2 if ever be 100% sensitive and speciﬁc in the diﬀerentiation between two or more entities but may assist in making a diagnosis more or less likely, in the context of the prior probabilities of the diagnosis as assessed by the pathologist on morphological grounds, in the context of the clinical and radiological background data. This is not to suggest that a pathologist in real-life practice would ever consciously undertake a Bayesian analysis on the immunocytochemical results of a test; however, I would argue that the possibility that immunocytochemical testing might be subject to base- rate-related cognitive error is suﬃciently plausible to warrant investigation. If such an error were to be widespread, this would suggest that pathologists might be at best at risk of unnecessary expense in ordering investigations that mini- mally aﬀect the probability of the diﬀerential diagnoses, and at worst might lead to misdiagnosis and inappropriate treat- ment. To the best of my knowledge the risk of base-rate error speciﬁcally in relation to the use of immunohistochemistry has not been previously investigated. The study reported here used a scenario mathematically similar to that used in Eddy’s mammography study [2], however the content and context was altered to reﬂect the practice of histopathology. 2. Materials and Methods A survey was conducted of cellular pathology consultants and trainees in which the following scenario was presented: “Please read the following hypothetical scenario: An experienced histopathologist after examin- ing a haematoxylin and eosin stained slide and taking into account the clinical and radiological context of the patient considers there to be a 99% chance that the patient has tumour A and a 1% chance that they have tumour B These tum- ours require diﬀerent treatment. Antibody X has been shown to be positive in 80% of cases of tumour B, and negative in 90% of cases of tumour A. The pathologist is surprised to ﬁnd that the lesion stains convincingly for antibody X. What would you estimate are the chances that the patient has tumour B? (Please state estimat- ed percentage)”. By Bayesian analysis, the “correct” answer can be derived from the following equation: P B | pos = P pos | B P(B) P pos | B P(B) + P pos | A P(A) In the above equation, P(B | pos) refers to the probability that the patient has tumour B given the positive stain for antibody X, P(pos | B) refers to the probability that if the tumour is B then it will stain for antibody X (sensitivity), P(B) refers to the prior probability that the patient has tumour B, P (pos | A) refers to the probability that if the tumour is A then it will stain for antibody X (false positive rate), and P(A) refers to the prior probability that the patient has tumour A. Pathology Research International In the example of this scenario, the ﬁgures would be: P(B | pos) = 0.8 × 0.01/((0.8 × 0.01) + (0.1 × 0.99)) = 0.075 (7.5%). The intention of the study was not to see whether the subjects could perform the calculation but to see how closely their intuitive estimate matched the mathematical calculation. The question was part of an anonymous survey related to postgraduate pathology education, which had the National Health Service research ethics committee and Royal Free Hampstead NHS Trust Research and Development Depart- ment approval. Four groups were surveyed—consultant cellular pathologists (cellular pathologists here deﬁned as histopathologists, cytopathologists, and neuropathologists), trainee cellular pathologists, medical doctors (consultants and trainees) who are not cellular pathologists, and medical students (4th year medical students at the University College London Medical School). All doctors surveyed were practic- ing in the United Kingdom at the time of the study. The survey was conducted predominantly online (with invitations to undertake the survey included within the email newsletter of the Royal College of Pathologists and also sent by email to personal contacts in the UK). A minority of re- sponses, predominantly those provided by medical students before lectures and tutorials, were obtained in paper form, and some of these forms distributed to medical students were restricted to the question related to base-rate error. As shown in Table 1, the numbers of responses were 82 (43), 38 (28), 23 (16), and 59 for consultant pathologists, trainee pathologists, other doctors, and medical students, respectively (with the numbers in parenthesis referring to the number responding to the speciﬁc question in the survey addressed in this paper). Many of the medical students were only given the question on base-rate error; therefore, the response rate for this question in the medical student group cannot be assessed. It is acknowledged that this method of sampling has lim- itations, including potential sample bias and response bias, and also that it is impossible to reliably assess the response rate to the survey; however, according to the Royal College of Pathologists workforce department, in 2007, there were 1448 consultant cellular pathologists and 555 trainees in the United Kingdom (personal communication). Therefore, it can be estimated that responses were obtained from approxi- mately 3.0% of the consultant cellular pathologists and 5.4% of the trainee pathologists practicing in the United Kingdom. All four groups showed remarkably similar overall results (see Table 1 and Figure 1). There was an extremely wide range of individual estimates in all groups. Each group contained individual responses giving estimates of the probability of tumour B of under 1% (including one response of 0% by a consultant cellular pathologist and responses of 0.08% by trainee pathologists and a medical student). The upper range of the estimates was also very high in all groups, including three responses of 99% and one of 100% in the consultant . (1) 3. Results and Discussion