OT: A test with dependent samples.

David,

If you really want to do a test on this data, I would suggest
a Fisher's Exact test, but you want to use hypergeometric
probabilities. You would probably want to try the CMH
test, if the function allows a single table and actually uses
hypergeometric probabilities.

My suggestion, would be to calculate the frequency of
vomiting, for animals that didn't vomit before, calculate
the CIs and then use some historical data on the vomiting
rate, for non-treated cats and see whether it falls inside the
CIs for your treated animals. If it does, then you might
conclude that the vomiting rate, for treated cats, is
similar to non-treated cats.

Murray M Cooper, Ph.D.
Richland Statistics
9800 N 24th St
Richland, MI, USA 49083
Mail: richstat at earthlink.net

----- Original Message ----- From: "David Winsemius" <dwinsemius at comcast.net 

To: "Rolf Turner" <r.turner at auckland.ac.nz>
Cc: "R-help Forum" <r-help at r-project.org>
Sent: Tuesday, February 10, 2009 4:50 PM
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

######################################################################
Attention:\ This e-mail message is privileged and confid... 
{{dropped: 9}}