[R] OT: A test with dependent samples.
Bert Gunter
gunter.berton at gene.com
Wed Feb 11 01:06:05 CET 2009
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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>>
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