Re: Is this enough information to make an inference?

"michalchik@xxxxxxx" <michalchik@xxxxxxx> wrote in
news:3b54f97d-f031-420e-a306-6c1fee27a366@xxxxxxxxxxxx
ooglegroups.com:

On Dec 30 2007, 5:34 pm, David Winsemius
<doe_s...@xxxxxxxxxxx> wrote:
"michalc...@xxxxxxx" <michalc...@xxxxxxx> wrote
innews:50af03db-c506-41ef-
a96d-cc7a283f214d@xxxxxxxxxxxxxxxxxxxxxxxxxxxx:

On Dec 29, 9:04 pm, David Winsemius
<doe_s...@xxxxxxxxxxx> wrote:
then you should check the
spellings underscored (if you read USENET with
monospcaced fonts
as is the accepted convention).

Sorry about the misspellings. They are mostly
typo's but I should
have used a spell checker. I am not going to
use this as a class
exercise in the foreseeable future. BTW you
misspelled mono-spaced
;-)

First Law of the Interent, eh?

Did you get the statistical perspective to answer
your questions. At
one point ISTR that you were asking about
attributable risk. I don't
think that the Tomsky invocation of Bayes' Theorem
actually gives you
AR. In epidemiology there are several terms that
are used to describe
the excess risk for condition X associated with
exposure Y.
Attributable risk and attributable risk percent
are distinct
concepts. Are you still looking for something
along those lines?

--
David Winsemius

Yep!

I don't mean to be ungrateful but it kind of amazes
me that we are on
message 27 and my questions really haven't been
answered yet ;-)


You didn't really frame your question in a manner
that would make an
audience take it particularly seriously. You were
asking a question in a
technical newsgroup. You presented a very sketchy
scientific basis for
asking the question. You could have done a bit of
googling and pointed
the audience to this website for instance:

<http://www.pbrc.edu/About_Us/The_Explorers/Faculty_Bi
o.asp?EmployeeID=2449>

When I googled a bit more, I found numbers for viral
antibody prevalence
among obese individuals of 30% and 11% among
non-obese persons.
<http://www.ncbi.nlm.nih.gov/pubmed/17908526>


The numbers that were presented (rounded to the
nearest 10%) appeared as
though they were probably pulled out of the air by a
teacher (as it
turned out you are, but perhaps they weren't
arbitrarily chosen. Nor did
you give us your educational background or reason for
the question so
that we could construct an appropriate answer. You
might want to look at:

<http://catb.org/~esr/faqs/smart-questions.html>

The questions again:
Given:
1) The virus is a causal risk factor for obesity and
that obesity is
not a risk factor for catching the virus.
(That is not actually "given" but rather the subject
of research.)
2) 20% of the general population tests positive for
the virus.
3) 40% of obese people test positive for the virus.
4) 30% of the United States is obese.

Can we infer?
1) What percentage of obesity in the general
population is
attributable to the effect of the virus.
2) What is the likelihood that you will become obese
if you contract
the virus.
---------------end your original
questions--------------


Epidemiologists usually set up their data as 2 x 2
tables (as always on
USENET, these need to be viewed in monospaced font):

Exposed | Not-exp row totals
Disease | a | b | a+b
----------------------------------------
Not_diseased| c | d | c+d
----------------------------------------------
col totals a+c b+d | N (if counts,
s, 1.0 if proportions)

The manner in which these groups are collected is
crucial to doing a
correct analysis and this was not specified in the
original question.

Virus+ | No-virus row totals
Obese | a | b | 0.30 <- from 4)
----------------------------------------
Not obese | c | d | 0.70 (by
subtraction)
----------------------------------------------
col totals 0.20 0.80 |1.0
^^from 2)^ \___by subtraction


The confusion exhibited by Afonso regarded how to
apply 3).

There is a difference between Pr(A|B) and Pr(A&B).
The first expression
is the probability of A given that B is true, while
the latter is the
probability of both A and B being true. You could
think of Pr(A|B) as
narrowing the consideration only to the B is true
population. Under
assumptions of independence (which are clearly not
applicable when A
causes B or vice versa) the "a" in the table above
would be 0.06 =
(0.3 X 0.2). But you told us that among the 30% of
the population which
was obese that 40% of them test positive. So a= 0.4 *
0.3 or 0.12, ...
twice what would be expected if "obese" and "virus"
were independent
(and assuming that the numbers were sufficient to
give nice, narrow
confidence intervals.) So the final table looks like:

Virus+ | No-virus row-totals
Obese | 0.12 | 0.18 | 0.30
----------------------------------------
Not-obese | 0.08 | 0.62 | 0.70 (by
subtraction)
----------------------------------------------
col-totals 0.20 | 0.80 | 1.0

Question 1: One way of thinking about "attributable
risk" is the excess
risk in the exposed groups above what would be
expected if there were no
virus. The prevalence of obesity in the non-viral
exposed group is
0.08/0.7 or 0.114. Prevalence of obesity in the viral
groups is ...40% as
given, ... so the excess risk could be calculated as
40%-11.4% or 28.6%.

There are other ways for expressing the risk after
exposure. This next
idea follows what is called the etiologic fraction by
some. You could
calculate an attributable risk percent (which might
be the prevalence of
exposure (0.20) times excess risk divided by
prevalence of obesity among
the viral exposed. 0.2*((28.6%)/40%) , ... or perhaps
you want a risk ratio.
Since you have not really told us what you are
looking for, I am not
going to list all the effect measures and their
definitions.

Question 2 seems a bit ambiguous to me. You could
just want the 40%
fraction that you offered. Or you could want the AR
or the AR% that was
calculated above. Or perhaps you wanted Tomsky's
Pr(obese&virus)
calculation ( which is the same as my "a" above.)


--
David Winsemius




Just a slight correction, Dave. In this lengthy thread which started last year, my original answer on Dec. 29, 5:48 P.M., was for Prob(obese|virus) obtained using Bayes formula.

Jack
.

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