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Editor—Ocular angioma (haemangioblastoma) is the most common presenting feature of the multisystem familial cancer syndrome von Hippel-Lindau disease (VHL).1 Recognition of VHL is important because of the opportunity to reduce morbidity and mortality by early diagnosis of renal cell carcinoma, phaeochromocytoma, and cerebellar, spinal, and ocular haemangioblastomas. Although the finding of typical and multiple ocular lesions indicates VHL, the risk of multisystem disease in those presenting with a single ocular lesion has not been determined. That such risk exists is shown by the presence of patients with solitary angiomas in families with VHL, and the identification of mutations in the VHL gene in affected subjects without a family history of disease owing to non-penetrance for VHL manifestations in relatives and a significant new mutation rate. Consequently, the management of patients with a solitary ocular lesion may be inappropriate, such that patients with VHL may be falsely reassured, and others without symptoms may be subjected to unnecessary surveillance. On the basis of previous estimates, we have used a Baysian approach to calculate approximate risks for VHL disease in a patient presenting with a single ocular angioma in the context of other clinical and molecular information available.

The proportion of VHL patients who have a solitary ocular angioma after ophthalmic examination has been calculated in previous work on a cohort of VHL gene carriers,2 and this proportion, like all the following proportions, can be used as an estimate of a corresponding conditional probability. However, calculation of the reverse conditional probability, that is, the probability of VHL given a diagnosis of solitary ocular angioma, requires the use of Bayes' theorem, as shown below:

*VHL‖s*) represents the probability of VHL disease in a patient presenting with a single ocular angioma. Pr(

*s*‖

*VHL*) represents the probability of a solitary angioma given a diagnosis of VHL disease, which has been estimated in a recent survey of VHL gene carriers2 as 0.20. Pr(

*VHL*) represents the population prevalence of VHL disease, which is taken as 18.9 × 10

^{-6}.3 Pr(

*s*‖ ̅V̅H̅L̅ ̅) represents the prevalence of patients who harbour a solitary ocular lesion, but who do not have underlying VHL disease. The existence of non-VHL ocular angioma has been confirmed recently in a British population using a joint molecular genetic and clinical approach, and its prevalence estimated as 9.0 × 10

^{-6}.4 The term Pr( ̅V̅H̅L̅ ̅) refers to the probability of a person in the population not being affected with VHL disease and this was taken as unity. Substitution of these values gives a probability of underlying VHL disease in a person presenting with a solitary angioma of 29.6%.

However, in the clinic, further information about the patient and their relatives is usually available, including the results of screening for extraocular features of VHL, a parental history, and the results of DNA analysis for VHL gene mutations. The significance of the first two factors in determining the risk of underlying VHL depends on the age of the patient, such that negative findings in an older patient or older parents decreases the likelihood of them being non-penetrant VHL carriers. If DNA analysis were completely sensitive, a negative result would exclude the diagnosis. However, with current DNA screening methods used in most laboratories and the possibilities of mosaicism or non-coding region gene mutations, it is prudent to assume a significant false negative detection rate. To allow for such additional information, we modified the Bayes equation, using the multiplication rule of probability calculus,5 as follows:

Pr(VHL‖C_{1} and any combination of C_{2}, C_{3} and C_{4}) =

_{1}) and any combination of: C

_{2}, a negative history in the parents for VHL complications, C

_{3}, negative systemic screening, and C

_{4}, negative DNA analysis, depending on the information available on the patient. Π[Pr(

*C*‖

_{i}*VHL*)] represents the product of the probabilities of a single ocular angioma in a VHL patient and one or more of each of these negative investigations occurring in the presence of VHL disease. These were derived as follows. Pr(C

_{1}‖VHL) is the probability of a single ocular angioma given VHL is as above. Pr(C

_{2}‖VHL) is the probability of neither parent of a VHL patient having suffered VHL related complications. This was taken as the sum of the two mutually exclusive probabilities of new mutation and non-pentrance in a VHL patient 20 years older than the subject, taken from the studies of Maher

*et al*3 and Maher

*et al*,1 respectively. Pr(C

_{3}‖VHL) is the probability of negative systemic screening given VHL is equivalent to the probability of non-penetrance after systemic investigation. This decreases with increasing age of a VHL gene carrier and values were taken from age of onset data from the study of Maher

*et al*.1Pr(C

_{4}‖VHL) is the probability of negative DNA analysis for a germline VHL gene mutation in a known VHL carrier was conservatively assumed to be 27% (using standard PCR and Southern techniques) (unpublished observations and ref 6). These probabilities and their derivation are summarised in table 1. The probabilities Pr(

*C*‖ ̅V̅H̅L̅ ̅) represent i=1 the probability of a solitary angioma in a non-VHL subject (above) and i=2 to 4 each of the other negative states occurring in a non-VHL person. The latter three probabilities were taken as unity.

_{i}Given these calculations, the age related risk estimates for underlying VHL in a patient with a single ocular angioma after careful ophthalmic examination, and a combination of other negative information, are summarised in table 2.

Although some caution should be exerted when extrapolating these results to other populations (for example, the mutation detection sensitivity will depend on the precise investigations performed and the prevalence of sporadic ocular angioma might vary), this analysis does, for the first time, provide clinicians with risk estimates for the likelihood of underlying systemic disease in patients with a solitary ocular angioma. This information will help determine the most appropriate investigation and management of such patients.

## Acknowledgments

We gratefully acknowledge the Guide Dogs for the Blind Association and the TFC Frost Trust for support and Dr C Bunce for advice.

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