On Fri, 7 Mar 2003, Marco Sandri wrote in part:

> I have a sample of M tumors from a set of N patients.
> For each tumor I measured a continuous variable pre and post
> treatment.
  < snip >
> In fact, some patients have more than one tumor.  Therefore I need
> some kind of corrected paired test which considers the effect of
> this non independence in the observations.

Useful answers might depend on how large M and N are.  But let me sort
of think aloud about your problem, and see if that helps.
Presumably you want to ask whether the "continuous variable" you've
measured has changed between pre and post treatment.  So you have
calculated the differences D = (post-pre) for each tumor.  The paired
t-test asks whether the mean D is far enough from zero for the results
to be interesting.

Let k = the number of tumors each patient has.  (Or, at any rate, the
number of tumors addressed by the treatment.)  For some patients, k=1
(since you write "some patients have more than one tumor", implying that
not all patients have more than one).  For others, k = 2, 3, ..., K
(say).  It would presumably be interesting if the size of the effect oftreatment 
differed between patients with one tumor and patients with
more than one.  So you might do an analysis of variance on the variable
D, using as groups the levels of k (and perhaps grouping together the
larger values of k, if there are few patients with many tumors).  If
there aren't detectable differences in D as a function of k, I don't
think you'd need to worry much about the slight lack of independence in
the paired differences for patients with more than one tumor.

Still, if you did want to worry about that (for one thing, patients with
two tumors would be counted twice as frequently as patients with one
tumor, and so on), you could always do the analysis on the average D for
each patient.

At some point I'd probably want to plot D vs k, just to see if there
were patterns that struck the eye that might not have been modeled in
the analysis;  and I'd probably do a plot both for individual tumors,
and for average D per patient.

> Unfortunately I am not aware if this test exists.
>
> Please, could you give me an idea on how to solve this problem ?

I hope this will have been helpful.     -- Don.
 -----------------------------------------------------------------------
 Donald F. Burrill                                            [EMAIL PROTECTED]
 56 Sebbins Pond Drive, Bedford, NH 03110                 (603) 626-0816

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