quality of life on the drugs on a scale from 0 to 1, where 1 means best possible quality of life and 0 means worst possible quality of life. The average rating for each drug is given in the table below. How would you use this information to compare the benefits and disadvantages of each drug? What is your final choice?

Drug A Drug B Drug C
Average survival time in years 2.8 3.5 4.2
Average quality of life rating 0.5 0.8 0.1
Cost per patient per year £350 £350 £350

To help you with these difficult decisions, read The economics of health.

Here are some possible answers to these questions.

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