Intended for healthcare professionals

Endgames Statistical Question

Screening tests: likelihood ratios

BMJ 2011; 342 doi: https://doi.org/10.1136/bmj.d3986 (Published 29 June 2011) Cite this as: BMJ 2011;342:d3986
  1. Philip Sedgwick, senior lecturer in medical statistics
  1. 1Section of Medical and Healthcare Education, St George’s, University of London, Tooting, London, UK
  1. p.sedgwick{at}sgul.ac.uk

The accuracy of asking patients two questions as a screening tool for depression in primary care was assessed.1 The questions focused on depression and pleasure within the past month. Consecutive patients not taking psychotropic drugs who attended their general practice were invited to participate, of whom 421 agreed. Patients were asked the two questions at any time during their consultation, and if the response to either was positive then screening was considered “positive” and the patient deemed at “high risk” of depression; otherwise screening was considered “negative” and the patient deemed at “low risk” of depression. A self completed, computerised international diagnostic interview was used to diagnose depression.

The two questions showed a sensitivity of 97% and specificity of 67% as a screening tool for depression. The likelihood ratio was 2.9 for a positive test result and 0.05 for a negative test result. Overall, 157 of the 421 patients (37%) screened positive for depression.

Which one of the following statements best describes the likelihood ratio for a “positive” test result on screening?

  • a) Patients with a “positive” screening result are 2.9 times as likely to have diagnosed depression as a patient with a “negative” screening result.

  • b) For patients with diagnosed depression, a “positive” screening result is 2.9 times as likely to occur as a “negative” screening result.

  • c) A “positive” screening result is 2.9 times as likely to occur for a patient with diagnosed depression compared with a patient without a diagnosis of depression.

Answers

Answer c is the likelihood ratio for a positive test result on screening. A positive test result on screening is 2.9 times as likely to occur for an individual with diagnosed depression than for an individual without a diagnosis.

The two questions showed a sensitivity of 97% as a screening tool for depression. Therefore the proportion of patients with diagnosed depression who were correctly identified by screening with a positive test result was 0.97. The specificity of the two screening questions was 67%, and therefore 67% of those patients without a diagnosis of depression were correctly identified by screening with a negative test result. Hence the proportion of patients without a diagnosis of depression identified with a positive test result and, therefore, incorrectly identified by screening was 0.33. The likelihood ratio for a positive test result is the ratio of the probability of a positive screening result for patients with diagnosed depression to those without a diagnosis of depression—that is, 0.97/0.33=2.9. The likelihood ratio for a positive screening test result is therefore calculated as sensitivity/(1–specificity).

The larger the value of the likelihood ratio for a positive test result, the more likely a positive screening test result is for patients with diagnosed depression than for those without a diagnosis of depression. Therefore, larger values for the likelihood ratio for a positive screening result are more desirable, since they indicate increased accuracy of the screening test at obtaining positive screening test results in diagnosed patients in comparison with those without a diagnosis.

The likelihood ratio for a negative screening test result is the proportion of patients with diagnosed depression who had a negative screening result, divided by the proportion of patients without a diagnosis who also had a negative screening result. Therefore, the likelihood ratio for a negative test result was derived as (1−sensitivity)/specificity=0.03/0.67=0.05. Smaller values for the likelihood ratio for a negative test result—that is, closer to zero—are more desirable, because the screening test has increased accuracy at obtaining negative screening test results in patients without a diagnosis of depression compared with those with a diagnosis.

Notes

Cite this as: BMJ 2011;342:d3986

Footnotes

  • Competing interests: None declared.

References

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