Use of Bayes' theorem in ophthalmodynamometry.

N UMEROUS investigators1-'2 have established the importance of ophthalmody-namometry in the diagnosis by safe and simple means of occlusion of the carotid artery proximal to the origin of the ophthalmic artery. In all their reports the significant observations are summarized by a statement giving the percentage of patients with proved carotid occlusion that was found to have significant lowering of the retinal artery pressure (RAP) on the side of occlusion. In the language of mathematical probability this percentage is the conditional probability per cent of significant RAP lowering given the condition of carotid occlusion. The highest value of 100 per cent for this probability was found by Wood and Toole,5 who studied five patients with proved carotid occlusion and the lowest value of 62 per cent by Croll et al.,'0 who studied 16 such patients. The value for this conditional probability is a measure of the degree of confidence with which one may interpret the findiiig of normal RAP measurements but it is not a direct answer to the question usually asked by the clinician, i.e., "What are the chances that this patient with a recent cerebral occlusive vascular le-sion and normal RAP measurements has in fact a patent carotid artery?" In more precise terms, a value is required for the conditional probability that the carotid artery is patent in a patient with a recent cerebral occlusive vascular lesion given the condition of normal RAP. Bayes' theorem, a simple derivation in elementary statistical mathematics , identifies this conditional probability with an expression composed of terms for which values can be found by direct observation and the required value so obtained by calcula-1312 tion.'3 Bayes' theorem is seldom used in the interpretation of clinical information, and it is believed that a demonstration of its application to the results of opththalmodynamom-etry might be of some interest. The theorem can be stated as follows: (1) P (B) where A is the occurrence of patent carotid arteries in a patient with a recent cerebral occlusive vascular lesion, B is the occurrence of normal RAP measurements in a patient with a recent cerebral occlusive vascular le-sion, P(A/B) (read as the probability of A, given B) is the conditional probability of patent carotid arteries in a patient with a recent cerebral occlusive vascular lesion given the condition of normal RAP, P (A) is the unconditional probability of patent carotid arteries in a patient with a recent …