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.

I appreciate the time and trouble that several people have taken to  
attempt
to answer my somewhat inchoate question.  I'm still trying to get my  
head
around McNemar's test, plus other ideas and suggestions.  As I've said,
I'm slow.  I am also remiss in never before having come to grips with  
McNemar
before now. Just another of the many lacunae in my knowledge.

I would like however to clarify (I hope) a few points in respect of  
Bert's
comments above.

The study was a retrospective study on cats being treated for cancer.
The objective, as I understand it, was basically to consider unwanted
side effects of the drug piroxicam which was used (in combination with
other therapies) on all 73 cats.

So it's not really correct to say that cats who were vomiting before
hand would've been excluded from the study.  The cats were being treated
for cancer, not studied.  The study came afterward.  It is possible that
a vet might say ``Oh-oh; this cat's been vomiting.  So we shouldn't use
the piroxicam treatment, we should do something else.''  It's possible,
but I would guess not.  I believe that piroxicam is a relatively new
treatment, and its side effects are still being figured out.

Cats do generally have a tendency to vomit from time to time.  A null
hypothesis of p = 0 is unrealistic, and moreover *any* incident of  
vomiting
would irrefutably disprove p = 0, wouldn't it?  It would be nice to have
some realistic value of p_0 for the probability of vomiting under  
``normal''
circumstances, but that's just not available.

Placebo controls could not possibly come into the situation at all.   
This
was real life, not a study, and the cats had cancer and had to be  
treated.
I'm sorry if my original posting was unclear or misleading in this  
regard.

Finally I think it's unfair to say that my friend ``messed up the  
design''.
There was no design.  It was a retrospective observational study of  
real-life
treatment procedures and their outcomes.

It seems pretty certain to me that the data are not ``completely  
useless''
to answer the question posed.  There *is* information content there.   
The
information may not be ideal, but there is information to be had.  In
particular it seems to me that my ad hoc proposal in my original email
does indeed (``validly'') test the null hypothesis that the treatment
has no effect on the propensity of cats to vomit.

(No one has commented on my proposed test as such; would anyone care  
to?)

I'm still not sure about McNemar, but I suspect it is ``valid'' as  
well, possibly
modulo an assumption about normality and possibly with some other  
assumption(s)
being thrown in.


	cheers,

		Rolf Turner

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