Published 27 May 2009, doi:10.1136/bmj.b2077
Cite this as: BMJ 2009;338:b2077

Endgames

Statistical question

Likelihood ratios

John Fletcher, clinical epidemiologist

1 BMJ, London WC1H 9JR

jfletcher{at}bmj.com

In a study of general practice records in the UK, the symptom of dysphagia was found to have a positive likelihood ratio of 300 for oesophageal cancer, which itself had an incidence of 1 case in every 10 000 persons per year. Which of the following statements, if any, are true?

a) Among people with dysphagia, the ratio of those with cancer to those without is 300 to 1
b) Cancer is 300 times more likely in patients with dysphagia than in the general population
c) More than 95% of people with dysphagia seeing their general practitioner will have cancer
d) More than 95% of people with dysphagia seeing their general practitioner will not have cancer

Show Answers

Answer

b, d—Answer b is an example of a diagnostic likelihood ratio when "likely" is measured in odds. The likelihood ratio for a positive result is the post-test odds of disease divided by the pre-test odds of disease. The likelihood ratio is easier to understand the way it is expressed in answer b. As long as the frequency of disease is rare, the vagueness of language does not make a material difference to the maths. When dealing with more common diseases, however, it is necessary to stick to odds or to use a chart (nomogram) to interpret data in terms of likelihood ratios and probabilities.

Despite the huge likelihood ratio of 300, dysphagia is far from pathognomonic for cancer in the primary care setting because oesophageal cancer is a rare disease. The incidence of oesophageal cancer rises from 1 case in every 10 000 people per year to roughly 300 cases in every 10 000 people per year in those with dysphagia. In hospitals, however, far more people have pathology since they have been screened from the general population. Hence in hospitals the symptom of dysphagia is far more predictive of oesophageal cancer than it is in primary care.

Cite this as: BMJ 2009;338:b2077


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