# RE: [IP] Re: D prevention

```Andrew Aronoff [mailto:email @ redacted] wrote:

> I realize this isn't a statistics course, but could you amplify a bit?
>
> I've never heard of a "random event with an apparent probability".
> I've heard of events with unknown causes, but such events are, by
> definition, *not* random, since they are distinct from the noise.

OK, let's start with a particular set of events.  The total number of events
is, in statistical terms, the universe of events.  In most cases, we cannot
record all events.  So, we sample the universe of events and infer that what
we see in the sample has the same distribution of events as in the universe.
This is the random sample.

The randomness comes from the sampling protocol in which each event has an
equal probability of being selected for study.  In a normal distribution
(the classic bell curve) events near the center of the distribution will be
chosen more frequently than those near the tails simply because there are
more of them.

When we do a statistical analysis of these data, we are looking for factors
that cause the distribution to deviate from the randomness of the sampling
protocol.  Where we are unable to detect them, we infer that the events are
random *WITH RESPECT TO THAT FACTOR*.  IOW, there is not a statistically
significant association between the factor and the event.

In the situation(s) that gave rise to this discussion, to say that multiple
cases of type 1 DM in a single family is a random occurrence is simply to
say that we cannot detect any association between hereditary factors and the
incidence of type 1.  Logic would tell us that there certainly *appears* to
be an association, but, since multiple research projects have not found it,
our current conclusion is that multiple cases in one family falls within the
observed random distribution of the universe of type 1 DM.

There is probably no completely random event in the universe, that meaning
that there is no force or other condition that would cause events to group
in some way.  In biological systems, and statistically, we look for an ideal
of a random normal distribution.  There are other distributions as well, and
those take different statistical tools to work with.  Take age of onset in
type 1, for example.  There's a reason that it is also known as juvenile
onset diabetes.  But because there are mature adults who develop type 1 (me,
for example - well, I may not be the best one to judge about the maturity!),
the upper tail is going to be quite long, with the central measure near 12
years old.

> Deirdre wrote:
> D> If type 1 diabetes occurs in 1 in 300 people, someone has a .33 of
> D> a percent chance of having type 1. However, if someone has a
> D> sibling with type 1, their odds of having it rise 15 fold to 5%.
>
> someone already had a sibling, then the odds of their next sibling
> would remain the same at 1 in 300. But it's not the same -- the odds
> fall (not rise) to 1 in 20.
>
> Why isn't this a non-random event in this family? What am I missing?

We have no way of knowing if it is random within the family.  It's much too
small a sample size to detect any associations.

But if we select 10000 families at random with at least one diabetic child,
what is the probability that more than one will have type 1?  Or if we
select 10000 families with at least two children (since we're looking at
multiple events, single child families wouldn't qualify for the study), what
are the probabilities that one child will develop type 1?  What are the
probabilities that more than one will develop it?

Let's make it a little more complicated: select 10000 families with two or
more children and a parent who has type 1.  Look at the probabilities again.
So far, the studies that have been done have not been able to detect a
non-random association between the cases.

If you're still with me, thanks for your forbearance.  I hope I haven't
confused the issue any further.

Jim Handsfield
email @ redacted OR
email @ redacted

The opinions expressed are mine and may not represent those of my wife who
runs our house and makes more important decisions than I do.
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