3
$\begingroup$

I have a set of patients that I split into two parts using some obscure algorithm (doesn't matter how): let the $X$ take on values $A$ and $B$. Each patient belongs to exactly one of 5 disease subtypes: let $S$ take on the values $a, b, c, d, e$. Here is the contingency table:

       A    B
a    116  109
b     64   87
c    161   86
d    123  140
e     77   38

Using Fisher's exact test, I get a p-value of $5.274e-07$. So I conclude that $X$ and $S$ are somehow associated (or not independent). What I'd like to ask next is which subtypes are significantly associated with $X$. For example, subtype $a$ doesn't seem to deviate much from the expected number of $A$s and $B$s if $a$ is independent of $X$, while there seems to be an overrepresentation of $A$s within the $e$ subtype.

What kind of test would be appropriate here?

Could I use Fisher's exact test again for each of the subtypes separately. Or should I use something like logistic regression?

Improve this question
$\endgroup$
2
  • $\begingroup$ The way the cross-classification occurs is important, nonetheless, since some tests assume that one or both marginal totals are fixed. Why a Fisher's test in this instance? A Pearson' $\chi^2$ would yield a comparable p-value (5.91e-07), for example; expected counts under the null for row e are 62.2 (A) and 52.8 (B), and the residuals are not much different in magnitude from those of row b. $\endgroup$
    – chl
    Oct 16, 2012 at 21:37
  • 1
    $\begingroup$ @chl Isn't Pearson's $\chi^2$ an approximation to Fisher's exact? So they should give similar results. Concerning the marginals, I can only say that the subtypes are fixed, but the classification algorithm (i.e., variable X) is not constrained and is free to classify any number of patients as either A or B. But this is similar to many situations where I have seen Fisher's exact test be applied. $\endgroup$
    – ALiX
    Oct 16, 2012 at 22:13

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.