I was challenged by Daniel's questions and elaborate somewhat
more on what -mhodds- would show. It can be deduced approximately
from the -logistic- output presented by Daniel.
I think that the -mhodds- output tells more clearly than the
-logistic- that:
1) romi is a confounder for the zlog-outcome association; without
adjusting for it we get a misleading result.
2) no_sec is an effect modifier; it modifies the effect
of zlog on outcome.
1. Stratifying by romi
======================
Approximate output from:
. mhodds outcome zlog
(The Odds Ratio estimate is an approximation to the odds ratio
for a one unit increase in zlog)
--------------------------------------------------------
Odds ratio chi2(1) P>chi2 [95% Conf. Interval]
--------------------------------------------------------
2.08 276 0.0000 1.91 2.27
--------------------------------------------------------
. mhodds outcome zlog , by(romi)
------------------------------------------------------------------
romi Odds ratio chi2(1) P>chi2 [95% Conf. Interval]
------------------------------------------------------------------
0 2.35 250 0.0000 2.11 2.61
1 3.04 108 0.0000 2.47 3.76
------------------------------------------------------------------
Mantel-Haenszel estimate controlling for romi
--------------------------------------------------------
Odds ratio chi2(1) P>chi2 [95% Conf. Interval]
--------------------------------------------------------
2.47 341 0.0000 2.25 2.72
--------------------------------------------------------
Test of homogeneity of ORs (approx): chi2(1) = 4.62
Pr>chi2 = 0.031
The two odds ratios (2.35, 3.04) are significantly different, but
this is a large study, so the question is whether the difference
is substantial (perhaps not). To me, the main finding is not one
of interaction (effect modification) but of confounding: In both
strata the ORs were higher than in the crude analysis.
2. Stratifying by no_sec
========================
Crude OR = 2.08 (1.91-2.27)
Approximate output from:
. mhodds outcome zlog , by(romi)
------------------------------------------------------------------
no_sec Odds ratio chi2(1) P>chi2 [95% Conf. Interval]
------------------------------------------------------------------
0 2.40 240 0.0000 2.15 2.68
1 1.82 69 0.0000 1.58 2.09
------------------------------------------------------------------
Mantel-Haenszel estimate controlling for romi
--------------------------------------------------------
Odds ratio chi2(1) P>chi2 [95% Conf. Interval]
--------------------------------------------------------
2.15 300 0.0000 1.97 2.34
--------------------------------------------------------
Test of homogeneity of ORs (approx): chi2(1) = 9.30
Pr>chi2 = 0.002
The two odds ratios are different, so there is interaction (effect
modification). But there is little confounding (compare the crude
and adjusted ORs).
Hope this helps
Svend
________________________________________________________
Svend Juul
Institut for Folkesundhed, Afdeling for Epidemiologi
(Institute of Public Health, Department of Epidemiology)
Vennelyst Boulevard 6
DK-8000 Aarhus C, Denmark
Phone, work: +45 8942 6090
Phone, home: +45 8693 7796
Fax: +45 8613 1580
E-mail: [email protected]
_________________________________________________________
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