Retinal detachment and Bayes’ theorem

I had my eyes tested yesterday, having put it off for several years. Happily, my vision seems not to have deteriorated in the last couple of years.

After the test, the optometrist told me that my short-sightedness meant that I was at risk of retinal detachment (RD). I asked if this was something to be worried about on a day-to-day basis. They said no, it was just something to be aware of: retinal detachment affects about 1 in 10,000 people, but 40% of cases happen in people with severe myopia.

I didn’t feel very comforted by this, since this information doesn’t directly tell you about my personal risk of retinal detachment given that I have severe myopia. To make sense of that figure, you need to know the prevalence of severe myopia.

According to Haimann et al. (1982) and Larkin (2006), the figure of 1 in 10,000 is actually an annual incidence: in a population of 10,000 healthy people, on average one new case of RD will develop after a year; the lifetime risk is therefore about 1 in 300. The prevalence of severe myopia (beyond −5 diopters) amongst Western Europeans aged 40 or over is about 4.6% (Kempen et al. 2004).

A calculation using Bayes’ theorem would predict that RD has an incidence, amongst people (Western Europeans aged 40 or over) with severe myopia, of about 1 in 1,000 per year, which corresponds to a lifetime risk of about 1 in 30.

This lifetime risk is surprisingly high, and not nearly as comforting as ‘1 in 10,000’. It is so much higher than the base incidence because severe myopia is fairly uncommon, and also because people live quite long lives; the exact relationship between lifetime risk and annual incidence depends on one’s lifespan, and the incidence is not uniform with age. Fortunately, the annual incidence of 1 in 1,000 is still quite small, so no, it’s not something to worry about every day.

This is an extremely simplified calculation using figures drawn from across different populations; the Haimann study was for Iowans of all ages. Myopia is much more common in China, but it’s unlikely that there’s any data out there specifically on Chinese ethnicity people living in Western Europe (both genetics and environment affect myopia). I’ve been unable to find any more detailed information on the prevalence of retinal detachment as a function of myopia strength.

Gariano and Kim (2004) describe the mechanism by which severe myopia might cause retinal detachment.

TL;DR: Opticians don’t understand conditional probabilities, causing me to stay up late browsing optometry and epidemiology papers.

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