Classroom activity: What's the best medicine?

03/03/2010

Guidance notes on What's the best medicine?

There are no hard and fast answers to these questions, but here are some suggestions for how to tackle them.

Question 1: Which drug would you choose to stay within budget and maximise average survival time?

Drug C gives the longest average survival time. For 2150 patients it costs

2150 × £470 = £1,010,500

per year. This exceeds your budget. Drug B costs

2150 × £400 = £860,000

per year, which is within budget. Since it gives a longer average survival time than drug A, you choose drug B.

Question 2: Which drug would you choose for men and which for women while staying within budget?

Drug C maximises average survival time for both men and women, but giving it to both groups would exceed your budget. Drug B gives the same average survival time for both men and women, so in the interest of equality you might decide to give drug B to both groups.

Another approach is to choose a combination of drugs that maximises overall average survival time. Apart from giving drug C to both groups, the two next best options are drug C for men and drug B for women, or drug A for men and drug C for women.

Giving drug C to men and drug B to women costs

800 × £470 + 1350 × £400 = £916,000,
so this option is within budget. The overall average survival time for this option is
(4.0 × 800 + 3.5 × 1350)/2150 = 3.69 years.

Giving drug A to men and drug C to women costs

800 × £350 + 1350 × £470 = £914,500,
so this option is also within budget. The overall average survival time for this option is
(3.9 × 800 + 4.3 × 1350)/2150 = 4.15 years.

Therefore, in terms of overall average survival time, giving drug A to men and drug C to women is the best option within budget.

Another question you might ask yourself is if it's really necessary to give all men the same drug and all women the same drug. Maybe it would make sense to give the most potent drug, drug C, to all those most severely affected by the cancer, regardless of their gender, and treat those less severely affected with the cheaper drugs. Further research would be needed to establish if this would make sense.

Question 3: How would you use the quality of life information to compare the benefits and disadvantages of each drug?

Is it better to live longer with a poor quality of life, or to live a little less long but with a much better quality of life? It's a difficult question. Drug C offers very poor quality of life, while drug B has a much better score. Since the difference in life expectancy between the two drugs in only a matter of a few months, you might therefore decide to go for drug B. On the other hand, you might think that the extra few months on drug C are worth the suffering caused by the side effects of the drug.

One way of comparing the three drugs objectively is to multiply the quality of life rating (QoL) by the average survival time. This gives the following scores:

 Drug A Drug B Drug C Average survival time × average QoL 1.4 2.8 0.42

Using this measurement, drug B performs best. In fact, this kind of calculation is used in practice to decide which drugs and treatments should be made available freely on the NHS. To find out more about difficult issues like this one and how they are resolved in practice, read The economics of health.