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Re: st: How to best describe interaction between a dummy variable and a continuous one in logistic regression?


From   "Svend Juul" <[email protected]>
To   <[email protected]>
Subject   Re: st: How to best describe interaction between a dummy variable and a continuous one in logistic regression?
Date   Sat, 4 Feb 2006 11:53:18 +0100

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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