[R] OT: A test with dependent samples.

[Gabor Grothendieck]

There are a number of others considerations as well.
Were all the cats given the same dose?   If we can establish
that the cats that vomited had a higher dose than the
ones that did not then this would be further evidence.  Or if
the cats that vomitted had a lower dose perhaps the drug
is protective.  Also can you find similar drugs for which the
same side effect occurred?  If you can then its more plausible
that this one will have the same effect.  Or if there are biological
grounds to believe that the effect is plausible then this should
be noted.   Another thing to look out for is confounding.  Were
they treated in any other way at the same time?  Can we be
sure that in the absence of treatment we would not have seen
the same thing, i.e. the effect is an effect of cancer rather
than the treatment?

On Tue, Feb 10, 2009 at 8:05 PM, Rolf Turner <r.turner at auckland.ac.nz> wrote:
>
> On 11/02/2009, at 1:06 PM, Bert Gunter wrote:
>
>> 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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