Why and when do we need medical statistics?

It is no secret that medical students don't like statistics, but they are an essential tool for doctors. In the first part of our new series, Wai-Ching Leung explains why

Observations of medical students confirmed that "statistics is, above all, the subject most disliked by students."¹ An eminent medical statistician could only console himself that "medical students may not like statistics, but as doctors they will."² Why don't medical students think that statistics are as important as their teachers do?

Statistics might seem irrelevant, because you can usually understand simple situations without them. In your career as a doctor, the situations are more complex: statistics are essential. When are statistics useful, and what can they do for you?

Situations when you don't need statistics

Remember science experiments at secondary school? In physics, you investigated how various factors--the length of the string, the mass of the bob, and the amplitude--affected the period of a pendulum. It was enough to time the period of pendulums with different lengths of string, amplitudes, and masses and to compare the results. You did not need statistics.

In your most exciting chemistry lesson, you witnessed the vigorous reaction of an alkali metal--sodium or potassium--with water. This reaction can be demonstrated clearly, over and over again.

In biology, you found that various factors affect the rate of photosynthesis in plants. You simply compared the amount of oxygen produced by the same amount of plant under different conditions, changing only one factor at a time. You reached sensible conclusions without ever resorting to statistics.

The same method works in everyday life: if you get home and find that your light doesn't work, you check systematically the bulb, fuse, etc, until you diagnose the fault. To find out whether you are liable for council tax, you go through the rules, one by one. In simple situations, statistics seem irrelevant.

A situation in which statistics are important

Consider a different example. Remember when you passed your driving test and you had to find the lowest quote for motor insurance? The insurance company had to estimate--as accurately as possible--the chances of you crashing and the likely size of the compensation claim in the next year. If it underestimates, the claims will exceed the premiums collected; an overestimate and the company will lose business to competitors. Premiums appropriate to the customer must be set; if the same premium is set for all customers, low risk customers will be lost to cheaper competitors.

But, how can an insurance company estimate the chance of you crashing and the size of your compensation claims within the next year better than you can? Surely, you have more accurate information about yourself, such as your temperament and confidence in driving, than anyone else.

From national data, insurance companies can find out which groups of drivers--by sex, age, driving experience, area of residence, crash history, etc--are more likely to crash and make bigger claims. It is not as straightforward, however, as the science experiments at school. To find out whether men have more incidents than women is not as simple as comparing the crash rates of 1000 men with 1000 women. It is almost impossible to find a group of men and a group of women who have the same distributions of age, driving experience, and area of residence; these characteristics, rather than sex, may be responsible.

Fortunately, statistics can take these differences into account and give an estimate of which drivers are more likely to crash. If the incident rate for men is higher than for women, we still have to decide whether this is because of chance or whether men are more prone to collisions than women. There are often other unknown factors--temperament, driving competencies, etc--for which information is lacking. Statistics can be used to estimate how likely it is that such differences arise by chance: statistics can tell you how uncertain your estimates are.

At least two problems arise if you estimate risk based on only your own experience. Firstly, you know only a few drivers. Secondly, you are unable to assess the information objectively--for example, you are more likely to remember recent incidents concerning a close friend than an acquaintance's mishap some time ago.

Why do these two groups of situations differ?

Events in the first group of situations are almost entirely predictable. The period of a pendulum is constant irrespective of its amplitude, and potassium always reacts violently with water. In simple situations, experience is sometimes sufficient to provide an answer. In the second group of situations, events are less predictable: although male drivers are more likely to crash than female drivers, other factors are important.

The events in the first group are easily measured and controlled as they depend on only a few factors--the amplitude of the swing or the length of the string. Crash rates, however, depend on a large number of factors, some of which are immeasurable, and most of which can't be controlled.

Events in the second group are unpredictable. An experienced middle aged woman, who has not crashed before, living in a "safe" area, could crash within the year. Conversely, a young newly qualified man living in a "dangerous" area might not. You cannot rely on your experience of a few individuals. Statistics of a large number of observations, however, such as crash rates for a large number of drivers, can provide information for estimating the chance of a crash.

Why and how are statistics relevant to medicine?

Doctors spend most of their time preventing, diagnosing, and treating diseases, as well as advising patients on their prognosis. The basic questions for each of these activities are:

• Preventing diseases--What causes diseases?
• Diagnosing diseases--What symptoms and signs do patients with a given disease present with?
• Treating diseases--What treatments are effective for a given disease and for which patients?
• Advising on prognosis--How will specific patients with a given disease fare in the long term?

The answers to these questions depend on a large number of largely unpredictable factors--for example, diseases can be caused by the environment, an agent (bacteria, viruses, etc), or patient factors (genetic, biological, behavioural, social, etc). Similarly, the presentation of symptoms and signs, the response to treatment, and the outcome of patients depend on many variables.

This is similar to the motor insurance situation: even if you know the patient well, you are likely to meet only a handful of patients with a given condition, especially if it is rare. Statistics performed on information from a large number of patients, however, can yield a better answer than your experience can.

I hope you are now convinced that statistics are relevant to medicine. In future articles, I'll go into more depth on using statistics and explore some pitfalls. Unless we are cautious, we can easily be misled by misapplied statistics: remember there are "lies, damned lies, and statistics."

Wai-Ching Leung, locum general practitioner, Norwich
Email: wai_chingleung@hotmail.com


studentBMJ 2002;10:215-258 July ISSN 0966-6494

1. Sinclair S. Making doctors: an institutional apprenticeship. Oxford: Berg, 1997.
2. Bland JM. Medical students may not like statistics, but as doctors they will. BMJ 1998;316:1674. http://bmj.com/cgi/content/full/316/7145/1674