The shocking implications of Bayes’ theorem for diagnosing herniated nucleus pulposus based on MRI scans

Abstract

We obtain the input data for Bayes Theorem, and use the theorem to determine the probability of a patient having a lumbar HNP, given only a positive MRI. We also enumerate the potential consequences that the clinician must keep in mind when making the diagnosis of lumbar HNP. We used the theorem by Bayes, in conjunction with well-established results in the orthopedic literature, to calculate the probability of lumbar HNP given only a positive MRI finding. The necessary information provided by the orthopedic literature includes the prevalence of lumbar HNP, the probability of a positive MRI finding given that there is no HNP, and the probability of a positive MRI finding given that there is HNP. We found that the probability of lumbar HNP given only a positive MRI finding was 8%. The probability that there is no lumbar HNP, even when there is a positive MRI finding, is 92%. Clearly, MRI scans cannot be trusted as the sole source of diagnostic information.

Keywords:

• Bayes’ theorem
• herniated nucleus pulposus
• MRI scans

Public Interest Statement

The article, “The shocking implications of Bayes’ theorem for diagnosing herniated nucleus pulposus based on MRI scans” shows that because of the low base rate for the disorder, and the substantial false alarm rate, the probability that a person has the disorder given that an MRI scan has diagnosed it, is only 8%. Thus, the probability of not having herniated nucleus pulposus (commonly called a “slipped disk”) is 92% when an MRI scan is positive. The importance of a proper examination is emphasized, as is the demonstration of the lack of validity of MRI scans for these sorts of diagnoses.

Competing interests

The authors declare no competing interest.

Additional information

Funding

Funding. The authors received no direct funding for this research.

Notes on contributors

David Trafimow

David Trafimow is a distinguished achievement professor of psychology at New Mexico State University, a fellow of the Association for Psychological Science, executive editor of the Journal of General Psychology, and also for Basic and Applied Social Psychology. He received his PhD in psychology from the University of Illinois at Urbana-Champaign in 1993. His current research interests include attribution, attitudes, cross-cultural research, ethics, morality, methodology, and potential performance theory.

Jordan H. Trafimow

Jordan H. Trafimow is an orthopedist with experience as a practicing doctor, as a medical researcher, and in administrative roles. He is currently retired from active surgery and is concentrating on medical research.