Dear all,
This is probably a basic statistics question, I would none the less like to
ask for any hints as to choice of method / test.
I want to analyze a study of events taking place in patients subjected to
either of two interventions, with patients enrolled in any of five
countries. I regard my data as a table of one row for each country, and one
column for each intervention. In each table cell, a number of patients
reside which either have experienced {zero events} or {one or more events}.
In each cell, the data x_{country,intervention} is considered to be
Binomial(n = n_{country,intervention}, p = p_{country,intervention}).
I would like to perform a homogeneity test, to test the hypothesis of p
being independent of country.
There is no obvious reason to believe in a difference between countries, but
there may be evidence of a difference between interventions.
A chi-square test sounds like the obvious solution, but I have not managed
find any formulation of the chi-square test that suits my data.
May plan is to perform some kind of permutation test, with a test variable Q
= Sum ( (observed - expected)^2/expected), where
observed = x_{country,intervention},
expected = n_{country,intervention} * p_{intervention},
p_{intervention} = estimate of the probability of an event under the given
intervention, using all countries' data.
In the permutation test, the estimate of p_{intervention} is held fixed at
its observed value, and the country labels are permuted, giving a
distribution Q*. Comparing the observed Q with the tails of Q*, a p value
is estimated.
I feel however that I am probably overlooking an obvious, and much simpler
solution to this.
I am grateful to any hints or advice,
Kind regards,
Sixten Borg.
============================================
Sixten Borg
Statistician / Modeller
Health Economics & Outcomes Research
Clinical Science
AstraZeneca R&D Lund, S-221 87 Lund, Sweden
Phone +46 46 33 77 13. Fax +46 46 33 75 53.
Email: Sixten.Borg@astrazeneca.com
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