[R] OT: A test with dependent samples.

Charles C. Berry cberry at tajo.ucsd.edu
Tue Feb 10 23:40:26 CET 2009

```73 cats were treated. None barfing before and 12 after.

This gives the table:

| After      | Yes | No | Total |
|------------+-----+----+-------|
| Before Yes | 0   | 0  |     0 |
| Before  No | 12  | 61 |    73 |
|------------+-----+----+-------|
| Total      | 12  | 61 |    73 |

and a McNemar Test will assess symmetry with chi-square = 12 on 1 d.f.,
rejecting symmetry at conventional p-values.

But I think symmetry is an unreasonable null in this context, as I guess
that one would not medicate a barfing cat. Certainly in the human oncology
context with which I am familiar, it would be most unusual to posit
symmetry of mucositis before and after chemotherapy when an agent that
might induce mucositis is to be given.

I'd try to elicit an upper bound for the acceptable fraction of such side
effects and then perform a test using that fraction as the alternative.

Failing that (because such elicitations are sometimes met with a blank
stare) and even in addition to that, I'd calculate the point estimate and
the 95% CI (or maybe even the 90% CI) and present those along with some
interpretative advice. prop.test(12,73) would do it.

HTH,

Chuck

On Tue, 10 Feb 2009, David Winsemius wrote:

> 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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