# probability of 3 close family members all having an eye disease

#### drrehak

##### New Member
Hi, I am a little rusty with my statistics. I am an eye doctor. The probability of a retinal detachment is 1/10,000. I just found out today my brother got one. He is probably having surgery later today!

Here is what is odd: My other brother already had one. And my wife has one!

so what are the odds here? I guess the qualifier is the odds that 3 close family members would get this...

#### drrehak

##### New Member
Good point. I agree. There are many factors that contribute to risk (amount of nearsightedness, genetics, history of trauma). However, for arguments sake, out of 5 close people, odds that 3 would have 1/10000 detachment?

#### ondansetron

##### TS Contributor
I think @Dason is making the point that the 1/10,000 might be a marginal probability (think of disease prevalence in the general population or lifetime incidence or something to that effect), but these are not independent cases because family members are genetically linked and the probability of retinal detachment is higher for those people with specific genotypes (think of Marfan's syndrome or homocystinuria) or those that are related, so it wouldn't be correct to assume each family member has 1/10,000 chance.

#### drrehak

##### New Member
yes, and I agreed to his point. However my wife WOULD be an independent case.

and for arguments sake, I just want to ballpark it. So maybe rephrase the problem:
Out of a sample of 5, what are the odds that 3 would have this condition?

#### Karabiner

##### TS Contributor
Maybe quite high. In your personal environment, you probably have quite a number of relatives,
friends, and maybe also colleagues of whom you would notice if they had a significant medical
condition; and there's quite a number of possible significant conditions which could appear in your
personal environement during your life. Asking after the fact how probable it is that EXACTELY
THESE 3 people (out of 50, 100 or maybe 200?) showed exactely THIS condition (out of 20? 50?
100? possible conditions), would mean to ignore that many more people in your environment
took part in the "lottery" than only those 3, and that many more "prizes" were in the lottery than only
one, and that the lottery has been continously performed over decades.

The more adequate question would be (in my humble opinion): how probable is it, that during
my whole life, 3 out of those many people I personally know, will show the same disease
(out of many potential diseases which can appear in the environment where I live)?

With kind regards

Karabiner

#### drrehak

##### New Member
YES!!! I love that analysis Karabiner! That is a much more intelligent question. Lets say the people I personally know sample size is 100.

The more adequate question would be (in my humble opinion): how probable is it, that during
my whole life, 3 out of those many people I personally know, will show the same disease
(out of many potential diseases which can appear in the environment where I live)?

With kind regards

Karabiner

#### ondansetron

##### TS Contributor
yes, and I agreed to his point. However my wife WOULD be an independent case.

and for arguments sake, I just want to ballpark it. So maybe rephrase the problem:
Out of a sample of 5, what are the odds that 3 would have this condition?
Well, right, of course your wife would be independent of you, but the point is who are you asking about? Your wife, her brother and you, for example is different from you your son and your daughter. (Since you are trying to generalize the question.)

#### Karabiner

##### TS Contributor
So there's the question how probable it is that 3 out of 100 subjects
experience the same event, which has a probability of 1/10,000 .

In addition, one could take into account that there are many more
rare events which would have attracted Attention; and perhaps, that
the investigation was/will be repeated year after year (e.g. 30 times or so).

With kind regards

Karabiner