Chi-squared Applicable?

[Pavel314]

I have some data on five-year survival rates for patients receiving
liver transplants, comparing one hospital against the national average
for certain diagnosis groups. These are given as percents, shown
below:

Hospital National
TypeA 88.8% 90.13%
TypeB 71.4% 80.78%

This looks like a Chi-square application but as I understand the
function, it only applies to counts, not to percentages. I thought of
cheating, multiplying all the values by a constant to get whole
numbers but I think that would distort the results as it assumes the
volumes of the hospital to be in the same range as the national, while
I know the national figures would be many times greater. I suppose I
could multiply hospital and national by different constants to reflect
their relative sizes.

Any ideas on how to get a meaningful comparison from the above will be
appreciated.

Paul

[Rich Ulrich]

On Sat, 17 Mar 2012 05:38:55 -0700 (PDT), Pavel314 <pin...@jhmi.edu>
wrote:

Maybe for 5-year followup it doesn't matter, but I do
kjnow that hospital comparisons are tricky from the start
because of extra variables like patient selection -- age,
severity of illness, etc.

You ought to have the national numbers, at least
approximately, but it won't make much difference if
it is 100 thousand or a million. (You can check this out
by trying both.) The power of the test depends
on the size of the much-smaller marginal total for the
single hospital. (Or - use tha actual national number if
you have it.) Get your big Ns for the national figures.

Okay - try "realistic" constant-multipliers for Hospital
and obtain the chisquared. That value is directily and
(approximately) linearly proportional to N, so you can
correct the N proportionately to adjust the X^2 to
about 3.84 (for a 5% test). Compute the test for the
adjusted N, and make another linear adjustment if it
is not within half a point.

You will see that TypeA requires a huge N to remove
"chance" as the main explanation ("1.33%" as the sinple
difference). Here is the N that *would* be significant
for the hospital. You can present this even though you
don't have the actual numbers for the hospital.

TypeB ("9.38%") has 7 times the difference, and
the 80% proportion has a larger variance than 90%,
so the requisite N to show a difference will be about
a ninth of TypeA.

TypeB shows a big enough difference that it might be
of clinical significance, which is not true for TypeA.
So you work your numbers more carefully for that one.

--
Rich Ulrich