OT: A test with dependent samples.

The only question at issue (i.e. capable of being addressed) is: is 
giving
the drug to non-vomiting cats associated with vomiting? (I would 
strongly
suspect that cats that were vomiting beforehand would have been 
excluded
from the study, as the researcher would have felt that one couldn't 
then
tell whether or not the drug caused vomiting problems for them. No?)

There were 73 non-vomiting cats, 12 of which started vomiting after
receiving the drug. All I can do is give a confidence interval for the
estimated proportion of nonvomiting cats that vomit when given this 
drug and
perhaps ask whether it is consistent with their nonvomiting status 
before.
Which is what I did. And it's pretty convincing that giving the pill 
is
associated with vomiting, right?

Whether the vomiting was associated with the giving of this 
**particular**
drug is, of course, impossible to tell, because the researcher failed 
to
include placebo controls. I chose 0 for a null as a representation of 
their
non-vomiting status, but the scientific question of interest is 
probably to
compare them to the proportion of cats that would vomit if given any 
pill at
all. Without any placebo controls, who can tell? Substitute a prior 
guess if
you like for a Null. Which is exactly the point that Marc Schwartz 
made --
that is, that the data are probably completely useless to answer the
question of interest because the researcher messed up the design.
-- Bert Gunter

-----Original Message-----
From: markleeds at verizon.net [mailto:markleeds at verizon.net] Sent: 
Tuesday, February 10, 2009 2:54 PM
To: Bert Gunter
Cc: 'David Winsemius'; 'Rolf Turner'; r-help at r-project.org
Subject: Re: [R] OT: A test with dependent samples.

  Hi: Bert:  can you do that because the null is that they are equal 
before and after,
  not that the proportion is zero ? Thank for any clarification to my 
lack of understanding.




On Tue, Feb 10, 2009 at  5:43 PM, Bert Gunter wrote:

Ah, experimental units,again ... a subject little taught by 
statisticians
that is often the crux of the matter. As here.

The cat is the experimental unit. There are 73 of them. 12 of them
experienced vomiting after treatment. What's a confidence interval 
for the
true proportion based on our sample of 73? binom.test(12,72) gives us 
.088
to .27 for an exact 2 sided interval (and a P value of 2.2e-16 for 
the null
= 0).

Seems rather convincing -- and simple -- to me!

-- Bert Gunter

-----Original Message-----
From: r-help-bounces at r-project.org 
[mailto:r-help-bounces at r-project.org] On
Behalf Of David Winsemius
Sent: Tuesday, February 10, 2009 1:51 PM
To: Rolf Turner
Cc: R-help Forum
Subject: Re: [R] OT: A test with dependent samples.

In the biomedical arena, at least as I learned from Rosner's 
introductory text, the usual approach to analyzing paired 2 x 2 
tables is McNemar's test.

?mcnemar.test

mcnemar.test(matrix(c(73,0,61,12),2,2))

	McNemar's Chi-squared test with continuity correction

data:  matrix(c(73, 0, 61, 12), 2, 2)
McNemar's chi-squared = 59.0164, df = 1, p-value = 1.564e-14

The help page has citation to Agresti.

-- 
David winsemius
On Feb 10, 2009, at 4:33 PM, Rolf Turner wrote:

I am appealing to the general collective wisdom of this
list in respect of a statistics (rather than R) question.  This 
question
comes to me from a friend who is a veterinary oncologist.  In a 
study that
she is writing up there were 73 cats who were treated with a drug 
called
piroxicam.  None of the cats were observed to be subject to vomiting 
prior
to treatment; 12 of the cats were subject to vomiting after 
treatment
commenced.  She wants to be able to say that the treatment had a 
``significant''
impact with respect to this unwanted side-effect.

Initially she did a chi-squared test.  (Presumably on the matrix
matrix(c(73,0,61,12),2,2) --- she didn't give details and I didn't 
pursue
this.) I pointed out to her that because of the dependence --- same 
73
cats pre- and post- treatment --- the chi-squared test is 
inappropriate.

So what *is* appropriate?  There is a dependence structure of some 
sort,
but it seems to me to be impossible to estimate.

After mulling it over for a long while (I'm slow!) I decided that a
non-parametric approach, along the following lines, makes sense:

We have 73 independent pairs of outcomes (a,b) where a or b is 0
if the cat didn't barf, and is 1 if it did barf.

We actually observe 61 (0,0) pairs and 12 (0,1) pairs.

If there is no effect from the piroxicam, then (0,1) and (1,0) are
equally likely.  So given that the outcome is in {(0,1),(1,0)} the
probability of each is 1/2.

Thus we have a sequence of 12 (0,1)-s where (under the null 
hypothesis)
the probability of each entry is 1/2.  Hence the probability of this
sequence is (1/2)^12 = 0.00024.  So the p-value of the (one-sided) 
test
is 0.00024.  Hence the result is ``significant'' at the usual 
levels,
and my vet friend is happy.

I would very much appreciate comments on my reasoning.  Have I made 
any
goof-ups, missed any obvious pit-falls?  Gone down a wrong garden 
path?

Is there a better approach?

Most importantly (!!!): Is there any literature in which this 
approach is
spelled out?  (The journal in which she wishes to publish will 
almost surely
demand a citation.  They *won't* want to see the reasoning spelled 
out in
the paper.)

I would conjecture that this sort of scenario must arise reasonably 
often
in medical statistics and the suggested approach (if it is indeed 
valid
and sensible) would be ``standard''.  It might even have a name! But 
I
have no idea where to start looking, so I thought I'd ask this 
wonderfully
learned list.

Thanks for any input.

	cheers,

		Rolf Turner



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