4 Previous data regarding the interpretation of unexpected test results in other contexts [1–4] has demonstrated a ten- dency of doctors to overinterpret the diagnostic signiﬁcance of the unexpected result. This was demonstrated by some of the respondents to this survey. For example, 38% of the consultant cellular pathologists gave an estimated probability of double or more the mathematically correct answer, and 30% of consultant pathologists and 32% of trainees gave a response of ﬁve times or more higher. If this can be ex- trapolated to routine diagnostic practice, this would suggest that approximately one third of cellular pathologists substan- tially overestimate the diagnostic signiﬁcance of unexpected immunohistochemical staining results. In contrast, 33% of consultant cellular pathologists and 39% of the trainees gave an estimated probability of half or less of the mathematically correct ﬁgure. Again, if this can be extrapolated to routine practice, this would suggest that approximately one third of pathologists underestimate the diagnostic signiﬁcance of an unexpected immunohisto- chemical result. The distribution range of the answers, with clusters of inappropriately high estimates, would suggest that there may be common cognitive mistakes made in the assessment of disease probability by all groups surveyed. Although the ﬁnding that approximately one third of pathologists underestimated the diagnostic signiﬁcance of the result, one third overestimated, and another third were reasonably close might not appear to be overly concerning, the range of individual estimates could be considered to be. The ﬁnding that positive staining with an antibody more frequently found in tumour B than tumour A altered the estimated probability of tumour B from 1% to between 0 and 100% by diﬀerent individual consultant cellular pathologists may be of concern. Gigerenzer et al. has extensively examined how altering the presentation of probability data in both professional and general public settings can improve the interpretation of statistical information [5, 6]. He consistently found that predictions were improved by presenting information as “natural frequencies” rather than percentage probabilities. For example, in the context of this study, the data could have been presented in a natural frequency format as “an experi- enced histopathologist after examining a haematoxylin- and eosin-stained slide and taking into account the clinical and radiological context of the patient considers that, out of 1000 patients with a similar slide, 990 will have tumour A and 10 will have tumour B. Antibody X is positive in 80% of cases of tumour B; therefore, it is likely that, of these 10 patients with tumour B, 8 will stain positively. On the other hand, of the 990 patients with tumour A, 99 would be expected to stain for antibody X. If the tumour stains for antibody X, how likely is it that the patient will have tumour B?”. Such a presentation was not used in this study, but, in the light of Gigerenzer et al.’s ﬁndings in similar scenarios presented to doctors, it is likely that such a presentation would have improved understanding. It could be argued that presenting the information in this study in the way that was chosen could have been designed to be misleading, however pathologists rarely have access to information regarding the stains they routinely use that is Pathology Research International presented in terms of natural frequencies. Natural frequency presentation takes away some of the cognitive load in such a calculation, by presenting data that is not reliant on the base rate of the condition in the relevant population. Unfor- tunately, in routine practice, it is at best extremely rare to have a clear indication of the probability of a disease in the relevant population. In the example given, the base rate of relevance is the population of patients who the pathologist would consider to have a similar haematoxylin- and eosin- stained slide. This will to some extent depend on the frequency of the diﬀerential diagnosis in the pathologist’s referral population, but will also be dependent on the pathologist’s own experience, ability, and biases. It is however vital for pathologists when interpreting studies describing the alleged sensitivity and speciﬁcity of stains to consider whether the population assessed is relevant to their own practice. For example, a study comparing the value of a stain in discriminating between a certain tumour and normal tissue may suggest greater sensitivity and speciﬁcity than a study comparing its value in discriminating between two morphologically similar but clinically distinct tumours. It appears from the ﬁndings in this study that pathol- ogists are not all immune from base-rate errors and that increasing diagnostic experience does not reduce the risk of such errors. The importance of the base-rate probability of a disease on the interpretation of an unexpected immuno- histochemical ﬁnding is underappreciated by many patholo- gists. This is a source of potential diagnostic error, and it is suggested that the trainees are made aware of base-rate errors in their training programmes. References [1] A. Tversky and D. Kahneman, “Evidential impact of base rates,” in Judgement under Uncertainty: Heuristics and Biases, D. Kahneman, P. Slovic, and A. Tversky, Eds., pp. 153–160, Cambridge University Press, New York, NY, USA, 1992. [2] W. Casscells, A. Schoenberger, and T. B. Graboys, “Interpre- tation by physicians of clinical laboratory results,” The New England Journal of Medicine, vol. 299, no. 18, pp. 999–1001, 1978. [3] D. M. Eddy, “Probablistic reaaoning in clinical medicine: problems and opportunities,” in Judgement under Uncertainty: Heuristics and Biases, D. Kahneman, P. Slovic, and A. Tversky, Eds., pp. 249–267, Cambridge University Press, New York, NY, USA, 1992. [4] G. H. Lyman and L. Balducci, “Overestimation of test eﬀects in clinical judgement,” Journal of Cancer Education, vol. 8, no. 4, pp. 297–307, 1993. [5] G. Gigerenzer, Calculated Risks: How to Know When Numbers Deceive You, Simon and Schuster, New York, NY, USA, 2002. [6] U. Hoﬀrage, S. Lindsey, R. Hertwig, and G. Gigerenzer, “Communicating statistical information,” Science, vol. 290, no. 5500, pp. 2261–2262, 2000.